Note: Descriptions are shown in the official language in which they were submitted.
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5-2-5 MATRIX ENCODER AND DECODER SYSTEM
Field of the Invention
This invention relates to sound reproduction
systems involving the decoding of a stereophonic pair of
input audio signals into a multiplicity of output signals
for reproduction after suitable amplification through a like
plurality of loudspeakers arranged to surround a listener,
as well as the encoding of multichannel material into two
channels.
Summary of the Invention
The present invention concerns an improved set of
design criteria and their solution to create a decoding
matrix having optimum psychoacoustic performance in
reproducing encoded multichannel material as well as
standard two channel material. This decoding matrix
maintains high separation between the left and right
components of stereo signals under all conditions, even when
there is a net forward or rearward bias to the input
signals, or when there is a strong sound component in a
particular direction, while maintaining high separation
between the various outputs for signals with a defined
direction, and non-directionally encoded components at a
constant acoustic level regardless of the direction of the
directionally encoded components of the input audio signals.
The decoding matrix includes frequency dependent circuitry
that improves the balance between front and rear signals,
provides smooth sound motion around a seven channel version
of the system, and makes the sound of a five channel version
closer to that of a seven channel version.
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Additionally, this invention concerns an improved
set of design criteria and their solution to create an
encoding circuit for the encoding of multichannel sound into
two channels for reproduction in standard two channel
receivers and by matrix decoders.
The present invention is part of a continuing
effort to refine the encoding of multichannel audio signals
into two separate channels, and the separation of the
resulting two channels back into the multichannel signals
from which they were derived. One of the goals of this
encode/decode process is to recreate the original signals as
perceptually identical to the originals as possible.
Another important goal of the decoder is to extract five or
more separate channels from a two channel source that was
not encoded from a five channel original. The resulting
five channel presentation must be at least as musically
tasteful and enjoyable as the original two channel
presentation.
The derivation of suitable variable matrix
coefficients and the variable matrix coefficients themselves
have been improved. To assist the understanding of these
improvements, this document makes reference to U.S. Patent
No. 4,862,502 (1989) (referred to in this document as the
"'89 patent"); U.S. Patent No. 5,136,650 (1992) (referred to
in this document as the "'92 patent"); U.S. Patent
Application No. 08/684,948, filed in July 1996 (now issued
patent No. 5,796,844 (1998)) (referred to in this document
as the "July '96 application"); and U.S. Patent Application
No. 08/742,460 (now issued patent no. 5,870,480 (1999))
(referred to in this document as the "November '96
application"). Commercial versions of the decoder based
upon the November '96 application will be referred to in
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this document as "Version I.II" or "VI.II". Some further
improvements were disclosed in Provisional Patent
Application 60/058,169, filed September 1997 (now issued
U.S. patent no. 6,697,491)(referred to in this document as
"Version 2.01" or "V2.01"). Further, Versions VI II and
V2.01, and the decoders presented in this application will
be referred to in this document collectively as the
"Logic 7~ decoders". Additionally, the following are
referenced in this application:
[1] "Multichannel Matrix Surround Decoders for Two-Eared
Listeners", David Griesinger, AES preprint #4402, October,
1996, and [2] "Progress in 5-2-5 Matrix Systems", David
Griesinger, AES preprint #4625, September, 1997.
An active matrix having certain properties that
maximize its psychoacoustic performance has been realized.
Additionally, frequency dependent modifications of certain
outputs of the active matrix have also been realized.
Further, active circuitry that encodes five input channels
into two output channels is provided that will perform
optimally with the decoders presented in this application,
standard two channel equipment, and industry standard
DolbyR Pro-Logic~ decoders.
The active matrix decoder has matrix elements
that vary depending on the directional component of the
incoming signals. The matrix elements vary to reduce the
loudness of directionally encoded signals in outputs that
are not involved in producing the intended direction, while
enhancing the loudness of these signals in outputs that are
involved in reproducing the intended direction, while at
all times preserving the left/right separation of any
simultaneously occurring input signals. Moreover, these
matrix elements restore the left/right separation of
decorrelated two channel material, which has been
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directionally encoded, by increasing or decreasing the blend
between the two inputs. For example, restoration is
achieved using stereo width control. In addition, these
matrix elements may be designed to preserve the energy
balance between the various components of the input signal,
as much as possible, so that the balance between vocals and
accompaniment is preserved in the decoder outputs. As a
consequence, these matrix elements preserve both the
loudness and the left/right separation of the non-
directionally encoded elements of the input sound.
Additionally, the decoders may include frequency
dependent circuits that improve the compatibility of the
decoder outputs when standard two channel material is
played, that convert the inputs into two surround outputs (a
five channel decoder) or four surround outputs (a seven
channel decoder), and that modify the spectrum of the rear
channels in a five channel decoder so that the sound
direction is perceived to be more like the sound direction
produced by a seven channel decoder.
The encoders mix five (or five full-range plus one
low frequency) input channels into two output channels so
that the energy of that input is preserved in the output
when the input level of a particular input is strong; the
direction of a strong input is encoded in the
phase/amplitude ratio of the output signals; the strong
signals can be panned between any two inputs of the encoder,
and the output will be correctly directionally encoded. In
addition, decorrelated material applied to the two rear
inputs of the encoder will be encoded into two output
channels so that the left/right separation of the inputs
will be preserved when the encoder output is decoded by the
decoders presented in this document; in-phase inputs will
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produce a two channel output that will be decoded to the
rear channels of the decoders presented in this document and
decoders using the Dolby° standard; anti-phase inputs will
produce outputs that will be decoded as a non-directional
signal when decoded by the decoders presented in this
document or by decoders using the Dolby° standard; and low
level reverberant signals applied to the two rear inputs of
the encoder will be encoded with a 3dB level reduction.
Brief Description of the Drawings
The novel features believed characteristic of the
encoders and decoders are set forth in the appended claims.
These encoders and decoders, as well as other features and
advantages of the encoders and decoders, will best be
understood by reference to the following detailed
description of an illustrative embodiment when read in
conjunction with the accompanying drawing figures, where:
FIG. 1 is a block diagram of a direction detection
section and a two to five channel matrix section of a
decoder;
FIG. 2 is a block diagram of a five-channel
frequency-dependent active signal processor circuit, which
may be connected between the outputs of the matrix section
of FIG. 1 and the decoder outputs;
FIG. 3 is a block diagram of a five-to-seven
channel frequency-dependent active signal processor, which
may alternatively be connected between the outputs of the
matrix section of FIG. 1 and the decoder outputs;
FIG. 4 is a block schematic of an active five-
channel to two-channel encoder;
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FIG. 5 is a three-dimensional graph of a Left
Front Left (LFL) matrix element from the '89 patent and
Dolby° Pro-Logic° scaled so that the maximum value is one;
FIG. 6 is a three-dimensional graph of a Left
Front Right (LFR) matrix element from the '89 patent and
Dolby° Pro-Logic° scaled by .71 so that the minimum value
is
-0.5 and the maximum value is +0.5;
FIG. 7 is a three-dimensional graph of the square
root of the sum of the squares of LFL and LFR matrix
elements from the '89 patent scaled so that the maximum
value is one;
FIG. 8 is a three-dimensional graph of the square
root of the sum of the LFL and LFR matrix elements from the
November '96 application No. scaled so that the maximum
value is 1;
FIG. 9 is a three-dimensional graph of the LFL
matrix element from V1.11;
FIG. 10 is a three-dimensional graph of a
partially completed LFL matrix element;
FIG. 11 is a graph showing the behavior of the LFL
and LFR matrix elements along the rear boundary between left
and full rear;
FIG. 12 is a three-dimensional graph of the fully
completed LFL matrix element as viewed from the left rear;
FIG. 13 is a three-dimensional graph of the fully
completed LFR matrix element;
FIG. 14 is a three-dimensional graph of the root
mean squared sum of the LFL and LFR matrix elements;
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FIG. 15 is a three-dimensional graph of the square
root of the sum of the squares of the LFL and LFR matrix
elements, including the correction to the rear level, viewed
from the left rear;
FIG. 16 is a graph showing the values of the
center matrix elements that should be used in a Dolby°
Pro-Logic° decoder as a function of cs in dB (the solid
curve), and the actual values of the center matrix elements
used in the Dolby~ Pro-Logic° decoder (the dotted curve);
FIG. 17 is a graph showing the ideal values for
the center matrix elements of the Dolby° Pro-Logic~ decoder
(the solid curve), and the actual values of the center
matrix elements used in the Dolby° Pro-Logic~ decoder (the
dotted curve);
FIG. 18 is a three-dimensional graph of the square
root of the sum of the squares of the LRL and Left Rear
Right (LRR) matrix elements, using the matrix elements of
V1.11;
FIG. 19 is a graph of the numerical solution for
GS(1r) and GR(lr) that result in a constant power level
along the cs=0 axis and zero output along the boundary
between left and center;
FIG. 20 is a three-dimensional graph of the square
root of the sum of the squares of LRL and LRR using values
for GR and GS determined according to the present invention;
FIG. 21 is a three-dimensional graph of the Center
Left (CL) matrix element of the four channel decoder in the
'89 patent and the Dolby° Pro-Logic° decoder, which can also
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represent the Center Right (CR) matrix element with left and
right interchanged;
FIG. 22 is a three-dimensional graph of the Center
Left (CL) matrix element in V1.11;
FIG. 23 is a graph showing the center output
channel attenuation needed for the new LFL and LFR matrix
elements (the solid curve), and the center attenuation for a
standard Dolby° Pro-Logic~ decoder (the dotted curve);
FIG. 24 is a graph showing the ideal center
attenuation for the "film" strategy (the solid curve),
another center attenuation for the "film" strategy (the
dashed curve), and the center attenuation for the standard
Dolby° decoder (the dotted curve);
FIG. 25 shows the center attenuation used for the
"music" strategy;
FIG. 26 is a graph showing the value of GF needed
for constant energy ratios with the "music" center
attenuation GC (the solid curve), the previous value of the
LFR matrix element sin(cs)*corrl (the dashed curve), and the
value of sin(cs) (the dotted curve);
FIG. 27 is a three-dimensional graph of the LFR
matrix element, including the correction for center level
along the lr=0 axis;
FIG. 28 is a three-dimensional graph of the CL
matrix element with the new center boost function; and
FIG. 29 is a graph of the output level from the
left front output (the dotted curve) and the center output
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(the solid curve) as a strong signal pans from center to
left.
Detailed Description of the Preferred Embodiments
1. General description of the decoder
The decoder will be described in terms of two
separate parts. The first part is a matrix that splits two
input channels into five output channels (the input channels
are usually identified as center, left front, right front,
left rear, and right rear). The second part consists of a
series of delays and filters that modify the spectrum and
the levels of the two rear outputs. One of the functions of
the second part is to derive an additional pair of outputs,
a left side and a right side, to produce a seven channel
version of the decoder. In contrast, the two additional
outputs described in the November '96 application were
derived from an additional pair of matrix elements, which
were included in the original matrix.
In the mathematical equations describing the
decoder and encoder the standard typographical conventions
will be used for most variables. Simple variables will be
in italic type, vector quantities will be in bold lower case
type, and matrixes will be in bold upper case type. Matrix
elements that are coefficients from a named output channel
resulting from a named input channel will be in normal upper
case type. Some simple variables such as 1r and cs will be
indicated by two-letter names that do not represent the
product of two separate simple variables. Other variables,
such as 1/r and c/s, represent the values of left-right and
center-surround ratios in terms of control signal voltages
derived from these ratios. These conventions have also been
used in the patents and patent applications cited in this
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document. Program segments in the Matlab language will also
be distinguished by the use of indented lines. Equations
will be numbered to distinguish them from Matlab assignment
statements, and to provide a reference for specific
features.
FIG. 1 is a block diagram of the first part of they
decoder, which is a two channel to five channel matrix 90.
The left half of FIG. 1; partitioned by a vertical dashed
line, shows a circuit for deriving the two steering voltage;
1/r and c/s. These steering voltages represent the degree
to which the input signals have an inherent or encoded
directional component in the left/right or front/back
directions, respectively. This part of FIG. 1 will not be
explicitly discussed in this application, because it has
been fully described in the patent and patent applications
cited in this document.
In FIG. 1 the directional detection circuit of
decoder 90 comprising elements 92 through 138 is followed by
a 5 x 2 matrix (shown to the right of the vertical dashed
line). The elements of this matrix, 140 through 158,
determine the amount of each input channel linearly combined
with another input channel to form each output channel.
These matrix elements are assumed to be real (the case of
complex matrix elements is described in the November '96
application). The matrix elements are functions of the two
steering voltages 1/r and c/s, mathematical formulae for
which are presented in the November '96 application.
Improvements have been made to these formulae.
2. A brief description of the steering voltages
As shown in FIG. 1, the steering voltages c/s and
1/r are derived from the logarithm of the ratio of the left
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input amplitude at terminal 92 to the right input amplitude
at terminal 94, and the logarithm of the ratio of the sum
amplitude (the sum of the left input amplitude and the right
input amplitude) to the difference amplitude (the difference
between the left input amplitude and the right input
amplitude). In Vl.ll and V2.01, the unit of the steering
voltages is decibels. However, when describing the matrix
elements, it is convenient to express 1/r and c/s as angles
that vary from +45 degrees to -45 degrees. The steering
voltages 1/r and c/s can be converted into angles lr and cs,
respectively, according to the following equations:
1r = 90 - arctan(10~((1/r)/20)) (la)
cs = 90 - arctan(10~ ( (c/s) /20) ) (lb) .
The angles lr and cs determine the degree to which
the input signals have a directional component. For
example, when the inputs to the decoder are decorrelated,
both 1r and cs are zero. For a signal that comes from the
center only, Ir is zero, and cs is 45 degrees. For a signal
that comes from the rear, lr is zero, and cs is -45 degrees.
Similarly, for a signal that comes from the left, lr is
45 degrees and cs is zero, and for a signal that comes from
the right, Ir is -45 degrees, and cs is zero. It may be
assumed that the input was encoded so that 1r = 22.5 degrees
and cs = -22.5 degrees for left rear signals, and
1r = 22.5 degrees, and cs = -22.5 degrees for right rear
signals.
Due to the definitions of 1/r and c/s and the
derivation of 1r and cs, the sum of the absolute value of lr
and cs cannot be greater than 45 degrees. Therefore, the
allowed values of 1r and cs form a surface bounded by the
locus of abs(1r)-abs(cs)=45 degrees. Any input signal that
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produces values of Ir and cs that lie along the boundary of
this surface is fully localized, which means that the input
signal consists of a single sound that has been encoded to
come from a particular direction.
In this application extensive use will be made of
graphs depicting the matrix elements as functions over this
two dimensional surface. In general, the derivation of the
matrix elements will be different in the four quadrants of
this surface. In other words, the matrix elements are
described differently depending on whether the steering is
to the front or to the rear, and whether the steering is to
the left or the right. Considerable work is devoted to
insuring that the surface is continuous across the
boundaries between quadrants, thus addressing the occasional
lack of continuity experienced by V1.11.
3. Frequency dependent elements
The matrix elements shown in FIG. 1 are real and
thus frequency independent. All signals in the inputs will
be directed to the outputs depending on the derived angles
Ir and cs. Additionally, low frequencies and very high
frequencies may be attenuated in the derivation of 1r and cs
from the input signals by filters not shown in FIG. 1.
However, the matrix itself is broadband.
There are several advantages to applying frequency
dependent circuits to the signals after the matrix. One of
these frequency dependent circuits, the phase shift
network 170 at the right side output 180 in FIG. l, is
described in the November '96 application. A five channel
version of the additional frequency dependent circuits is
shown in FIG. 2. These circuits do not have fixed
parameters and the frequency and level behavior is dependent
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on the steering angles 1r and cs. The frequency dependent
circuits accomplish several purposes. First, in both a five
channel and a seven channel decoder, the additional elements
allow the apparent loudness of the rear channels to be
adjusted when the steering is neutral (lr and cs 0) or
toward the front (cs > 0). In the November '96 application,
this attenuation was performed as part of the matrix itself
and was frequency independent. It has been found through
theoretical studies and listening tests that it is highly
desirable for the low frequencies to be reproduced from the
sides of the listener. Thus, in the decoder presented here,
only the high frequencies are attenuated by variable low
pass filters 182, 184, 188, and 190.
The high frequencies are attenuated in the rear
channels when the steering is nearly always neutral or
forward. Elements 188 and 190 attenuate the frequencies
above 500Hz and elements 182 and 184 attenuate the
frequencies above 4kHz using a background control signal 186
(to be defined later). The occasional presence of sounds
that are steered rearwards reduces the attenuation, which is
a feature that automatically distinguishes surround encoded
material from ordinary two channel material.
Elements 192 and 194, in the five channel version
modify the spectrum of the sound when the steering is toward
the rear (cs < 0) using the c/s signal 196, such that the
loudspeakers are perceived as being located behind the
listener even if the actual position of the loudspeakers is
to the side. The modified left surround and right surround
signals appear at terminals 198 and 200, respectively.
Additional details of this circuit will be presented in a
later section.
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FIG. 3 shows the seven channel version of the
frequency dependent elements. As before the first set of
filters 182, 184, 188, and 190, attenuate the upper
frequencies of the side and rear outputs when the steering
is neutral or forward, and are controlled by the background
control signal 186. This attenuation also results in a more
forward sound image, and can be adjusted to the listener's
taste. As the steering represented by the c/s signal 196
moves to the rear, additional circuits 202, 204, 206,
and 208, act to differentiate the side outputs from the rear
outputs. As steering moves rearward, the attenuation in the
side speakers is removed by elements 204 and 206 to produce
a side oriented sound. As steering moves further to the
rear, the attenuation of elements 204 and 206 is reinstated
and increased. This causes the sound to move smoothly from
the front loudspeakers to the side loudspeakers) and then
to the rear loudspeakers. However, the sound in the rear
loudspeakers has a delay of about 10 ms, which is produced
by the delay elements 202, and 208. Because the low
frequencies are not affected by these circuits, the low
frequency loudness in the side speakers (which is
responsible for the perception of spaciousness) is not
affected by the motion of the sound.
4. General description of the encoder
FIG. 4 shows a block diagram of an encoder
designed to automatically mix five input channels into two
output channels. The architecture is quite different from
the encoder described in the November '96 application. An
object of the encoder in FIG. 4 (the "new encoder") is to
preserve the musical balance of the five channel original in
the two output channels, while providing phase/amplitude
cues that allow the original five channels to be extracted
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from the two output channels by a decoder. The new encoder
includes active elements that ensure that the musical
balance is preserved. Another object of the new encoder is
to automatically create a two channel mix from a five
channel recording, that can be reproduced by an ordinary two
channel system with the same artistic quality as the five
channel original.
Unlike the encoder of the November '96
application, the new encoder allows input signals to be
panned between any of the five inputs of the encoder. For
example, a sound may be panned from the left front input to
the right rear input. When the resulting two channel signal
is decoded by the decoder described in this application, the
result will be quite close to the original sound. Decoding
through an earlier surround decoder will also be similar to
the original.
5. Desian coals for the decoder active matrix elements
The goals of the current decoder include: having
variable matrix values that reduce directionally encoded
audio components in outputs that are not directly involved
in reproducing them in the intended direction; enhancing
directionally encoded audio components in the outputs that
are directly involved in reproducing them in the intended
direction to maintain constant total power for such signals;
preserving high separation between the left and right
channel components of non-directional signals, regardless of
the steering signals; and maintaining the loudness (defined
as the total audio power level of non-directional signals)
at an effectively constant level, whether directionally
encoded signals are present and regardless of their intended
direction.
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Most of these goals are ostensibly shared by all
matrix decoders. One of the most important goals is
explicitly maintaining high separation between the left and
right channels of the decoder under all conditions. All
previous four channel decoders are unable to maintain
separation in the rear because they provide only a single
rear channel. Five other channel decoders can maintain
separation in many ways. The decoder described in this
application meets this goal in a manner similar to that used
by V1.11, and meets additional goals as well.
The November '96 application also describes many
smaller improvements to a decoder, such as circuits to
improve the steering signals accuracy, and a variable phase
shift network to switch the phase shift of one of the rear
channels during strong rear steering. These features
(included in Vl.ll) are retained in the current decoder.
In FIG. 4 the front input signals L, C and R are
applied to input terminals 50, 52, and 54 respectively.
L and R go directly to adders 278 and 282 respectively,
while C is attenuated by a factor fcn in attenuator 372
before being applied to adders 278 and 282. A gain of 2.0
is applied to the low frequency effects signal LFE by
element 374 before LFE is applied to adders 278 and 282.
The surround input signals LS and RS are applied
to input terminals 62 and 64, respectively. The LS signal
passes through attenuator 378, which has gain fs(l,ls), and
the RS signal passes through attenuator 380, which has gain
fs(r,rs). The outputs of these attenuators 378 and 380 are
passed into cross-coupling elements 384 and 386,
respectively, each having a gain factor of -crx, where crx
is nominally 0.383. The cross-coupled signals from cross-
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coupled elements 386 and 384 are fed to summers 392 and 394,
respectively, which also receive the attenuated LS and RS
signals, respectively, from 0.91 attenuators 388 and 392,
respectively. The outputs of summers 392 and 394, are
applied to inputs of the adders 278 and 282, respectively.
This positions the side elements at 45 degrees left and
right, respectively, of center rear in the decoded space.
LS and RS also pass through attenuator 376, which
has gain fc(l,ls), and attenuator 382, which has gain
fc(r,rs), respectively, and then through a similar
arrangement of cross-coupling elements 396, 398, 402, 404,
406, and 408. The summers 406 and 408 have outputs that
position the left rear and right rear inputs at 45 degrees
left and right, respectively, of center rear, as before.
However, LS and RS also pass through phase shifter elements
234 and 246, respectively, while the left and right signals
from adders 278 and 282, respectively, pass through phase
shifter elements 286 and 288, respectively. Each of these
phase shifter elements is an all-pass filter, where the
phase response for elements 286 and 288 is ~(f), and for
elements 234 and 246 is ~(f)-90°. Calculation of the
component values required in these filters is well known in
the art. The phase shifter elements cause the outputs of
summers 406 and 408 to lag the outputs of adders 278 and 282
by 90 degrees at all frequencies. The outputs of all-pass
filters 234 and 286 are combined by summer 276 to produce
the A (or left) output signal at terminal 44, while the
outputs of all-pass filters 246 and 288 are combined by
summer 280 to produce the B (or right) output signal at
terminal 46.
The gain functions fs and fc are designed to allow
strong surround signals to be presented in phase with the
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other sounds while weak surround signals pass through the
90 degree phase-shifted path to retain constant power for
decorrelated "music" signals. The value of crx can also
change and varies the angle from which the surround signals
are heard.
6. Design improvements since the November '96 application
One of the most noticeable improvements made to
the decoder and encoder of the November '96 application is
the change in the center matrix elements and the left and
right front matrix elements when a signal is steered in the
center direction. There were two problems with the center
channel as previously encoded and decoded. The most obvious
problem was that, in a five channel matrix system, the use
of a center channel was inherently in conflict with the goal
of maintaining as much left/right separation as possible.
If the matrix is to produce a sensible output from
conventional two channel stereo material when the two input
channels have no left/right component, the center channel
must be driven with the sum of the left and right input
channels. Thus both the left decoder input and the right
decoder input will be reproduced by the center speaker and
sounds that were originally only in the left or right
channel will also be reproduced from the center. This
results in the apparent position of these sounds being drawn
to the middle of the room. The degree to which this occurs
depends on the loudness of the center channel.
The '89 patent and the '92 patent used center
matrix elements that had a minimum value of 3dB compared to
the left and right channels. When the inputs to the decoder
were decorrelated, the loudness of the center channel was
equal to the loudness of the left and right channels. As
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steering moved forward, the center matrix elements increased
another 3dB, which strongly reduced the width of the front
image. Instruments that should have sounded as if
positioned to either the left or the right of the sound
image are always drawn toward the center of the sound image.
The November '96 application used center matrix
elements that had a minimum value 4.5dB less than values
previously used. This minimum value was chosen on the basis
of listening tests and caused a pleasing spread to the front
image when the input material was uncorrelated (which is the
case with orchestral music). Therefore, the front image was
not seriously narrowed. However, as the steering moved
forward, these matrix elements were increased and ultimately
reach the values used in the Dolby~ matrix.
Experience with V1.11 showed that although the
reduction in center channel loudness solved the spatial
problem, the power balance in the input signals was not
preserved through the matrix. Mathematical analysis
revealed that not only was V1.11 in error with regard to the
power balance, but the Dolby° decoder and other previous
decoders were also in error. Paradoxically, although the
center channel was too strong from the standpoint of
reproducing the width of the front image, it was too weak to
preserve power balance. The problem was particularly severe
for the standard Dolby° decoder (the decoder of Mandel). In
the standard Dolby° decoder, the rear channels are stronger
than in the decoder of the '89 patent. As a result, the
center channel must be stronger to preserve the power
balance. The lack of power balance in the center channel
has been a continual problem for the Dolby~ decoder. In
fact, Dolby° recommends that the sound mix engineer always
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listen to the balance through the matrix, so compensation
can be made during the mixing process for the lack of power
balance in the matrix during the mixing process.
Unfortunately, modern films are mixed for five-channel
release, and automatic encoding to two channels can lead to
problems with the dialog level.
Additional analysis and listening tests showed
that films and music require different solutions to the
balance problem. For films, it is most useful to preserve
the left and right front matrix elements from the November
'96 application. These elements eliminate the center
channel information from the left and right front channels
as much as possible, which minimizes dialog leakage into the
front left and right channels. In a new "film" design, the
power balance is corrected by changing the center matrix
elements so that the center channel loudness increases more
rapidly than in the standard decoder as the steering moves
forward (as cs becomes greater than zero). In practice it
is not necessary for the final value of the center matrix
elements to be higher than those in the standard decoder,
because this condition is reached when only the center
channel is active. It is only necessary for the center
channel level to be stronger than the standard decoder when
there are approximately equal levels in the center, left and
right channels.
In the "film" strategy, the center channel
loudness is increased to preserve the power balance in the
input signals, while minimizing the center channel component
in all the other outputs. This strategy seems to be ideal
for films, where the major use of the center channel is for
dialog, and dialog from positions other than the center is
not expected. The major disadvantage of this strategy is
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that anytime there is significant center steering, such as
that which occurs in many types of popular music, the front
image is narrowed. However, the advantages for film, which
include minimum dialog leakage into the front channels and
excellent power balance, outweigh this disadvantage.
For music another strategy is adopted, in which
the center channel loudness is permitted to increase at the
same rate described in the November '96 application, up to a
middle value of the steering (where cs > 22.5 degrees). To
restore the musical balance, the left and right front matrix
elements are altered so that the center component of the
input signals is not entirely removed. The amount of the
center channel component in the left and right front
channels is adjusted so that the sound power from all the
outputs of the decoder matches the sound power in the input
signals, without excessive loudness in the center.
In this strategy, all three front speakers
reproduce center channel information present in the original
encoded material. The most useful version of this strategy
limits the steering action when the center component of the
input is 6dB stronger in the center output than in either of
the two other front outputs. This is done by simply
limiting the positive value of cs.
This new strategy, which allows the center channel
component to come from all three front speakers, and limits
the steering action when the center is 6dB louder than the
front left and right, is excellent for all types of music.
Encoded five-channel mixes and ordinary two-channel mixes
are decoded with a stable center and adequate separation
between the center channel and the left and right channels.
Note that unlike previous decoders, the separation between
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center and left and right is deliberately not complete. A
signal intended to come from the left is eliminated from the
center channel, but not the other way around. For music,
the high lateral separation and stable front image that this
strategy offers outweighs this lack of complete separation.
Listening tests using this setting on films reveal that
although there was some dialog coming from the left and
right front speakers, the stability of the resulting sound
image was quite good. The resulting sound was pleasant and
not distracting. Therefore, hearing a film with the decoder
set for music does not detract from the artistic quality of
the film. However, listening to a music recording with the
decoder set for film is more problematic.
Possibly the next most obvious improvement made to
the decoder and encoder of the November '96 application is
the increase in separation between the front channels and
the rear channels when a signal is steered to the left front
or the left rear directions. V1.11 used the matrix elements
of the '89 patent for the front channels under these
conditions. These matrix elements did not fully eliminate a
rear steered signal unless it was steered to the full rear
position (which is the position half way between left rear
and right rear). When steering was to left rear or right
rear (not full rear), the left or right front output had an
output that was 9dB less than the corresponding rear output.
In the present decoder the front matrix elements are
modified to eliminate sound from the front when steering is
anywhere between left rear and right rear.
7. Improvements to the rear matrix elements
The improvements to the rear matrix elements are
not immediately obvious to a typical listener. These
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improvements correct various errors in the continuity of the
matrix elements across the boundaries between quadrants.
They also improve the power balance between steered signals
and unsteered signals under various conditions. A
mathematical description of the matrix elements that
includes these improvements will be given later in this
document.
8. Detailed description of the active matrix elements
The Matlab language
The math used to describe the matrix elements is
not based on continuous functions of the variables cs
and 1r. In general there are conditionals, absolute values,
and other non-linear modifications to the formulae. For
this reason the matrix elements will be described using a
programming language. The Matlab language provides a simple
method of checking the formulation graphically. Matlab is
very similar to Fortran or C. The major difference is that
variables in Matlab can be vectors which means that each
variable can represent an array of numbers in sequence. For
example, the variable x can be defined according to an
expression "x = 1:10". Defining x in this manner in Matlab
creates a string of ten numbers with the values of one to
ten. The variable x includes all ten values and is
described as a vector (which is a 1 by 10 matrix). An
individual number within each vector can be accessed or
manipulated. For example, the expression "x(4) - 4" will
set the fourth member of the vector x equal to 4. A
variable can also represent a two dimensional matrix and
individual elements in the matrix can be assigned in a
similar way. For example, the expression "X(2,3) - 10" will
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assign the value 10 to the matrix element in the second row
and third column of the matrix X.
9. Matrix decoders in equations and graphics
Reference [1] presented the design of a matrix
decoder that can be described by the elements of a n x 2
matrix, where n is the number of output channels. Each
output can be seen as a linear combination of the two
inputs, where the coefficients of the linear combination are
given by the elements in the matrix. In this document the
elements are identified by a simple combination of letters.
Reference [1] described a five-channel and a seven-channel
decoder. Because the conversion from five channels to seven
channels can now be done in the frequency dependent part of
the decoder, what follows is description of a five-channel
decoder only.
Due to symmetry, the behavior of only six elements
(such as the left elements) need to be described. These six
elements include the center elements, the two left front
elements, and the two left rear elements. The right
elements can be found from the left elements by simply
switching the identity of left and right. The left elements
are indicated by the following notation:
CL: The matrix element for the Left input channel to
the Center output channel.
CR: The matrix element for the Right input channel to
the Center output channel.
LFL: The Left input channel to the Left Front output
channel.
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LFR: The Right input channel to the Left Front output
channel.
LRL: The Left input channel to the Left Rear output
channel.
LRR: The Right input channel to the Left Rear output
channel.
These elements are not constant. Their value
varies as a two dimensional function of the apparent
direction of the input sounds. Most phase/amplitude
decoders determine the apparent direction of the input by
comparing the ratio of the amplitudes of the input signals.
For example, the degree of steering in the right/left
direction is determined from the ratio of the left input
channel amplitude to the right input channel amplitude. In
a similar way, the degree of steering in the front/back
direction is determined from the ratio of the amplitudes of
the sum and the difference of the input channels.
In this document, the apparent directions of the
input signals will be represented as angles, including one
angle for the left/right direction (Ir), and one for the
front/back (also known as the center/surround) direction
(cs). The two steering directions lr and cs are signed
variables. When the two input channels are uncorrelated,
both 1r and cs are zero and the input signals are,
therefore, unsteered. When the input consists of a single
signal which has been directionally encoded, the two
steering directions have their maximum value however, they
are not independent. The advantage to representing the
steering values as angles is that when there is only a
single signal, the sum of the absolute value of each of the
two steering values must equal 45 degrees. When the input
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includes some decorrelated material along with a strongly
steered signal, the sum of the absolute values of each of
the steering values must be less than 45 degrees as
indicated by the following equation:
~ lr~ + ~ cs~ < 45 (2) .
If the values of the matrix elements are plotted
over a two-dimensional plane formed by the steering values,
the center of the plane will have the value (0, 0) and the
valid values for the sum of the absolute values of the
steering values will not exceed 45. In practice, it is
possible for the sum to exceed 45, due to the behavior of
non-linear filters. To prevent this, a circuit that limits
the lessor of lr or cs so their sum does not exceed
45 degrees may be used, such as the circuit described in the
November '96 application. When the matrix elements are
graphed the values will arbitrarily be set to zero when the
valid sum of the input variables is exceeded. This allows
the behavior of the element along the boundary trajectory
(the trajectory followed by a strongly steered signal) to be
viewed directly. The graphics were created using Matlab.
In the Matlab language, the unsteered position is (46, 46)
because Matlab requires the angle variable to be 1 more than
the actual angle value.
Previous designs for matrix decoders tended to
consider only the behavior of the matrix in response to a
strongly steered signal, which is the behavior of the matrix
elements around the boundary of the surface formed by
plotting the matrix elements over a two-dimensional plane
defined by the steering values. This is a fundamental error
in outlook because, in real signals (for example, those
found in either film or music), the boundary of the surface
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is very seldom reached. For the most part, signals wobble
around the middle of the plane, which is slightly forward of
the center. The behavior of the matrix under these
conditions is of vital importance to the sound. When the
elements described in this document are compared to previous
elements, a striking increase in the complexity of the
surface in the middle regions can be seen. It is this
complexity which is responsible for the improvement in the
sound.
However, such complexity has a price. The
elements described in this document are designed to be
almost entirely described by one-dimensional lookup tables,
which are trivial in a digital implementation. However,
unlike the matrix of the '89 patent, designing an analog
version with similar performance is not trivial.
In the sections that follow, several different
versions of the matrix elements are contrasted. The
earliest are elements from the '89 patent. These elements
are identical to the elements of a standard (Dolby°)
surround processor in the left, center, and right channels,
but not in the surround channels. In the design of the '89
patent, the surround channel is treated symmetrically to the
center channel. In the standard (Dolby°) decoder, the
surround channel is treated differently.
The elements presented are not always correctly
scaled. In general they are presented so that the unsteered
value of the non-zero matrix elements for any given channel
is one. In practice, the elements are usually scaled so
that the maximum value of each element is one or lower. In
any case, the scaling of the elements is additionally varied
in the calibration procedure. It may be assumed that the
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matrix elements presented in this document are scalable by
the appropriate constants.
10. The left front matrix elements in our '89 patent
Assume that cs and 1r are the steering directions
in degrees in the center/surround and left/right axis
respectively. In the '89 patent, the equations for the
front matrix elements are defined according to equations
(3a) , (3b) , (3c) , (3d) , (3e) , (3f) , (3g) , and (3h) . In the
left front quadrant:
LFL = 1 - 0 . 5*G (cs) + 0 .41*G (lr) (3a)
LFR = - 0.5*G(cs) (3b) .
In the right front quadrant:
LFL = 1 - 0.5*G(cs) (3c)
LFR = - 0.5*G(cs) (3d) .
In the left rear quadrant (cs is negative):
LFL = 1 - 0 . 5*G (cs) + 0.41*G (lr) (3e)
LFR = - 0.5*G(cs) (3f).
In the right rear quadrant:
LFL = 1 - 0.5*G(cs) (3g)
LFR = - 0.5*G(cs) (3h) .
The function G(x) was determined experimentally in
the '89 patent and was specified mathematically in the '92
patent. G(x) varies from 0 to 1 as x varies from 0 to
45 degrees. 4~Ihen steering is in the left front quadrant (Ir
and cs are both positive), G(x) is equal to 1-~r~/~1~ where
Ir~ and ~1~ are the right and left input amplitudes. G(x)
can also be described in terms of the steering angles using
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various formulae. One of these is given in the '92 patent,
and another will be given later in this document. Graphical
representations of the LFL and LFR matrix elements plotted
three dimensionally against the lr and cs axes are shown in
FIG. 5 and FIG. 6.
In reference [1], these elements were improved by
adding a requirement that the loudness of unsteered material
should be constant regardless of the direction of the
steering. Mathematically this means that the root mean
square sum of the LFL and LFR matrix elements should be a
constant. This goal should be altered in the direction of
the steering, which means that when the steering is full
left, the sum of the squares of these matrix elements should
rise by 3dB. FIG. 7 shows the sum of the squares of these
elements and demonstrates that the above matrix elements do
not meet the requirement of constant loudness. In FIG 7,
the value is constant at .71 along the axis from unsteered
to right. The value along the axis from unsteered to left
rises 3dB to one, and the value along the axis from
unsteered to center or from unsteered to rear falls 3dB
to 0.5. The value along the axis from unsteered to rear is
hidden by the peak at left. The rear direction level is
identical to that at the center direction.
In the November '96 application and Reference [1],
the amplitude errors in FIG. 7 were corrected by replacing
the function G(x) in the matrix equations with sines and
cosines: FIG. 8 shows a graph of the sum of the squares of
the corrected elements LFL and LFR, which are described by
the equations (4a) - (4h) below. Note the constant value
of .71 in the entire right half of the plane, and the gentle
rise to one toward the left vertex. For the left front
quadrant:
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LFL = cos (cs) + 0 .41*G (lr) (4a)
LFR = -sin(cs) (4b).
For the right front quadrant:
LFL = cos (cs) (4c)
LFR = -sin(cs) (4d) .
For the left rear quadrant:
LFL = cos (-cs) + 0 .41*G (lr) (4e)
LFR = sin (-cs) (4f ) .
For the right rear quadrant:
LFL = cos (-cs) (4g)
LFR = sin (-cs) (4h) .
11. Improvements to the left front matrix elements
To improve the performance of the matrix elements
with stereo music that was panned forward and to increase
the separation between the front channels and the rear
channels when stereo music was panned to the rear, an
additional boost along the cs axis was added in the front,
and a cut along the cs axis was added in the rear,
respectively (the "March '97 version"). However, the basic
functional dependence among these matrix elements was
maintained. For the front left quadrant:
LFL = (cos (cs) + 0.41*G (lr) ) *boostl (cs) (5a)
LFR = (-sin(cs) ) *boostl (cs) (5b) .
For the right front quadrant:
LFL = (cos (cs) ) *boostl (cs) (5c)
LFR = (-sin(cs) ) *boostl (cs) (3d) .
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For the left rear quadrant:
LFL = (cos (-cs) + 0.41*G (Ir) ) /boost (cs) (5e)
LFR = (sin(cs) ) /boost (cs) (5f) .
For the right rear quadrant:
LFL = (cos ( cs) ) /boost ( cs) ( 5g)
LFR = (sin(cs) ) /boost (cs) (5h)
where the function G(x) is the same as the one in the '89
patent. When expressed with angles as an input, G(x) is
equal to:
G(x) - 1 - tan (45 - x) (6) .
In the March '97 circuit, the function boostl(cs)
was a linear boost of 3dB that was applied over the first
22.5 degrees of steering and was decreased back to OdB in
the next 22.5 degrees of steering. Boost(cs) is given by
corr(x) in the Matlab code below, in which comment lines are
preceded by the percent symbol %:
calculate a boost function of +3dB at 22.5 degrees
corr(x) goes up 3dB and stays up. corrl(x) goes up
then down again
for x = 1:24; % x has values of 1 to 24 representing 0
to 23 degrees
corr (x) - 10~ (3* (x-1) / (23*20) ) ; % go up 3dB over this
range
corrl (x) - corr (x) ;
end
for x = 25:46 % go back down for corrl over this range
24 to 45 degrees
corr(x) - 1.41;
corrl (x) - corr (48-x) ;
end.
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FIG. 9 shows a plot of LFL resulting from equations
(5a)-(5h). Note that as the steering moves toward center,
the boost is applied both along the lr=0 axis, and along the
left to center boundary. Note also the reduction in level
as the steering moves to the rear.
The performance of the March '97 circuit can be
improved. The first problem with the March '97 version is
in the behavior of the steering along the boundaries between
left and center, and between right and center. As shown in
FIG. 9, the value of the LFL matrix element increases to a
maximum half-way between left and center as a strong single
signal pans from the left to the center. This increase is
an unintended consequence of the deliberate increase in
level for the left and right main outputs as a center signal
is added to stereo music.
When a stereo signal is panned forward, it is
desirable for the levels of the left and right front outputs
to rise to compensate for the removal of the correlated
component from these outputs by the matrix. However, this
level increase 1 should only occur when the lr component of
the inputs is minimal (when there is no net left or right
steering). Therefore, the boost is only needed along the
1r = 0 axis. When 1r is non-zero, the matrix element should
not be boosted.
The increase implemented in the March of '97
circuit was independent of 1r, and therefore resulted in a
level increase when a strong signal was panned across the
boundary. This problem can be solved by using an additive
term to the matrix elements, instead of a multiply. A new
steering index (the boundary limited cs value) is defined
with the following Matlab code:
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Assume both Ir and cs > 0 - we are in the left front
quadrant
(assume cs and 1r follow the Matlab conventions of
varying from 1 to = 46)%
find the bounded c/s
if (cs < 24)
bcs = cs - (lr - 1) ;
if (bcs < 1) % this limits the maximum value
bcs = 1;
end
else
bcs = 47 - cs - (lr - 1) ;
if (bcs < 1)
bcs = 1;
end
end.
If cs < 22.5 and 1r =0, (in the Matlab convention
cs < 24 and lr = 1) bcs is equal to cs. However, bcs will
decrease to zero as 1r increases. If cs > 22.5, bcs also
decreases as Ir increases.
To find the correction function needed, the
difference between the boosted matrix elements and the non-
boosted matrix elements are found along the 1r=0 axis. This
difference is called cos tbl plus and sin tbl plus. Using
Matlab code:
a = 0:45; % define a vector in one degree steps. a has
the values of 0 to 45 degrees
al = 2*pi*a/360: % convert to radians
now define the sine and cosine tables, as well as the
boost tables for the front
sin tbl - sin (al) ;
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cos tbl- cos
(al)
;
cos tblplus cos(al). *corrl(a+1);
=
cos- tblplus cos tbl plus - cos-tbl; % this is
= the
one we use
cos tblminus = cos(al)./corr(a+1);
sin tblplus sin(al). *corrl(a+1);
=
sin -tblplus sin tbl plus - sin-tbl; % this is
= the
one we use
sin tbl minus = sin(al)./corr(a+1).
The vectors sin-tbl plus and cos-tbl plus are the
difference between a plain sine and cosine, and the boosted
sine and cosine. LFL and LFR are defined according to the
following equations:
LFL = cos (cs) + 0.41*G (lr) + cos tbl plus (bcs) (7a)
LFR = -sin(cs) - sin tbl plus(bcs) (7b).
In the front right quadrant LFL and LFR are similar, but do
not include the +0.41*G term. These new definitions lead to
the matrix element shown graphically in FIG. 10. In FIG 10,
the new element has the correct amplitude along the left to
center boundary, as well as along the center to right
boundary.
The steering in the rear quadrant is not optimal
either. When the steering is toward the rear, the above
matrix elements are given by:
LFL = cos tbl minus(-cs) + 0.41*G(-cs) (8a)
LFR = sin tbl minus(-cs) (8b).
These matrix elements are very nearly identical to
the elements in the '89 patent. Consider the case when a
strong signal pans from left to rear. The elements in the
'89 patent were designed so that there was a complete
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cancellation of the output from the front left output only
when this signal is fully to the rear (cs = -45. 1r=0).
However, it is desirable for the left front output to be
zero when the encoded signal reaches the left rear direction
(cs =-22.5 and lr = 22.5), and for = the left front output
to remain at zero as the signal pans further to full rear.
The matrix elements used in March '97 circuit result in the
output in the front left channel being about -9dB when a
signal is panned to the left rear position. This level
difference is sufficient for good performance of the matrix,
but it is not as good as it could be.
Performance can be improved by altering the LFL
and LFR matrix elements in the left rear quadrant. The
concern here is how the matrix elements vary along the
boundary between left and rear. The mathematical method
given in reference [1] can be used to find the behavior of
the elements along the boundary. If it is assumed that the
amplitude of the left front output should decrease with the
function F(t) as t varies from 0 degrees (left) to -22.5
degrees (left rear), the matrix elements are defined
according to the following equations:
LFL = cos ( t) *F ( t) -/+ sin ( t) * ( sqrt ( 1-F ( t) ~2 ) ) ( 9a)
LFR = (sin (t) *F (t) +/- cos ( t) * (sqrt (1-F (t) ~2) ) ) (9b) .
If F(t) - cos(4*t) and the correct sign is chosen,
equations (9a) and (9b) simplify to the following equations:
LFL = cos ( t) *cos (4* t) +sin ( t) *sin (4* t) (9c)
LFR = (sin ( t) *cos (4* t) -cos ( t) *sin (4* t) (9d) .
A plot of these coefficients is shown in FIG. 11, where LFL
(solid curve) and LFR (dotted curve) are plotted as a
function of t. Because all angles in Matlab are integers,
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the slight glitch in the middle is due to the absence of a
point at 22.5 degrees.
These elements work well. As shown in FIG. 11,
the front left output is reduced smoothly to zero as t
varies from 0 to 22.5 degrees. However, it is desirable for
the output to remain at zero as the steering continues from
22.5 degrees to 45 degrees (full rear). Along this part of
the boundary, LFL and LFR are defined according to the
following equations:
LFL = -sin ( t) (l0a)
LFR = cos ( t) ( lOb) .
These matrix elements are a far cry from the
matrix elements along the Ir=0 boundary where, in
reference [1], the values were defined according to the
following equations:
LFL = cos (cs) (lOc)
LFR = sin(cs) (lOd) .
These matrix elements are designed to behave
properly with a strongly steered signal (where both cs and
lr have maximum values). The previous matrix elements were
successful for signals where lr is near zero (stereo signals
that have been panned to the rear). Therefore, a method of
smoothly transforming the earlier matrix elements into the
newer matrix elements as lr and cs approach the boundary is
needed. One may include approach linear interpolation.
Another approach, which is particularly useful where
multiplies are expensive, includes defining the minimum of
lr and cs as a new variable. One example of this approach
is shown in the Matlab segment below:
% new - find the boundary parameter
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bp=x;
if (bp > y)
bP = Y;
end
and a new correction function which depends on bp:
for x = 1:24
ax = 2*pi* (46-x), 360;
front boundary-tbl (x) - (cos (ax) -
sin (ax) ) / (cos (ax) +sin (ax) ) ;
end
for x = 25:46
ax = 2*pi* (x-1) /360;
front boundary-tbl (x) - (cos (ax) -
sin (ax) ) / (cos (ax) +sin (ax) ) ;
end.
LFL and LFR are then defined in this quadrant
according to the following equations:
LFL = cos(cs)/(cos(cs)+sin(cs)) -
front boundary-tbl(bp) + 0.41*G(Ir) (11a)
2o LFR = sin(cs)/(cos(cs)+sin(cs)) +
front boundary tbl(bp) (llb).
Note the correction of cos(cs)+sin(cs). when
cos(cs) is divided by this factor, the function
1 - 0.5*G(cs) is obtained, which is the same as the Dolby°
matrix in this quadrant. Then sin(cs) is divided by this
factor and the earlier function +0.5*G(cs) is obtained.
Similarly in the right rear quadrant, LFL and LFR
are defined according to the following equations:
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LFL = cos (cs) / (cos (cs) +sin(cs) ) - 1 - 0.5*G(cs) . (12a)
LFR = sin(cs) / (cos (cs) +sin(cs) ) - 0.5*G(cs) (12b) .
A graphical display of LFL and LFR is shown in FIG 12 and
FIG. 13, respectively.
In FIG 12, which presents the left rear of the
coefficient graph, there is a large correction along the
left-rear boundary. This large correction causes the front
left output to go to zero when steering goes from left to
left rear. The output remains zero as the steering
progresses to full rear. The function is identical to the
Dolby° matrix along the lr = 0 axis and in the right rear
quadrant.
In FIG 13 there is a large peak in the left to
rear boundary. This works in conjunction with the LFL
matrix element to keep the front output at zero along this
boundary as steering goes from left rear to full rear. Once
again, the element is identical to the Dolby° matrix in the
rear direction along the lr = 0 axis and the rear right
quadrant.
One of the major design goals for the matrix is
that in any given output, the loudness of unsteered material
presented to the inputs of the decoder should be constant,
regardless of the direction of a steered signal present at
the same time. As explained previously, this means that the
sum of the squares of the matrix elements for each output
should be one, regardless of the steering direction.
However, as explained before, this requirement must be
altered when there is strong steering in the direction of
the output in question. That is, if with regard to the left
front output, the sum of the squares of the matrix elements
must increase by 3dB when the steering goes full left. The
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above elements also alter the requirement somewhat when the
steering moves forward and backward along the lr = 0 axis.
FIGs. 14 and FIG. 15 show plots of the square root
of the sum of the squares of the matrix elements for the
revised design. In FIG. 14, the 1/(sin(cs)+cos(cs))
correction in the rear quadrant was deleted so that the
accuracy of the resulting sum could be better visualized.
In FIG. 15, there is a 3dB peak in the left direction, and a
somewhat lesser peak as a signal goes from unsteered to
22.5 degrees in the center direction. This peak is a result
of the deliberate boost of the left and right outputs during
half-front steering. Note that in the other quadrants the
rms sum is very close to one, which was the intent of the
design. Because the method used to produce the elements was
an approximation, the value in the rear left quadrant is not
quite equal to one. However, it is a pretty good match.
In FIG. 15, the unsteered (middle) to right axis
has the value one, the center vertex has the value 0.71, the
rear vertex has the value 0.5, and the left vertex has the
value 1.41. Note that there is a peak along the middle to
center axis.
12. Rear matrix elements during front steeri
The rear matrix elements in the '89 patent, to
which a scaling by 0.71 has been introduced to show the
effect of the standard calibration procedure, are defined
according to equations (13a), (13b), (13c) and (13d). For
the front left quadrant:
LRL = 0.71* (1 - G(lr) ) (13a)
LRR = 0.71* (-1) (13b) .
For the rear left quadrant:
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LRL = 0.71* (1 - G(lr) + .41*G(-cs) ) (13c)
LRR = -0.71*(1 + 0.41*G(-cs)) (13d)
(the right half of the plane is identical but switches LRL
and LRR) .
After a similar calibration, the rear matrix
elements in the Dolby° Pro-Logic° are defined according to
equations (14a), (14b), (14c), and (14d). For the front left
quadrant:
LRL = 1 - G(lr) (14a)
LRR = -1 (14b).
For the rear left:
LRL = 1 - G(lr) (14c)
LRR = -1 (14d) .
The right half of the plane is identical, but switches LRL
and LRR. Note that the Dolby° elements and the elements of
the '89 patent are calibrated to be equal in the rear left
quadrant when cs = -45 degrees.
13. A brief digression on the surround level in Dolby°
Pro-Logic°
The Dolby° elements are similar to the elements
given in the '89 patent, except that the boost is not
dependent on cs in the rear. This difference is quite
important, because after the standard calibration procedure,
the elements have quite different values for unsteered
signals. In general, the description in this document of
the matrix elements does not consider the calibration
procedure for these decoders and all the matrix elements are
derived with a relatively arbitrary scaling. In most cases,
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the elements are presented as if they had a maximum value
of 1.41. In fact, for technical reasons, the matrix
elements are all eventually scaled so they have a maximum
value of less than one. In addition, when the decoder is
finally put to use, the gain of each output to the
loudspeaker is adjusted. To adjust the gain of each output,
a signal which has been encoded from the four major
directions (left, center, right, and surround) with equal
sound power is played, and the gain of each output is
adjusted until the sound power is equal in the listening
position. In practice, this means that the actual level of
the matrix elements is scaled so the four outputs of the
decoder are equal under conditions of full steering. This
calibration has been explicitly included in the equations
for the rear elements above.
The 3dB difference in the elements in the forward
steered or unsteered condition is not trivial. During
unsteered conditions, the elements from the '89 patent have
the value 0.71, and the sum of the squares of the elements
has the value of one. This is not true of the calibrated
Dolby~ rear elements. LRL has the unsteered value of one,
and the sum of the squares is 2, which is 3dB higher than
the outputs in the '89 patent. Note that the calibration
procedure results in a matrix that does not correspond to
the "Dolby° Surround°" passive matrix when the matrix is
unsteered. The Dolby° Surround° passive matrix specifies
that the rear output should have the value of
0. 71* (Ain - Bin) , and the Dolby Pro-Logic~ matrix does not
meet this specification. As a result, the rear output will
be 3dB stronger than the others when the A and B inputs are
decorrelated. If there are two speakers sharing the rear
output, each will be adjusted to be 3dB softer than a single
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rear speaker, which will make all five speakers have
approximately equal sound power when the decoder inputs are
uncorrelated. When the matrix elements from the '89 patent
are used, the same calibration procedure results in 3dB less
sound power from the rear when the decoder inputs are
uncorrelated.
The issue of how loud the rear channels should be
when the inputs are decorrelated is a matter of taste. When
a surround encoded recording is being played, it may be
desirable to reproduce the balance heard by the producer
when the recording was mixed. Achieving this balance is a
design goal for the decoder and encoder as a combination.
However, with standard stereo material, the goal is to
reproduce the power balance in the original recording, while
generating a tasteful and unobtrusive surround. The problem
with the Dolby° matrix elements is that the power balance in
a conventional two channel recording is not preserved
through the matrix, in that the surround channels are too
strong, and the center channel is too weak.
To see the importance of this issue, consider what
happens when the input to the decoder consists of three
components, an uncorrelated left and right component, and a
separate and uncorrelated center component.
Ain = Lin - .71*Cin (15a)
Bin = Rin + .71*Cin (15b) .
When Ain and Bin are played through a conventional
stereo system, the sound power in the room will be
proportional to Lint + Rin2 + Cin2. If all three components
have roughly equal amplitudes, the power ratio of the center
component to the left plus right component will be 1:2.
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It may be desirable for the decoder to reproduce
sound power in the room with approximately the same power
ratio as stereo, regardless of the power ratio of Cin to Lin
and Rin. This can be expressed mathematically. Essentially,
the equal power ratio requirement will specify the
functional form of the center matrix elements along the cs
axis, if all the other matrix elements are taken as given.
If it is assumed that the Dolby° matrix elements, calibrated
such that the rear sound power is 3dB less than the other
three outputs when the matrix is fully steered (i.e. 3dB
less than the standard calibration), then the center matrix
elements should have the shape shown in FIG. 16. If the
same thing is done for the standard calibration, the results
in FIG. 17 emerge.
In FIG. 16, the solid curve shows the values of
the center matrix elements as a function of cs assuming the
power ratios in the decoder outputs are identical to the
power ratios in stereo, and using the rear Dolby° matrix
elements calibrated 3dB lower in level than is typically
used. The dotted curve shows the actual value of the center
matrix elements in Pro-Logic°. While the actual value gives
reasonable results for an unsteered signal and a fully
steered signal, the actual value is about l.SdB too low in
the middle.
In FIG. 17, the solid curve shows the value of the
center matrix elements assuming equal power ratios to stereo
given the matrix elements and the calibration actually used
in Dolby° Pro-Logic. The dotted curve shows the actual
values of the center matrix elements in Pro-Logic~. The
actual values are more than 3dB too low for all values
of cs.
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These two figures show something of which mix
engineers are often aware - that a mix prepared for playback
on a Dolby° Pro-Logic° system can require more center
loudness than a mix prepared for playback in stereo.
Conversely, a mix prepared for stereo playback will lose
vocal clarity when played over a Dolby° Pro-Logic° decoder.
Ironically, this is not true of a passive Dolby° Surround°
decoder.
14. Creating two independent rear outputs
The major problem with both the elements of the
'89 patent and the elements of the Dolby° Pro-Logic° decoder
is that there is only a single rear output. The '92 patent
disclosed a method for creating two independent side
outputs, and the math in the '92 patent was incorporated in
the elements of the front left quadrant of reference [1] and
the November '96 application. The goal for the elements in
this quadrant was to eliminate the output of a signal
steered from left to center, while maintaining some output
from the left rear channel for unsteered material present at
the same time. To achieve this goal, it was assumed that
the LRL matrix element would have the following form for the
left front quadrant:
LRL = 1 - GS(lr) - 0.5*G(cs) (16a)
LRR = -0 . 5*G (cs) - G (lr) (16b) .
These matrix elements are very similar to the
elements in the '89 patent, but further include a G(lr) term
in LRR, and a GS term in LRL. G(lr) was included to add
signals from the B input channel of the decoder to the left
rear output to provide some unsteered signal power as the
steered signal was being removed. GS(lr) was determined
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according to the criterion that there should be no signal
output with a fully steered signal that is moving from left
to center. The formula for GS(lr) was determined to be
equal to G2(lr). However, a more complicated representation
of the formula is given in the '92 patent. The two
representations can be shown to be identical.
In reference [1] these elements are corrected by a
boost of (sin(cs)+cos(cs)) so that they more closely
approximate constant loudness for unsteered material. While
completely successful in the right front quadrant, this
correction is not very successful in the left front
quadrant. As shown in FIG. 18, the matrix elements are
identical to the LRL and LRR elements in the '89 patent for
the right front quadrant. In FIG. 18, there is a 3dB dip
along the line from the middle to the left vertex in the
front left quadrant, and nearly a 3dB boost in the level
along the boundary between left and center. The "mountain
range" in the rear quadrant will be discussed later. For
the plot shown in FIG. 18, the "tv matrix" correction in
V1.11 has been removed to allow better comparison to the
present invention, which is shown in FIG. 20.
Several problems with the sound power are shown in
FIG.18. For example, there is a dip in the sum of the
squares along the cs = 0 axis. This dip exists because the
functional shape of G(1r) in LRR is not optimal. In fact,
the choice of G(1r) was arbitrary. This function already
existed in an earlier design of the decoder, and was easily
implemented in analog circuitry.
It may be desirable to have a function GR(1r) in
this equation, choose GS(lr) and GR(1r) in such a way as to
keep the sum of the squares of LRL and LRR constant along
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the cs = 0 axis, and keep the output zero along the boundary
between left and center. It may also be desirable for the
matrix elements to be identical to the matrix elements in
the right front quadrant along the lr = 0 axis. It is
assumed that:
LRL = cos (cs) - GS (Ir) (17a)
LRR = -sin(cs) - GR(1r) (17b).
So that the sum of the squares are one along the cs=0 axis:
(1 - GS (1r) ) 2 + (GR (1r) ) 2 - 1 (18)
and so that the output is zero for a steered signal, or as t
varies from zero to 45 degrees:
LRL*cos ( t) + LRR*sin ( t) - 0 (19) .
l~lhen solving for GR ( lr) and GS ( lr) , equations ( 18 )
and (19) result in a messy quadratic equation, which is
solved numerically and shown in FIG. 19. As intended, use
of the values obtained for GS and GR, as shown in FIG. 19,
results in a large improvement in the power sum along the
cs = 0 axis. However, the peak in the sum of the squares
along the boundary between left and center (shown in
FIG. 18) remains.
In a practical design it is probably not very
important to compensate for this error. However, this
compensation may be accomplished heuristically by dividing
both matrix elements by a factor that depends on a new
combined variable ("xymin") that is based on lr and cs.
Alternatively, both matrix elements may be multiplied by the
inverse of xymin. For example, in Matlab notation:
find the minimum of x or y
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xymin = x;
if (xymin > y)
xymin = y;
end
if (xymin > 23)
xymin = 23;
end
note that xymin varies from zero to 22.5 degrees.
The correction to the matrix elements along the
boundary may be found using xymin. In the front left
quadrant:
LRL = (cos (cs) - GS (Ir) ) / (1 + .29*sin (4*xymin) ) (20a)
LRR = (-sin(cs) - GR(Ir) ) / (1 + .29*sin(4*xymin) ) (20b) .
In the front right quadrant:
LRL = cos(cs) (20c)
LRR = -sin(cs) (20d) .
In reference [2], these elements are also multiplied by the
"tv matrix" correction. FIG. 20 shows the matrix elements
without the "tv matrix" correction. The "tv matrix"
correction is handled by frequency dependent circuitry that
follows the matrix, which will be described later. As shown
in FIG. 20, the sum of the squares is close to one and
continuous, except for the deliberate rise in level in the
rear.
15. The rear matrix elements during rear steeri
The rear matrix elements given in the '92 patent
were not appropriate for a five-channel decoder, and,
therefore, may be modified heuristically. Reference [1] and
the November '96 application presented a mathematical method
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for deriving these elements along the boundary of the left
rear quadrant. The method worked along the boundary, but
resulted in discontinuities along the lr = 0 axis, and the
cs = 0 axis. These discontinuities were mostly repaired by
additional corrections to the matrix elements, which
preserved the behavior of the matrix elements along the
steering boundaries.
These discontinuties may also be corrected using
interpolation. A first interpolation fixes discontinuities
along the cs = 0 boundary for LRL. This interpolation
causes the value of LRL to match the value of GS(lr) when cs
is zero, and allows the value of LRL to rise smoothly to the
value given by the previous math as cs increases negatively
toward the rear. A second interpolation causes the value of
LRR to match the value of GR(1r) along the cs = 0 axis.
16. Left side/rear outputs during rear steering from Right
to Riaht Rear
Consider the LRL and LRR matrix elements when the
steering is neutral or anywhere between full right and right
rear (Ir can vary from 0 to -45 degrees, and cs can vary
from 0 to -22.5 degrees). Under these conditions, the
steered component of the input should be removed from the
left outputs, which means there should be no output from the
rear left channel when the steering is toward the right or
right rear.
The matrix elements given in the '92 patent
achieve this goal and are essentially the same as the rear
matrix elements in a 4 channel decoder with the addition of
a sin(cs)+cos(cs) correction for the unsteered loudness.
Therefore, the matrix elements are simple sines and cosines
and are defined according to the following equations:
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LRL = cos (-cs) - sri (-cs) (21a)
LRR = sin(-cs) - sric(-cs) (21b)
where sric(x) is equal to sin(x) over a value with a range
of 0 to 22.5 degrees, and sri(x) is equal to cos(x). These
functions will also be used to define the Left Rear matrix
elements during Left steering.
17. Left side and rear outputs during rear steering from
Right Rear to Rear
Consider the same matrix elements as cs becomes
greater than -22.5 degrees (cs varies from -22.5 to -45).
As stated in reference [1], the July '96 application and the
November '96 application, LRL should rise to one or more
over this range, and LRR should decrease to zero. Simple
functions fulfill these requirements:
LRL = (cos (45+cs) + rboost (-cs) ) - (sri (-cs) +
rboost (-cs) ) (22a)
LRR = sin (45+cs) - sric (-cs) (22b)
where rboost(cs) is defined in reference [1] and the
November '96 application. rboost(cs) is closely equivalent
to the function 0.41*G(cs) in the earlier matrix elements,
except that rboost(cs) is zero for 0 > cs > -22.5, and
varies from zero to 0.41 as cs varies from -22.5 degrees to
-45 degrees. The exact functional shape of rboost(cs) is
determined by the desire to keep the loudness of the rear
output constant as sound is panned from left rear to full
rear. The Left Rear matrix elements during right steering
are now complete.
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18. The Left Rear matrix elements during steering from left
to left rear
The behavior of the LRL and LRR matrix elements is
complex. The LRL element must quickly rise from zero to
near maximum as 1r decreases from 45 to 22.5 or to zero.
The matrix elements given in reference [1] satisfy this
requirement, but as shown previously, there are problems
with continuity at the cs = 0 boundary.
One solution to the continuity problems uses
functions of one variable and several conditionals. In
reference [1], the problem at the cs = 0 boundary arises
because the LRL matrix element is given by GS(1r) on the
forward side of the boundary (cs > 0). On the rear side of
the boundary (cs < 0), the function given by reference [1]
has the same end points, but is different when 1r is not
zero or 45 degrees.
The mathematical method in reference [1] provides
the following equations for the Left Rear matrix elements
over the range 22.5 < Ir < 45 (in reference [1] , t = 45-lr)
LRL = cos (45-lr) *sin (4* (45-Ir) ) -sin (45-lr) *cos (4* (45-
1r) ) - sra (Ir) (23a)
LRR = - (sin (45-Ir) . *sin (4* (45-Ir) ) +cos (45-
lr) . *cos (4* (45-Ir) ) ) - srac (1r) (23b)
where sra(lr) and srac(Ir) are two new functions defined
over this range.
If cs > 22.5, lr can still vary from 0 to 45.
Reference [1] defines LRL and LRR (when the range of lr is
0 < 1r < 22.5; see FIG. 6 in reference [1]), respectively,
as:
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LRL = cos (1r) - sra (lr) (23c)
LRR = -sin(lr) - -srac(lr) (23d)
which defines the two functions sra(x) and srac(x) for
0 < 1r < 45.
19. March 1997 version
There are two discontinuities in the March 1997
version. Along the cs = 0 boundary, the LRR for the rear
must match the LRR for the forward direction, which shows
LRR = -G(1r) along the cs = 0 boundary. A somewhat
computationally intensive interpolation, which is based on
cs over the range of values of 0 to 15 degrees, is used to
correct LRR. When cs is zero G(1r) is employed to find LRR
and as cs increases to 15 degrees, LRR is interpolated to
the value of srac ( 1r) .
A discontinuity along the lr = 0 axis is also
possible. This discontinuity was corrected somewhat by
adding a term to LRR, which is found by using a new variable
("cs bounded"). The correction term becomes simply
sric(cs bounded), which will insure continuity across the
lr = 0 axis. cs bounded may be defined according to the
following Matlab notation:
cs bounded = lr - cs;
if (cs bounded < 1)% this limits the maximum value
cs bounded = 0;
end
if (45-~lr~ < cs bounded)% use the smaller of the two
values
cs bounded = 45-lr;
end
for cs = 0 to 15
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LRR = (- (srac (lr) + (srac (lr) -G (lr) ) * (15-cs) /15) +
sric(cs bounded));
for cs = 15 to 22.5
LRR = (-srac(lr) + sric(cs bounded)).
20. LRL as implemented in the present invention
In the present invention, LRL is computed using an
interpolation similar to that used for LRR. In Matlab
notation:
for cs = 0 to 15
LRL = ( (sra (lr) + (sra (lr) -GS (lr) ) * (15-cs) /15) +
sri (-cs) ) ;
for cs = 15 to 22.5
LRL = (sra (lr) + sri (-cs) ) .
21. Rear outputs during steering from Left Rear to Full
Rear
As the steering goes from left rear to full rear
the elements follow those given in reference [1], however,
corrections for rear loudness are added. In Matlab
notation:
For cs > 22.5, lr < 22.5
LRL = (sra (lr) + sri (cs) + rboost (cs) )
LRR = -srac (lr) + sric (cs bounded) .
This completes the LRL and LRR matrix elements
during left steering. The values for right steering can be
found by swapping left and right in the definitions.
-~ .-~~.,.-, ~ .. ~. .., -, .- ~.; ~r .., ....,.. r.- ..
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The '89 patent and Dolby° Pro-Logic~ both have
center matrix elements defined by equations (24a), (24b),
(24c) and (24d) . For front steering:
CL = 1 - G (1r) + 0 .41*G (cs) (24a)
CR = 1 + 0.41*G(cs) (24b).
For rear steering:
CL = 1 - G (lr) (24c)
CR = 1 (24d) .
Because the matrix elements have symmetry about
the left/right axis, the values of CL and CR for right
steering can be found by swapping CL and CR. FIG. 21 shows
a graphical representation of CL, in which the middle of the
graph and the right and rear vertices have the value 1, and
the center vertex has the value 1.41. In practice, this
element is scaled so that its maximum value is one.
In the November '96 application and reference [1],
these elements are defined by sines and cosines according to
equations (25a) and (25b). For front steering:
CL = cos (-45-1r) *sin(2* (45-1r) ) - sin (45-Ir) *cos (2* (45-
Ir) ) + 0.41*G(cs) (25a)
CR = sin (45-Ir) *sin (2* (45-1r) ) + cos (45-1r) *cos (2* (45-
Ir) ) + 0.41*G(cs) (25b) .
However, the March 1997 version used the elements
defined in the '89 patent, but with a different scaling, and
a boost function different than G(cs). It was important to
reduce the unsteered level of the center output, therefore,
a value 4.5dB less than the value used in Dolby° Pro-Logic~
was chosen and the boost function (0.41*G(cs)) was changed
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to increase the value of the matrix elements back to the
value used in Dolby Pro-Logic~ as cs increases toward
center. The boost function in the March 1997 version was
chosen heuristically through listening tests.
In the March 1997 version, the boost function of
cs starts at zero as before, and increases with cs such that
CL and CR increase by 4.5dB as cs goes from zero to
22.5 degrees. The increase in CL and CR is a constant
number (in dB) for each dB of increase in cs. The boost
function then changes slope such that the matrix elements
increase another 3dB in the next 20 degrees and then remain
constant. Thus, the new matrix elements are equal to the
neutral values of the old matrix elements when the steering
is "half front" (8dB or 23 degrees). As the steering
continues to move forward, the new and the old matrix
elements become equal. The output of the center channel is
thus 4.5dB lower than the old output when steering is
neutral, but increases to the old value when the steering is
fully to the center. FIG. 22 shows a three-dimensional plot
of the CL matrix element. In this plot, the middle value
and the right and rear vertices have been reduced by 4.5dB.
Addionally, as cs increases, the center rises to the value
of 1.41 in two slopes.
However, the center elements used in the
March 1997 version are not optimal. Considerable experience
with the decoder in practice has shown that the center
portion of popular music recordings and the dialog in some
films tends to get lost when switching between stereo (two
channel) reproduction, and reproduction using the matrix.
In addition, a listener who is not equidistant from the
front speakers can notice the apparent position of a center
voice moving as the level of the center channel changes.
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This problem was extensively analyzed as the new center
matrix elements presented here were developed. There is
also a problem when a signal pans from left to center or
from right to center along the boundary. The matrix
elements given in the November '96 application result in a
center speaker output that is too low when the pan is half
way between.
23. Center channel in the new design
While it is possible to remove a strongly steered
signal from the center channel output using matrix
techniques, any time the steering is frontal but not biased
either left or right, the center channel must reproduce the
sum of the A and B inputs with some gain factor. In other
words, it is not possible to remove uncorrelated left and
right material from the center channel. The only option is
to regulate the loudness of the center speaker.
How loud the center speaker should be depends on
the behavior of the left and right main outputs. The matrix
values presented above for LFL and LFR are designed to
remove the center component of the input signals as the
steering moves forward. If the input signal has been
encoded to come from the forward direction using a cross
mixer, such as a stereo width control, the matrix elements
given above (the elements of the '89 patent, reference [1],
the March 1997 version, and those presented earlier in this
paper) completely restore the original separation.
However, the input to the decoder may consist of
uncorrelated left and right channels to which an unrelated
center channel has been added. For example, the input
channels may be defined according to the following
equations:
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Ain = Lin + 0.71*Cin (26a)
Bin = Rin + 0.71*Cin (26b) .
When this is the case, as the level of Cin increases relative
to Lin and Rin, the C component of the L and R front outputs
of the decoder is not completely eliminated unless Cin is
large compared to Lin and Rin. In general, a bit of Cin
remains in the L and R front outputs. However, what will a
listener hear?
There are two ways of calculating what a listener
hears depending on whether the listener is exactly
equidistant from the Left, Right, and Center speakers. If a
listener is exactly equidistant from the Left, Right, and
Center speakers, they will hear the sum of the sound
pressures from each speaker. This is equivalent to summing
the three front outputs. When the listener is in this
position, any reduction of the center component of the left
and right speakers will result in a net loss of sound
pressure from the center component, regardless of the
amplitude of the center speaker. This net loss of sound
pressure from the center component is a result of deriving
the signal in the center speaker from the sum of the A and B
inputs. Therefore, as the amplitude of the signal in the
center speaker is raised, the amplitude of the Lin and Rin
signals must rise along with the amplitude of the Cin signal.
However, if the listener is not equidistant from
each speaker, the listener is much more likely to hear the
sum of the sound power from each speaker, which is
equivalent to the sum of the squares of the three front
outputs. In fact, extensive listening has shown that the
sum of the sound power from each speaker is actually what is
important. Therefore, the sum of the squares of all the
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outputs of the decoder, including the rear outputs, must be
considered.
To design the matrix so that the ratio of the
amplitudes of Lin, Rini and Cin are preserved when switching
between stereo reproduction and matrix reproduction, the
sound power of the Cin component from the center output must
rise in exact proportion to the reduction in the sound power
of the Cin component from the left and right outputs, and the
reduction in the sound power of the Cin component in the rear
outputs. An additional complication comes from the up to
3dB level boost applied to the left and right front outputs
(described previously). Because of the level boost, the
center will need to be somewhat louder to keep the ratios
constant. This requirement may be expressed as a set of
equations for the sound power. Using these equations, a
gain function, which can be used to increase the loudness of
the center speaker, can be determined.
The solid curve of FIG. 23 shows the center gain
needed to preserve the energy of the center component of the
input signal in the front three channels as steering
increases toward the front. The dotted curve of FIG. 24
shows the gain in a standard decoder. As shown by the solid
curve, the level of the center channel requires a steep
increase on the order of many dB of amplitude per dB of
steering value.
As previously mentioned, there are two solutions
to this problem. One solution is the "film" solution, which
is not entirely mathematical. The function shown in FIG. 23
rose too steeply, in that the change in level of the center
channel was too obvious. Therefore, the power requirement
was relaxed slightly so that the power in the center was
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about 1dB less than the ideal. The relaxed power
requirement may be used to recalculate the center values,
which are indicated by the solid line of FIG. 24. In
practice a linear rise can be substituted for the early part
of the curve, as indicated by the dashed line in FIG. 24.
These center values have yielded excellent results for
films. Because the curve indicated by the solid line in
FIG. 24 rises to steeply, the linear slope indicated by the
dashed line works better.
In contrast, music requires a different solution.
The center attenuation shown in FIGS. 23 and 24 was derived
using the matrix elements previously given for LFL and LFR.
However, what if different elements were used?
Specifically, would the center component need to be
aggressively removed from the left and right front outputs?
Listening tests show that the previous left and
right front matrix elements are needlessly aggressive about
removing the center component during music playback.
Acoustically there is no need. Energy removed from the left
and right front must be given to the center loudspeaker.
If, however, this energy is not removed, it will come from
the left and right front speakers, and, therefore, the
center speaker need not be as strong and the sound power in
the room remains the same. The trick is to put just enough
energy into the center speaker to create a convincing front
image for an off-axis listener, while minimizing the
reduction of stereo width for a listener who is equidistant
from the front left and right speakers.
As done in the November '96 application, the
optimal center loudness can be found by trial and error.
The matrix elements needed in the front left and right to
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preserve the power of the Cin component in the room may then
be determined. As before, it is assumed that the center
channel is reduced in level by 4.5dB below the level in the
decoder disclosed in the '89 patent, which is a total
attenuation of -7.5dB total attenuation, which is
about 0.42. The matrix elements for the center can be
multiplied by this factor, and a new center boost function
(GC) can be defined.
For front steering:
CL = 0.42* (1-G (lr) ) + GC (cs) (27a)
CR = 0 .42 + GC (cs) (27b) .
For rear steering:
CL = 0.42* (1-G(Ir) ) (27c)
CR = 0.42 (27d) .
Several functions were tried for GC(cs). The
function given below may not be ideal, but seems good
enough. The function is specified in terms of the angle cs
in degrees, and was obtained by trial and error.
In MATLAB notation:
center max = 0.65;
center rate = 0.75;
center max2 - 1;
center rate2 - 0.3;
center rate3 - 0.1;
if (cs < 12)
gc(cs - 1) - 0.42* 10, (db*center_rate/(20));
tmp = gc (cs + 1) ;
elseif (cs < 30)
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gc (cs + 1) - tmp*10~ ( (cs - 11) *center rate3/ (20) ) ;
if (gc (cs + 1) > center max)
gc (cs + 1) - center max;
end
else
gc(cs+1)=center max*10~((cs-29)*center rate2/(20));
if (gc (cs+ 1) > center max2)
gc ( cs+ 1 ) - center max2 ;
end
end.
The function (0.42 + GC(cs)) is plotted in
FIG. 25. Note the quick rise from the value 0.42 (4.5dB
lower than Dolby° Surround~), followed by a gentle rise, and
finally by a steep rise to the value 1.
The function needed for LFR may be determined if
functions for LFL, LRL, and LRR are assumed. This involves
determining the rate at which the Cin component in the left
and right outputs should decrease, and then designing matrix
elements that provide this rate of decrease. These matrix
elements should also provide some boost of the Lin and Rin
components, and should have the current shape at the left to
center boundary, as well as the right to center boundary.
It is assumed that:
LFL = GP (cs) (28a)
LFR = GF (cs) (28b)
CL = 0 .42* (1 - G (lr) ) + GC (cs) (28c)
CR = 0 . 42 + GC (cs) (28d) .
Power from the front left and right can then be computed as
follows:
PLR = (GPz + GF2) * (Line + Rin2) + (GP - GF) 2*Cin2 (29a) .
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Power from the center is:
PC = GCZ* (Line + Rin2) + 2*GC2*Cin2 (29b) .
Power from the rear depends on the matrix elements
used. It was assumed that the rear channels are attenuated
by 3dB during forward steering, and that LRL is cos(cs) and
LRR is sin(cs). From a single speaker:
PREAR = (0.71* (cos (cs) * (Lin + 0.71*Rin) - sin(cs) * (Rin +
0 . 71*Cin) ) ) 2 (29C) .
If it is assumed that Line=Rin2, then, for two
speakers:
PREAR = 0.5*Cin2* ( (cos (cs) - sin (cs) ) 2) + Line (29d) .
The total power from all three speakers is PLR + PC + PREAR:
PT = ( GP2 + GF2+ GC2 ) * ( Lin2 + Rin2 ) + ( ( GP - GF ) 2 +
2 * GC2 ) * Cin2 + PREAR ( 3 0 ) .
The ratio of Cin power to Lin and Rin power (assuming Lint -
Rin2 ) 1 S
RATIO = ( ( (GP (cs) -GF (cs) ) 2 + 2* (GC (cs) 2) + 0. 5*
(cos (cs) -sin (cs) ) 2) ) *Cin2 / ( (2* (GP (cs) 2 + GC (cs) 2 -
+ GF (CS) 2) + 1) *Lin2) (31a)
RATIO = (Cin2 / Line) * ( (GP (CS) -GF (CS) ) 2 + 2* (GC (CS) 2)
+ 0 . 5* (cos (cs) - sin (cs) ) 2) / (2* (GP (cs) 2 + GC (cs) 2 +
GF (cs) 2) + 1) (31b) .
For normal stereo, GC=0, GP=1, and GF=0.
Therefore, the center to LR power ratio is:
2 5 RAT I O = ( Cin2 / Line ) * 0 . 5 ( 3 2 ) .
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If this ratio is to be constant regardless of the
value of Cin2 ~ Lin2 for the active matrix, then:
( (GP (cs) -GF (cs) ) 2 + 2* (GC (cs) 2) + 0 . 5* (cos (cs) -sin (cs) ) 2)
- ( (GP(cs)2 + GC(cs)2 + GF(cs)2) + 0.5) (33) .
The equation above can be solved numerically.
Assuming the GC above, and GP = LFL as before, the result is
shown in FIG. 26. In FIG. 26 the solid curve is the GF
needed for constant energy ratios with the new "music"
center attenuation GC. The dashed curve is the LFR element
of the March '97 version (sin(cs)*corrl). The dotted curve
is sin(cs), which is the LFR element without the correction
term corrl. Note that GF is close to zero until cs reaches
30 degrees, and then GF increases sharply. In practice it
is best to limit the value of cs to about 33 degrees. In
practice, the LFR element derived from these curves has a
negative sign.
GF gives the shape of the LFR matrix element along
the 1r = 0 axis, as cs increases from zero to center. A
method is needed of blending this behavior to that of the
previous LFR element, which must be preserved along the
boundary between left and center, as well as from right to
center. A method of doing this when cs < 22.5 degrees is to
define a difference function between GF and sin(cs). This
function may then be limited in various ways. In Matlab
notation:
gf diff = sin(cs) - gf (cs)
for cs = 0:45;
if (gf diff (cs) > sin(cs) )
gf diff (cs) - sin(cs) ;
end
if (gf diff(cs) < 0)
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gf diff(cs) - 0;
end
end
%find the bounded c/s
if (y < 24)
bcs = y-(x-1);
if (bcs < 1) % this limits the maximum value
bcs = l;
end
else
bcs = 47-y-(x-1);
if (bcs < 1) %> 46)
bcs = 1; %46;
end
end.
The LFR element can now be written in Matlab
notation:
this neat trick does an interpolation to the boundary
the cost, of course, is a divide!!!
if (y < 23) % this is the easy way for half the region
lfr3d (47-x, 47-y) - -sin_tbl (y) +gf diff (bcs) ;
else
tmp - ( (47-1-x) / (47-1) ) *gf diff (y) ;
lfr3d (47-x, 47-y) - -sin_tbl (y) +tmp;
end.
Note that the sign of gf diff is positive in the
equation above. Thus gf diff cancels the value of sin(cs),
reducing the value of the element to zero along the first
part of the lr = 0 axis, as shown in FIG. 27.
In FIG. 27, the value is zero in the middle of the
plane (where there is no steering) and remains zero as cs
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increases to ~30 degrees along the lr = 0 axis. The value
then falls off to match the previous value along the
boundary from left to center and from right to center.
24. Panning error in the center output
The new center function may be written as follows:
CL = 0.42* (1 - G(lr) ) + GC(cs) (34a)
CR = 0 .42 + GC (cs) (34b) .
As defined in equations (34a) and 34(b), the new center
function works well along the Ir = 0 axis, but causes a
panning error along the boundary between left and center,
and between right and center. However, the values in
reference [1] give a smooth function of cos (2*cs) along the
left boundary and create smooth panning between left and
center. It is desirable for the new center function to have
similar behavior along this boundary.
A correction to the matrix element that will do
the job includes adding an additional function "xymin",
which may be expressed in Matlab notation as:
center fix tbl = .8*(corrl-1);
Then:
CL = 0.42-0.42*G(lr)+GC(cs)+center-fix_table(xymin)
(35a)
CR = 0.42+GC(cs)+center-fix-table(xymin) (35b).
A three-dimensional representation of the CL matrix element
is shown in FIG. 28. While not perfect, this correction
works well in practice. In FIG. 28, note the correction for
panning along the boundary between left and center, which is
fairly smooth.
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FIG. 29 shows a graph of the left front (dotted
curve) and center (solid curve) outputs, where the center
steering is to the left of the plot, and full left is to the
right. In the "music" strategy, the value of cs is limited
to about 33 degrees (about 13 on the axis as labeled), where
the center is about 6dB stronger than the left.
25. Technical details of the encoder
There are two major goals for the Logic 7~
encoder. First, the Logic 7~ encoder should be able to
encode a 5.1 channel tape in a way that allows the encoded
version to be decoded by a Logic 7~ decoder with minimal
subjective change. Second, the encoded output should be
stereo compatible, which means that it should sound as close
as possible to a manual two channel mix of the same
material. Stereo compatibility should include the output of
the encoder giving identical perceived loudness for each
sound source in an original 5 channel mix when played on a
standard stereo system. The apparent position of the sound
source in stereo should also be as close as possible to the
apparent position of the sound source in the 5 channel
original.
The goal of stereo compatibility, as described
above, cannot be met by a passive encoder. A five channel
recording where all channels have equal foreground
importance must be encoded as described above. This
encoding requires that surround channels be mixed into the
output of the encoder in such a way as to preserve the
energy. That is, the total energy of the output of the
encoder should be the same, regardless of which input is
being driven. This constant energy setting will be
necessary for most film sources and for five channel music
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sources where instruments have been assigned equally to all
loudspeakers, although such music sources are not common
at the present time, they will become common in the future.
Music recordings in which the foreground
5 instruments are placed in the front three channels, and
reverberation is placed primarily in the rear channels,
require a different encoding. Music recordings of this type
were successfully encoded in a stereo compatible form when
the surround channels were mixed with 3dB less power than
the other channels. This -3dB level has been adopted as a
standard for surround encoding in Europe. However, the
European standard specifies that other surround levels can
be used for special purposes. The new encoder contains
active circuits, which detect strong signals in the surround
channels. When the active circuits detect that such signals
are occasionally present, the encoder uses full surround
level. If the active circuits detect that the surround
inputs are consistently -6dB or less compared to the front
channels, the surround gain is gradually lowered 3dB, which
corresponds to that of the European standard.
These active circuits were also present in the
encoder in the November '96 application. However, tests
involving the encoder of the November '96 application,
performed at the Institute for Broadcast Technique (IRT? in
Munich, revealed that the direction of some sound sources
was encoded incorrectly. Therefore, a new architecture was
developed to solve this problem. The new encoder is clearly
superior in its performance on a wide variety of difficult
material. The original encoder was developed first as a
passive encoder. The new encoder will also work in a
passive mode, but is primarily intended to work as an active
encoder. The active circuitry corrects several small errors
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inherent in the design. However, even without the active
correction, the performance is better than the previous
encoder.
Through extensive listening, several other small
problems with the first encoder were discovered. Many of
these problems have been addressed in the new encoder. For
example, when stereo signals are applied to both the front
and the rear terminals of the encoder at the same time, the
resulting encoder output is biased too far to the front.
The new encoder compensates for this by increasing the rear
bias slightly. Likewise, when a film is encoded with
substantial surround content, dialog can sometimes get lost.
This problem was greatly improved by the changes to the
power balance described above. However, the encoder is also
intended for use with a standard (Dolby°) decoder and
compensates for this by raising the center channel input to
the encoder slightly when used in this manner.
26. Explanation of the design
The new encoder handles the left, center, and
right signals in a manner identical to that of the previous
design and the Dolby° encoder, providing that the center
attenuation function fcn is equal to 0.71, or -3dB.
The surround channels look more complicated than
they are. The functions fc() and fs() direct the surround
channels either to a path with a 90 degree phase shift
relative to the front channels, or to a path with no phase
shift. In the basic operation of the encoder, fc is one,
and fs is zero, which means that only the path which uses
the 90 degree phase shift is active.
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crx controls the amount of negative cross feed for
each surround channel and is typically 0.38. As in the
previous encoder, the A and B outputs have an amplitude
ratio of .38/.91 when there is only an input to one of the
surround channels. The amplitude ratio results in a
steering angle of 22.5 degrees to the rear. As usual, the
total power in the two output channels is unity (the sum of
the squares of .91 and .38 is one).
While the output of this encoder is relatively
simple when only one channel is driven, it becomes
problematic when both surround inputs are driven at the same
time. If the LS and the RS input are driven with the same
signal (a common occurrence in film), all the signals at the
summing nodes are in phase, so the total level in the output
channels is .38 + .91, which is 1.29. This output level is
too strong by the factor of 1.29, which is 2.2 dB.
Therefore, active circuitry is included in the encoder that
reduces the value of the function fc by up to 2.2 dB when
the two surround channels are similar in level and phase.
Another error occurs when the two surround
channels are similar in level and out of phase. In this
case, the two attenuation factors subtract, so the A and B
outputs have equal amplitude and phase, and a level of
.91-.38, which is .53. This signal will be decoded as a
center direction signal, which is a severe error. The
previous encoder design produced an unsteered signal under
these conditions, which is reasonable. However, it is not
reasonable that signals applied to the rear input terminals
result in a center oriented signal. Thus, active circuitry
is supplied, which increases the value of fs when the two
rear channels are similar in level and antiphase. Mixing
both the real path and the phase shifted path for the rear
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channels results in a 90 degree phase difference between the
output channels A and B. This results in an unsteered
signal, which is desired.
As previously mentioned, a surround encoder using
the European standard attenuates the two surround channels
by 3dB and adds them into the front channels. Thus, the
left rear channel is attenuated and added to the left front
channel. A surround encoder using the European standard has
many disadvantages when encoding multichannel film sound or
recordings that have specific instruments in the surround
channels. One such advantage is that both the loudness and
the direction of these instruments will be incorrectly
encoded. However, a surround encoder using the European
standard works rather well with classical music, for which
the two surround channels are primarily reverberation. The
3dB attenuation of the European standard was carefully
chosen through listening tests to produce encoding that is
stereo-compatible. Therefore, the new encoder should
include this 3dB attenuation when classical music is being
encoded. The presence of classical music can be detected
through the relative levels of the front channels and the
surround channels in the encoder.
A major function of the function fc in the
surround channels is to reduce the level of the surround
channels in the output mix by 3dB when the surround channels
are much softer than the front channels. Circuitry is
provided to compare the front and rear levels, and reduce
the value of fc to a maximum of 3dB when the rear levels are
3dB less than the front levels. Maximum attenuation is
reached when the rear channels are 8dB less strong than the
front channels. This active circuit appears to work well
and makes the new encoder compatible with a surround encoder
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using the European standard for classical music. The action
of the active circuits causes instruments, which are
intended to be strong in the rear channels, to be encoded
with full level.
The real coefficient mixing path fs has another
function for the surround channels. When a sound is moving
from the left front input to the left rear input, active
circuitry detects when these two inputs are similar in level
and in phase. Under these conditions, fc is reduced to zero
and fs is increased to one. This change to real
coefficients in the encoding results in a more precise
decoding of this type of pan. In practice, this function is
probably not essential, but seems to be an elegant
refinement.
There is an additional active circuit- a level
detecting circuit. Level detecting circuits look at the
phase relationship between the center channel and the front
left and right. Some popular music recordings that use five
channels mix the vocals into all three front channels. When
there is a strong signal in all three inputs, the encoder
output will have excessive vocal power, because the three
front channels will add together in phase. When this
occurs, active circuits increase the attenuation in the
center channel by 3dB to restore the power balance in the
encoder output.
In summary, active circuits are provided to:
1. Reduce the level of the surround channels by 2.2dB
when the two channels are in phase;
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2. Sufficiently, increase the real coefficient mixing
path for the rear channels to create an unsteered condition
when the two rear channels are out of phase;
3. Decrease the level of the surround channels by up
to 3dB when the surround level is much lower than the front
levels;
4. Increase the level and negative phase of the rear
channels when the level of the rear channels is similar to
the level of the front channels;
5. Cause the surround channel mix to use real
coefficients when a sound source is panning from a front
input to the corresponding rear input;
6. Increase the level of the center channel in the
encoder when the center level and the level of the front and
surround inputs are approximately equal; and
7. Decrease the level of the center channel in the
encoder when there is a common signal in all three front
inputs.
27. Frequency dependent circuits in the decoder
FIG. 2 is a block diagram that includes frequency
dependent circuits that follow the matrix in a five channel
version of the decoder. The frequency dependent circuits
include three sections: a variable low pass filter, a
variable shelf filter, and a HRTF (Head Related Transfer
Function) filter. The HRTF filter changes its
characteristics depending on the value of the rear steering
voltage c/s. The first two filters change their
characteristics in response to a signal that is intended to
represent the average direction of the input signals to the
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decoder during pauses between strongly steered signals.
This signal is called the background control signal.
28. The background control signal
One of the major goals of the current decoder is
to optimally create a five channel surround signal from an
ordinary two channel stereo signal. It is also highly
desirable for the decoder to recreate a five channel
surround recording that was encoded into two channels by the
encoder described in this application. These two goals
differ in the way in which the surround channels are
perceived. With an ordinary stereo input, the majority of
the sound needs to be in front of the listener. The
surround speakers should contribute a pleasant sense of
envelopment and ambience, but should not draw attention to
themselves. With an encoded surround recording, the
surround speakers need to be stronger and more aggressive.
To play both types of input optimally without any
adjustment by the user, it is necessary to discriminate
between a two channel recording and an encoded five channel
recording. The background control signal is designed to
make this discrimination. The background control signal
("BCS") is similar to and derived from the rear steering
signal cs. BCS represents the negative peak value of cs.
That is, when cs is more negative than BCS, BCS is made to
equal cs. When cs is more positive than BCS, BCS slowly
decays. However, the decay of BCS involves a further
calculation.
Music of many types consists of a series of strong
foreground notes, or in the case of a song, sung words.
There is a background between the foreground notes that may
consist of other instruments playing other notes or
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reverberation. The circuit that derives the BCS signal
keeps track of the peak level of the foreground notes. When
the current level is -7dB less than the peak level of the
foreground, the level of cs is measured. The value of cs
during the gaps between foreground peaks is used to control
the decay of BCS. If the material in the gaps is
reverberation, cs may tend to have a net rearward bias in a
recording that was made by encoding a five channel original.
This is because the reverberation on the rear channels of
the original will be encoded with a rearward bias. The
reverberation in an ordinary two channel recording will have
no net rearward bias. cs for this reverberation will be
zero or slightly forward.
BCS derived in this way tends to reflect the type
of recording. Any time there is significant rear steered
material, BCS will always be strongly negative. However,
BCS can be negative even in the absence of strong steering
to the rear if the reverberation in the recording has a net
rearward bias. The filters that optimize the decoder for
stereo versus surround inputs may be adjusted using BCS.
29. Frequency dependent circuits: five channel version
The first of the filters in FIG. 2 is a simple 6dB
per octave low pass filter with an adjustable cutoff
frequency. This filter is set to a value that is user
adjustable when BCS is positive or zero, but is typically
about 4kHz. The cutoff frequency of the filter is raised as
BCS becomes negative until BCS is more rearward than 22
degrees. At this point, the filter is not active. This low
frequency filter makes the rear outputs less obtrusive when
ordinary stereo material is played. In earlier decoders the
filter was controlled by cs, and not by BCS.
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The second filter is a variable shelf filter that
implements the "sound stage" control in the current decoder.
In the November '96 application, the "soundstage" control
was implemented through the matrix elements using the "tv
matrix" correction. The earlier decoders reduced the
overall level of the rear channels when the steering was
neutral or forward. In the new decoder, the matrix elements
do not include the "tv matrix" correction. The second
filter of FIG. 2 includes a low frequency section (the pole)
that is fixed at 500Hz and a high frequency section (the
zero) that varies depending on user adjustment and BCS.
The high frequency section of the shelf filter is
set equal to the low frequency section when the soundstage
control is set to "rear" in the new decoders. In other
words, the shelf has no attenuation, and the filter has flat
response. However, the setting of the high frequency zero
varies when the soundstage control is set to "neutral" in
the new decoders. The zero moves to 710Hz when BCS is
positive or zero, resulting in a 3dB attenuation of higher
frequencies. The result is the same as that of the earlier
decoders for the high frequencies. There is a 3dB
attenuation when the steering is neutral or forward.
However, the low frequencies are not attenuated and come
from the sides of the room with full level. This results in
greater low frequency richness and envelopment, without the
distracting high frequencies in the rear. The high
frequency zero moves toward the pole as BCS becomes negative
so that the shelf filter has an attenuation when BCS is
about 22 degrees to the rear. While the action is similar
when the soundstage control is set to "front", but the zero
moves to lkHz when BCS is zero or positive. This gives the
high frequencies an attenuation of 6dB. Once again, the
attenuation is removed as BCS goes negative.
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The third filter is controlled by c/s and not by
BCS. This filter is designed to emulate the frequency
responses of the human head and pinnae when a sound source
is approximately 150 degrees in azimuth from the front of
the listener. This type of frequency response is called a
"Head Related Transfer Function" or HRTF. These frequency
response functions have been measured for many angles and
for many different people. In general, there is a strong
notch in the frequency response at about 5kHz when a sound
source is about 150 degrees from the front. A similar notch
at about 8kHz exists when a sound source is in front of a
listener. Sound sources to the side of the listener do not
produce these notches. The presence of the notch at 5kHz is
one of the ways in which the human brain detects that a
sound source is behind the listener.
The current standard for five channel sound
reproduction recommends that the two rear speakers be placed
slightly behind the listener at +/- 110 or 120 degrees from
the front. This speaker position supplies good envelopment
at low frequencies. However, listening rooms often do not
have a size or shape appropriate for placing loudspeakers
fully behind the listener and a side position is the best
that can be achieved. However, a sound generated to the
side of a listener does not produce the same level of
excitement as a sound that is generated fully behind a
listener. In addition, film directors often want a sound
effect to come from behind the listener, and not from the
side.
The HRTF filter in the decoder adds the frequency
notches of a rear sound source so that a listener hears the
sound as if it were generated further behind the listener
than the actual positions of the loudspeakers. The filter
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is designed to vary with cs so that the filter is maximum
when cs is positive or zero, which causes ambient sounds and
reverberation to seem to be more behind the listener. The
filter is reduced as cs becomes negative and is completely
removed when cs is approximately -15 degrees. At this
point, the sound source appears to come fully from the side.
The filter is once again applied as cs goes further negative
so that the sound source appears to go behind the listener.
The filter is slightly modified to correspond to the HRTF
function when cs is fully to the rear.
30. Frequency dependent circuits: the seven channel version
FIG. 3 shows the frequency dependent circuits in
the seven channel version of the decoder, which consisting
of three sections. However, the second two sections can be
combined into one circuit. The first two sections are
identical to the two sections in the five channel decoder,
and perform the same function. The third section is unique
to the seven channel decoder. In version V1.11 and the
November '96 application the side and rear channels had
separate matrix elements. The action of the elements was
such that the side and the rear outputs were identical,
except for delay, when cs was positive or neutral. The two
outputs remained identical until cs was more negative than
22 degrees. As the steering moved further to the rear, the
side outputs were attenuated by 6dB, and the rear outputs
were boosted by 2dB. This caused the sound to appear to
move from the sides of the listener to the rear of the
listener.
In the present decoder, the differentiation
between the side output and the rear output is achieved by a
variable shelf filter in the side output. The third shelf
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filter in FIG. 3 has no attenuation when cs is forward or
zero. However, the zero in the shelf filter moves rapidly
toward 1100Hz when cs becomes more negative than 22 degrees,
resulting in an about 7dB attenuation of the high
frequencies. Although this shelf filter has been described
as a filter separate from the shelf filter that provides the
"soundstage" function, the action of the two shelf filters
can be combined into a single shelf through suitable control
circuitry.
While the preferred embodiments of the invention
have been described and illustrated in this document, many
other possible embodiments exist. These and other
modifications and variations will be apparent to those
skilled in the art without departing from the spirit of the
invention.
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