Note: Descriptions are shown in the official language in which they were submitted.
CA 02525944 2011-01-12
RECIPROCAL INDEX LOOKUP FOR BTSC COMPATIBLE COEFFICIENTS
BACKGROUND
1. Field of the Invention
The present invention relates to audio companding systems and, more
specifically,
to an apparatus for digitally implementing the compression and expansion
functions in a
BTSC decoder and encoder.
2. Description of the Prior Art
BTSC-compatible encoders and decoders are used to encode and decode stereo
audio signals into NTSC television compatible audio signals. Existing systems
typically
use an analog approach. The analog approach is environmentally sensitive and,
in the
case of the encoder, requires extra circuitry to be compatible with digital
television
systems.
Existing digital BTSC encoder and decoder implementations require complex
circuitry to facilitate determination of BTSC variable spectral preemphasis
and
deemphasis filter coefficients. The encoder implements the variable spectral
preemphasis
function. The decoder implements the variable spectral deemphasis function. In
the case
of the encoder, a feedback function is utilized to calculate the coefficients.
In the case of
the decoder, a feedforward function is utilized to calculate the coefficients.
The transfer
function of the decoder variable de-emphasis filter is simply the inverse of
the encoder
preemphasis filter. The filter coefficients are calculated in the same manner
for both the
encoder and decoder. Such circuitry is made complex because the feedback
(feedforward)
functions used to calculate the coefficients tend to exhibit a sharp bend,
thereby causing
the function to behave in a nonlinear fashion. Such non-linearity reduces the
precision of
interpolated coefficients. Therefore, there is a need for a circuit that
employs a nearly
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linear aspect of the BTSC feedback (feedforward) function to facilitate more
precise
interpolation of BTSC filter coefficients.
SUMMARY
In the following, where a component that has applicability in a compressor and
in
an expander is described, the compressor-related descriptor will be used
followed by the
expansion-related complementary descriptor in parenthesis.
One aspect is a method of calculating a variable spectral compression
(expansion)
filter coefficient in a BTSC compatible stereo encoder (decoder) from a
feedback
(feedforward) variable. A reciprocal value that is proportional to a
reciprocal of the
feedback (feedforward) variable is calculated. A lookup table is indexed using
a
preselected set of bits of the reciprocal value to generate at least one
parameter of the
filter coefficient function. An approximation of the compression filter
coefficient is
linearly interpolated based on the, at least, one parameter of the filter
coefficient function.
In another aspect, a method of calculating a variable spectral compression
(expansion) filter coefficient in a BTSC compatible stereo encoder (decoder)
from a
feedback (feedforward) variable. A reciprocal value that is proportional to a
reciprocal of
the feedback (feedforward) variable is calculated. A lookup table is indexed
using a
preselected set of high order bits of the reciprocal value. A first portion of
the lookup
table stores a plurality of discrete values at index points of a line segment
corresponding
to a filter coefficient function approximation. The first portion of the
lookup table
generates an initial discrete value corresponding to the filter coefficient
function at a
value of the high order bits. A second portion of the lookup table stores a
plurality of
slope values with each slope value indicating a slope of a line segment of the
filter
coefficient function. The second portion of the lookup table generates a slope
value of a
line segment corresponding to the filter coefficient function at the value of
the high order
bits. An approximation of the compression filter coefficient is linearly
interpolated based
on the slope value, the initial discrete value and a preselected set of low
order bits of the
reciprocal value.
In yet another aspect, an apparatus that includes circuitry that calculates a
variable
spectral compression (expansion) filter coefficient in a BTSC compatible
stereo encoder
(decoder) from a feedback (feedforward) variable. The apparatus includes a
reciprocal
value circuit that calculates a reciprocal value that is proportional to a
reciprocal value of
the feedback (feedforward) variable. The apparatus also includes a lookup
table that is
indexed by a preselected set of high order bits of the reciprocal value,
wherein a first
portion of the lookup table stores a plurality of discrete values at index
points of a line
segment corresponding to a filter coefficient function approximation, so as to
generate an
initial discrete value corresponding to the filter coefficient function at a
value of the high
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order bits, and wherein a second portion of the lookup table stores a
plurality of slope
values, each slope value indicating a slope of a line segment of the filter
coefficient
function, so as to generate a slope value of a line segment corresponding to
the filter
coefficient function at the value of the high order bits. A linear
interpolation circuit
interpolates an approximation of the compression filter coefficient based on
the slope
value, the initial discrete value and a preselected set of low order bits of
the reciprocal
value.
In yet another aspect, an apparatus is described for digitally implementing
the
entire expander portion of a BTSC decoder. This implementation includes the
variable
to spectral expander, two feedforward loops, a decimator and fixed deemphais
functions.
The apparatus utilizes digital models of the BTSC expander continuous time
transfer
functions. The circuitry also includes decimation and sampling circuitry that
allows the
implementation to utilize a variety or sampling rates.
These and other aspects of the invention will become apparent from the
following
description of the preferred embodiments taken in conjunction with the
following
drawings. Many variations and modifications of the invention may be effected
without
departing from the spirit and scope of the novel concepts of the disclosure.
BRIEF DESCRIPTION OF THE DRAWINGS
FIG. 1 is a schematic diagram of the compressor portion of a BTSC-compatible
encoder according to one embodiment of the invention.
FIG. 2 is a schematic diagram of a serial multiplier employed in the
embodiment
of FIG.1.
FIG. 3 is a schematic diagram of a digital phase locked loop employed in the
embodiment of FIG.1.
FIG. 4 is a schematic diagram of a positive square root finder employed in the
embodiment of FIG. 1.
FIG. 5 is a schematic diagram of a serial divider employed in the embodiment
of
FIG.1.
FIG. 6A is a schematic diagram of a circuit that generates filter
coefficients, in
accordance with one aspect of the invention.
FIG. 6B is a schematic diagram of an interpolation circuit.
FIG. 6C is a graph showing one implementation of linear interpolation.
FIG. 7 illustrates a block diagram of the expander portion of a BTSC-
compatible
encoder according to one embodiment of the invention.
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DETAILED DESCRIPTION
Referring to the drawings, like numbers indicate like parts throughout the
views.
As used herein, a digital BTSC-compatible stereo television difference signal
is one
component of a digital stereo audio signal that can be decoded (expanded) by a
decoder
that complies with the BTSC stereo television standard. The difference signal
begins
simply as the difference between the left and right audio signals of a stereo
audio source.
A BTSC stereo encoder then compresses it. The input to the expander section of
a BTSC
decoder is this compressed difference signal. The expander restores the
original
difference signal. One skilled in the art will appreciate that the decoder
typically
1o performs functions that are the inverse of corresponding functions at an
encoder. One
skilled in the art will also appreciate that the compressor and expander
functions of a
BTSC encoder and decoder are also applied to the Second Audio Program (SAP)
channel
in a BTSC audio system.
As shown in FIG. 1, the BTSC-compatible encoder is an application specific
integrated circuit 100 in which a low pass filter 110 receives a digital
representation 102
of an audio signal, having a sample rate of Fs. The audio signal could include
difference
left minus right components or it could include a SAP component, depending
upon the
specific application. The low pass filter 110 generates a corresponding second
digital
signal having a pseudo-interpolated sampling rate of 4Fs. A digital infinite
impulse
response pre-emphasis filter 112 generates a pre-emphasized output signal
corresponding
to the second digital signal, in accordance with the BTSC standard. A digital
signal
compressor 120 receives the pre-emphasized output signal and generates a
compressed
digital difference signal 104.
A digital phase locked loop 140 that is responsive to a video sync pulse 108
, having a sync pulse frequency (FH) generates a third digital signal 144
corresponding to a
sinusoid having a frequency equal to twice the sync pulse frequency and a
having a
sampling frequency equal to 4Fs. A first digital multiplier 142 multiplies the
compressed
digital signal 104 by the third digital signal 144 to generate a digital BTSC-
compatible
stereo television difference signal 106. Multiplier 142 facilitates amplitude
modulation of
carrier signal 144 with signal 104. One embodiment 340 of the digital phase
locked loop
140 is shown in FIG. 3.
Returning to FIG. 1, the digital signal compressor 120 includes a second
digital
multiplier 122 that multiplies the pre-emphasized output signal by a first
feedback signal
134, thereby generating a digital feedback-multiplied signal. (The multiplier
could be a
serial multiplier 222 of the type shown in FIG. 2.) An infinite impulse
response variable
coefficient compressor 124, that is responsive to the feedback-multiplied
signal and
responsive to a digital coefficient feedback signal 136, generates a digital
dynamic range-
limited signal corresponding to the feedback-multiplied signal limited to a
predetermined
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dynamic range. Essentially, the infinite impulse response variable coefficient
compressor
124 narrows the dynamic range of the feedback-multiplied signal. A saturation
logic
circuit 126 generates a digital amplitude-limited signal corresponding to the
digital
dynamic range-limited signal limited to a predetermined amplitude range. A
digital band-
limited infinite impulse response low pass filter 128, that is responsive to
the amplitude-
limited signal, generates a digital band-limited signal corresponding to the
amplitude-
limited signal that serves as the compressed digital difference signal 104. In
the disclosed
embodiment, the digital band-limited infinite impulse response low pass filter
128 cuts
off signals above 13 KHz, thereby eliminating certain harmonics. Although
various
1o cutoff frequencies may be chosen for a particular application, the cutoff
of 13 KHz was
chosen for a low cost subscriber implementation. A cutoff of 15 KHz could be
used for a
headend application or a higher fidelity subscriber application. The cutoff
frequency for a
SAP implementation would typically be 10 KHz.
A first feedback circuit 130, that is responsive to the band-limited signal,
includes
a root-mean-squared (RMS) level detector and generates the first feedback
signal
indicative of an amplitude of the band-limited signal (In one embodiment, the
RMS level
detector includes a positive square root finder 430, as shown in FIG. 4.) The
first
feedback circuit 130 also includes a band pass filter that passes signals in a
relatively
higher frequency range. In the disclosed embodiment, this filter passes
frequencies
around 11 KHz. A second feedback circuit 132, responsive to the band-limited
signal,
generates the coefficient feedback signal based on the band-limited signal.
The second
feedback circuit 132 also includes an RMS level detector and a band pass
filter that
passes lower frequencies. In the disclosed embodiment, this frequency range is
between
approximately 30 Hz and 3000 Hz. The second feed back circuit 132 also employs
a
divider 502 (as shown in FIG. 5) to generate a reciprocal signal value.
The digital coefficient feedback signal 136 may actually comprise several
variable
spectral compression filter coefficients. As shown in FIG. 6A, in one
illustrative
embodiment, a coefficient calculating circuit 630 calculates the filter
coefficients ao, al,
bo, and bl from a feedback variable that was output by the variable
coefficient
compressor 124, which in one embodiment is a first order Infinite Impulse
Response (IIR)
filter. Each filter coefficient al, bo, and bl is calculated by a different
approximating
circuit 640a (for al), 640b (for bo) and 640c (for bi). (In this embodiment,
the value for
ao is set at a constant value of "1.") While for this embodiment the IIR
requires four filter
coefficients, it will be understood that other IIR's could require a different
number of
filter coefficients.
The coefficient calculating circuit 630 includes a reciprocal value circuit
632 that
calculates a reciprocal value that is proportional to a reciprocal value of
the feedback
variable. A lookup table 644 is indexed by the high order bits of the
reciprocal value. A
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first portion of the lookup table 644 stores a plurality of discrete values at
index points of
a line segment corresponding to a filter coefficient function approximation.
The first
portion of the lookup table 644 generates an initial discrete value
corresponding to the
filter coefficient function at a value of the high order bits. A second
portion of the lookup
table 644 stores a plurality of slope values, wherein each slope value
indicates a slope of a
line segment of the filter coefficient function. The second portion of the
lookup table 644
generates a slope value of the line segment corresponding to the filter
coefficient function
at the value of the high order bits. It will be appreciated by those skilled
in the art that the
lookup table 644 could include several physically separate lookup tables with
each
1o indexed by the high order bits.
Because of the nature of the coefficient functions, the coefficient functions
of the
reciprocal of the feedback variable tend to behave more linearly than the
coefficient
functions of the non-reciprocal feedback variable. Therefore, using the
reciprocal of the
feedback variable to index the lookup table 642 allows for the use of linear
interpolation
to approximate the filter coefficients ao, al, bo, and bl.
A linear interpolation circuit 642 interpolates an approximation of the
compression filter coefficient based on the slope value, the initial discrete
value and a
preselected set of low order bits of the reciprocal value. In one embodiment,
as shown in
FIG. 6B, the interpolation circuit 642 includes a multiplier 650 that
multiplies the slope
value by the value of the low order bits of the reciprocal value to generate a
product
value. An adder 652 adds the initial discrete value from the lookup table 644
to the
product value, thereby generating an approximation of the compression filter
coefficient.
Returning to FIG. 6A, a feedback signal conditioning circuit 616 conditions
the
signal for use by the coefficient calculating circuit 630. The signal
conditioning circuit
616 includes a multiplier 618 that multiplies the encoded output of the low
pass filter 128
by a scaling constant c to generate a scaled version of the encoded output. A
band pass
filter 620 weighted to high frequencies generates a filtered signal from the
scaled signal.
A root-mean-squared 622 circuit generates a root-mean-squared version of the
output of
the conditioning circuit 616. The root-mean-squared version of the output of .
the
conditioning circuit 616 is then transmitted to the coefficient calculating
circuit 630.
One illustrative implementation of linear interpolation that may be used with
the
invention is shown in FIG. 6C. As shown in FIG. 6C, the coefficient function
670 may
be plotted on a graph 660 having a 1/b axis 662 and a filter coefficient axis
664. The
high order bits of 1/b are used to index the lookup table to retrieve two
parameters of a
line segment 672 that locally approximates the filter coefficient function
670. The
retrieved parameters include an initial value 678 of the line segment 672 and
the slope
676 of the line segment. The low order bits 680 of 1/b times the slope 676
give a filter
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coefficient axis 664 offset 682 from the initial value 678 to provide the
approximate value
674 of the filter coefficient.
The overall design strategy of the circuit disclosed includes: limiting output
bandwidth to 13KHz to simplify filter requirements; employing linear
interpolation to
two times the input sampling frequency before pre-emphasis; employing linear
interpolation to four times the input sampling frequency, Fs, before bandwidth-
limit filter;
allowing the bandwidth limit filter to remove residual images from the
interpolation;
using the digital phase locked loop 140 to create sinusoidal FH and 2 FH at a
sampling rate
of 4 Fs; and modulating the left and right components of the audio signal by 2
FH and
inserting the FH pilot digitally. All of this may be embodied on an
application specific
integrated circuit to reduce costs.
It will be appreciated that principles similar to those described above are
applicable to a decoder as well as an encoder, as low cost filter components
are beneficial
in a decoder as well as an encoder. United States Patent Number 6,259,482 to
Easley, et.
al. (`the `482 patent"), describes methods and system for digitally encoding
stereo audio into a BTSC signal.
Specifically, column 11 line 26 thru column 18 line 18 of the `482 patent
describe a way
to digitally implement the compressor portion of a BTSC encoder. Column 13
line 40
thru column 14 line 30, of the `482 patent, provides a description of an
alternative
technique for calculating the variable spectral compressor coefficients. This
technique
does not exploit the linear coefficient function obtained by taking the
reciprocal of the
feedback value. As described in U.S. Patent No. 7,397,850, a decoder used to
decode a BTSC signal to
produce an uncompressed stereo audio signal implements method steps that are
complimentary to
corresponding steps in a corresponding encoder.
Turning now to FIG. 7, a block diagram of the expander portion of a BTSC
decoder 702 is shown. A compressed L+R BTSC compatible signal 703 is subject
to
deemphasis at 705 so as to provide a deemphasized L+R BTSC compatible signal,
while
the compressed L-R BTSC compatible signal 704 is applied to an input of the
decoder
702. Signal 704 is the equivalent of signal 104 in FIG. 1. It will be
appreciated that
signal 704 is typically a demodulated signal. the demodulation operation
offsetting the
amplitude modulation performed by multiplier 142 of FIG. 1. In this way the
compressor and expander can be visualized as cascaded respectively with the
feedback
paths of the encoder and the feed-forward paths of the decoder processing the
same
signal. Part of the input signal 702 is routed to band limiting low pass
filter 706 so as to
limit the response of the feed forward loops to only those spectral components
that are
present in the compressed difference channel. The output of low pass filter
706 is
provided to spectral control band pass filter 708, which attenuates
frequencies that are
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not preemphasized, based on a predetermined preemphasis scheme. Spectral
control
band pass filter 708 is identical to that implemented in the encoder, or
compressor. The
output from spectral control band pass filter 708 is provided to RMS converter
710,
which generates the RMS value of the signal that passes through band pass
filter 708.
Thus, the output of RMS converter 710 is the RMS value of the portion of the
input
signal for which preemphasis was applied at an encoder, as described in the
'482 patent
at col. 16, line 23-col. 17, line 40. This preemphasis RMS value is used to
determine
spectral expansion coefficients at spectral expansion coefficient generator
712. These
coefficients, shown as al, bo and bi in the figure, are used to expand signal
704 so that its
spectral balance matches that of the signal before compression by an encoder.
It will be
appreciated that the transfer function of the spectral expander in the decoder
is the
reciprocal of the transfer function of the spectral compressor in the encoder;
the
computation of coefficients is similar. The expander numerator coefficients
are the
compressor denominator coefficients, and likewise, the expander denominator
coefficients are the compressor numerator coefficients.
Spectral expander 714 uses coefficients generated by coefficient generator 712
to
expand/decode the compressed signal 704. Each set of coefficients corresponds
to a
specific level of spectral expansion.
Following the application of the coefficients to the digital signal, the
conditioned
digital from expander 714 is combined with a signal proportional to the
reciprocal of the
bandlimited portion of signal 704. After signal 704 passes through bandlimiter
706, the
bandlimited signal is passed through bandpass filter 716. Then, RMS converter
718
generates the RMS value of the signal from bandpass filter 716 and passes said
RMS
signal to reciprocal calculation block 720. The output of the reciprocal
calculation block
720 is divided from the output of spectral expander 714 by divider 722. The
signal output
from divider 722 is then processed through decimator 724. A digital embodiment
of this
implementation for an encoder is described in column 15 line 1 through column
16 line
22 of the `482 patent. This present decoder embodiment is identical except for
the fact
that the decoder multiplies the signal by the reciprocal value. It will be
appreciated that
dividing the signal by the reciprocal of the feedforward value in the decoder
offsets the
effect of multiplying by the reciprocal of the feedback value in the encoder.
Decimator 724, which is calibrated to a predetermined sample rate, decimates
the
signal to a lower sample rate so that it can be output to an inexpensive audio
digital to
analog converter. While decimating, the decimator filter 724 also performs
fixed de-
emphasis to the signal. The fixed deemphasis transfer function is typically
the reciprocal
of the fixed preemphasis transfer function used in the decoder. A digital
implementation
of the fixed preemphasis filter is described in column 12 line 31 through
column 13 line 2
of the `482 patent.
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It will be appreciated that the decoder, or expander 702, can function at
sample
rates that may be integer multiples of the horizontal sync frequency, FH, or
at sample rates
that are not multiples thereof, as described in the `482 patent at col. 20,
line 41 - col. 22,
line 17.
In an alternative embodiment, the coefficients are retrieved from lookup table
726,
as discussed above.
The previous discussion has focused solely on the BTSC compressor and
expander portion of a BTSC encoder and decoder. The input to this
functionality is the
difference (left minus right, or L-R) or SAP signals. In order to fully
recover the left and
1o right audio channels at the output of the decoder, a sum (left plus right,
or L+R) channel
must be processed and transmitted. The processing on this channel is a simple
fixed
preemphasis filter in the encoder and a reciprocal fixed deemphasis filter in
the decoder.
A digital implementation of sum channel processing is given in column 17, line
42
through column 18, line 18 of the `482 patent.
The above-described embodiments are given as illustrative examples only. It
will
be readily appreciated that many deviations may be made from the specific
embodiments
disclosed in this specification without departing from the invention.
Accordingly, the
scope of the invention is to be determined by the claims below rather than
being limited
to the specifically described embodiments above.
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