Note : Les descriptions sont présentées dans la langue officielle dans laquelle elles ont été soumises.
lO~i833
This is a division of Canadian patent application
Serial No. 283,026, which was filed on l9 July 1977.
Back~round of the Invention
This invention relates to the elimination of echoes in
communication signal paths and, more particularly, to
effective cancellation of echoes by use of an accurate and
highly efficient model of the echo path transfer function.
Since echoes in telephone circuits have a disturbing
influence on conversation, a number of techniques have
been devised to mitigate their effect. Echo suppression
was the first technique to be contrived. Typically, echo
- suppression involves some form of selective attenuation
automatically operated in response to voice levels in the
transmission paths so that the echo that would otherwise
be returned to the talker is suppressed. Such
arrangements are generally satisfactory for terrestrial
communication paths in which the echo delay or the round- -
trip propagation time between the source of the signal and
the return of the echo is not long.
In communication paths via satellite links, the
transmission delays are much longer and the echo is more
- disturbing and disrupts conversation. Echo suppression
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~echniques basically interrupt the return signal path and
have a tendency to mutilate speech by chopping the return
signal during intervals wherein both parties are talking;
i.e., double talking. This degradation of quality of the
communication is subjectively more severe when the signals
experience long propagation delays in
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transmission between the parties. Thus, echo suppressors
will probably introduce their own signal degradation in
the process of eliminating echoes.
Another more sophisticated approach utilizes
echo cancellation wherein a replica of the echo is automatically
constructed or adaptively synthesized from the original
signal and subtracted from the return signal to eliminate
the echo. Most conventional echo cancellers synthesize the
replica using a tapped delay line with adjustable multipliers
in an adaptive feedforward arrangement also called a transversal
filter. The multipliers are automatically adjusted by a
- control signal derived from the difference between the echo
and the replica. Since the impulse response of an echo
path may be rather long, accurate synthesis of the replica
by transversal filters to effect echo cancellation may require
many taps and associated multipliers, an arrangement which is
, complex and costly. In fact, echo cancellers have not been
generally utilized to any great extent because of their high
cost.
Feedback or recursive arrangements which have an
inherently long impulse response appear to be able to
synthesize the`replica accurately. Since resursive arrangements
are simpler, their use would seem to provide a reduction in
complexity and a corresponding lower cost in achieving
echo canceilation. However, an inherent difficulty with the
recursive arrangement is that its operation cannot be readily
` ~ adapted by automatic control in order to minimize the
. mean-squared residual echo. In a practical application,
the recursive circuit will not likely converge to the operating
point that will provide
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the most effective echo cancellation because characteris-
tically there are several sub-optimum multiplier tap
settings to which the adaptation algorithm can converge
rather than an optimum unique minimum as is the case for
the conventional feedforward echo canceller.
S~mmarY of the Invention
In accordance ~ith an aspect of the invention there is
provided in an echo canceller of the type having a trans-
versal filter means for synthesizing from an input signal
on a receiving signal path a replica to approximate an
echo signal on a sending signal path for subtraction from
the echo signal, means for subtracting the replica from
the echo signal to produce a residual echo, said trans-
versal filter means responsive to the residual echo for
changing the replica to reduce the residual echo, said
canceller further comprising first adaptive signal process-
; ing means responsive to the residual echo for modifying
the echo signal on said sending signal path before the
subtraction, and second adaptive signal processing means
coupled to receive the replica and responsive to saidfirst adaptive processing means, said second adaptive
processing means selectively altering the replica to make
an altered replica suitable for subtraction directly from
the echo signal, and subtracting means for combining the
altered replica and the echo signal on said sending path
to provide a clear sending signal essentially free of the
echo signal.
A primary object of this invention is to provide a
recursive-like arrangement for providing a greater degree
of echo cancellation than conventional echo cancellers of
equivalent circuit complexity.
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A related object of the invention is to provide a
readily adaptive structure having a unique minimum in its
operating characteristic and capable of modeling the
transfer function of an echo return path by a rational
expression possessing both poles and zeros.
The invention in its various aspects overcomes the
limitations of the prior-art echo cancellers. Broadly,
the invention includes an adaptive control loop comprising
two adaptive transversal filters arranged to have
recursive-like modeling capability, but readily adaptable
and stable, and a recursive filter completely adapted in
accordance with a selected one of the transversal filters.
, The recursive filter is instrumental in providing a clear
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signal path essentially free of echo signals. This
arrangement provides more efficient echo cancellation by
achieving a higher level of echo cancellation than ls
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provided by conventional transversal filter echo
cancellers of equivalent overall circuit complexity.
, In its broader aspects, the invention takes the form
of an adaptive echo canceller connected to sending and
receiving signal paths wherein the sending signal
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path is subjected to an echo signal. The canceller is of the
type having a transversal filter for synthesizing, from an
input signal on the receiving signal path, a replica to
appro~.imate an echo signal for subtraction. In the canceller,
an adaptive control loop minimizes the mean, or average,
square value of the residual echo resulting from the
subtraction and includes a first adaptive signal processing '
circuit or network for producing a modification of the echo signal
on the sending signal path. The canceller has a second
adaptive signal processing circuit or network responsive
to the first adaptive signal processing circuit, but removed
from the control loop and coupled to the sending signal path.
The first adaptive signal processing circuit compensates
for the effect of transmission poles in the echo signal
path and greatly simplifies the complexity of the ~ransversal
filter in the control loop, The second adaptive signal
processing circuit performs an operation inverse to that of
the first circuit and serves to provide a clear sending
- signal path essentially free of echo.
In some of the more specific aspects of the invention,
the second signal processing circuit may be used to complete
: the synthesis of the replica of the transversal filter or
directly in the sending signal path to compensate for the
signal processing of the first circuit. The first adaptive
signal processing circuit takes the form of a feedforward
circuit which serves to alter the transfer function of the
path of the echo signal so that the synthesis of the transversal
; filter in providing a replica of the echo signal models
the combined transfer function of the first adaptive signal
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processing circuit and that of the echo signal path. The
first adaptive signal processing circuit includes a delay
line having a plurality of taps and combines a weighting
of the signals at the taps to provide the modification of
the echo signal. The second adaptive signal processing
circuit takes the form of a feedback circuit wi~h a delay
line including a plurality of taps and provides a weighting
function having the same magnitude but opposite signs to
the weighting of the first adaptive signal processing
circuit.
Brief Description of the Drawinq
The present invention, taken in conjunction with the
,i invention described in Canadian patent application Serial
'f No. 283,026, filed 19 July 1977, will be described in
detail hereinbelow with the aid of the accompanying
drawing~, in which:
F~G. 1 is a diagram of apparatus arranged in
, accordance with the invention.
FIG. 2 is a detailed diagram of one of the transversal
filters generally shown in the arrangement of FIG. 1.
FIG. 3 is a detailed diagram of another of the
transversal filters employed in the arrangement of FIG. 1.
FIG. 4 is a detailed diagram of the recursive filter
utilized in the arrangement of FIG. 1.
FIG. 5 is a diagram of an alternate arrangement in
accordance with the invention which appears on the same
sheet as FIG. 1.
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Detailed Description
In FIG. 1, if we can for the moment ignore the
apparatus enclosed by dashed-line box 100, a single trans-
mission terminal is basically illustrated for interconnecting
a single two-way circuit 111 with two one-way circuits 112
and 113 by way of hybrid network 114. Hybrid network 114
may generally include a balancing network (not shown) for
impedance matching purposes. In telephone terminology, two-
way circuit 111 is referred to as a two-wire circuit and one-way
circuits 112 and 113 form a so-called four-wire circuit.
The former is usually used for local circuits, for example,
telephone subscriber loops, while the latter is typically used
in toll circuits for distant transmission and may take the form
of a carrier transmission system.
Ideally, all signals orginating on circuit 112 are only
passed on to circuit 111 and incoming signals from the latter
are passed on to one-way return circuit 113 by hybrid
114 However, since impedance mismatches cannot be
prevented in the actual transmission circuits connected to
hybrid 114, a portion of the signal energy
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in circuit 112 appears on circuit 116 and, in the absense
of some form of echo suppr~ssion or cancellation, is returned -
on circuit 113. Due to the transmission delays encountered ;
as the signal propagate over circuits 112, 113 and 116 in FIG.
1, th~ return signal is preceived as an echo. The complete
echo return signal path includes circuit 112, the leakage
signal path that traverses hybrid 114, and circuit 116.
Accordingly, echo cancelling apparatus 100, which will be
discussed hereinafter~ is employed to eliminate the return
signal without any preceptible interrruption in the return
signal path between circuit 116 and 113. Circuits 112 and 116 -
may be, in actuality, carrier systems in which case apparatus
100 will probably be geographically removed from hybrid
114. Furthermore, another echo canceller, most likely identical
to apparatus 100, is typically used at the other end oP
tran~misBion circuit 112 and 113 (not shown in FIG. 1) to
provide echo cancellation for signals originating on circuit
x 113 which are partially returned on circuit 112 as an écho.
The echo cancelling apparatus of FIG. 1 is
shown in digital form. Accordingly, analog-to-digital
converters 117 and 118 and digital-to-analog converter 119
are utilized to~perform the appropriate signal conversions
between the analog and digital apparatus of FIG. 1. At
this point, it is again stressed that the transmission
apparatus in FIG. 1 may take on a number of different
forms. For instance, if the signals on circuit ll2 and
113 are digital signals, the type of converters shown in
FIG. 1 may not be required. In this case, conversions
between digital-to-analog and vice versa would become an
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Gitlin-Thompson 3-4
1 integral part of circuits 112 and 116 and terminate the two
2 one-way signal paths to provide an analog signal interface
3 for hybrid 114. The echo cancelling apparatus may even be
4 designed to work directly from these digital signals.
However, it should be pointed out that the echo cancelling
6 apparatus may also be readily implemented using analog
7 circuitry if desired by those skilled in the art. In
8 this latter situation, no signal conversions would
9 be necessary if the actual transmission signals on
circuits 112 and 113 are also analog.
11 The echo cancelling apparatus of FIG. 1 includes -
12 transversal filter circuits 200 and 300 which are
13 supplied digital signals by converters 117 and 118. The
14 outputs of c,rcuits 200 and 300 are applied to signal
lS comblner 121 to produce a d1fference signal which is fed
16 b~ck to c~rcuits Z00 and 300 via switch 122and amplifiers
17 123 and 124. Since the character of the echo signal is
18 altered by changes in the local two-wire circuit 111, such
19 as ~nnection or disconnection of an extension formed
during a conversat~on, or transfer of calls via telephone
21 sets with multiple lines or PBX's, it is necessary to adjust
22 or adapt circuits 200 and 300 in accordance with each
23 change. Of course, any changes directly in circuits 112
24 and 116 are in the echo return path and will necessitate
a responsive adaptation thereto. This adjustment is done
26 upon closure of switch 122. Even in situations involving
27 no change in circuit 111, but rather a change in the
28 character of the signal transmitted over circuit 112,
29 adjustment of circuits 200 and 300 is necessary to provide
effective echo cancellation. Since automatic adjustment
31 is performed using the signals actually transmitted, the
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apparatus automatically and conveniently provides this
feature.
The primary return signal path from circuit 116
to circuit 113 includes converter 118, circuit 300, signal
combiner 121, recursive circuit 400, switch 126, and
finally, converter 119. This signal path is also
considered to clear or transparent signal path which
will be appreciated from the discussion to follow. Circuits
200, 300 and 400 wi~l be considered in detail later, but
for present purposes it is sufficient to state that transversal
filter circuits 200 and 300 are in the form of tapped delay line
structures including adjustable gain coefficients or weighting
at the taps so that they can be adjusted to effect echo
cancellation. Circuit 400 also has a tapped delay line with
associatea adjustable taps but in a feedback or recursive
circult rather than a feedforward transversal circuit.
The arrangement of FIG, 1 is split since circuit
200 shunts hybrid 114 and circuit 300 is serially disposed
in the return transmission path of hybrid 114. The split
arrangement provides recursive-like echo cancellatlon
because it includes nonrecursive filters able to emulate
the characteristic of a recursive filter exhibiting both
poles and zeros. The poles and zeros exhibited by the
filter are used to cancel out and eliminate the effect
of the transmission poles and zeros in the echo path.
In the process of adapting circuits 200 and 300, the
former synthesizes a partial replica of the echo signal
while the latter modifies the echo return signal on
circuit 116. Combiner 121 subtracts the two signals from,
each other and provides a control signal output to whlch
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circuits 200 and 300 respond. A minimum absolute value
of the control signal indicates optimum automatic adjustment
of circuits 200 and 300. In other words, circuit 200 is adapted
to model the combined transfer function of the echo return
signal trave~ling through circuit 112, the leakage path
transversing hybrid 114, circuit 116 including converter
118, and the signal path through circuit 300. From another
perspective, circuits 200 and 300 in this configuration
cooperate to form a~model of the frequency transfer function
of the echo path, which is a rational mathematic expression or
fraction wherein the numerator and denominator are poly-
nominals in the frequency variable. In the echo path
transmission, transmission zeros are the roots of the
numerator polynomtnal and transmission poles are the roots
of the denominator polynominal. As circuit 200 eliminates
the effect of thé tra~smission zero~ in the echo path
upon the output of combiner 121, circuit 300 eliminates
the effect of the transmission poles in the same path upon
the same output. A time domain interpretation of the
modeling process to effect echo cancellation is that circuit
300 time-compresses the overall impulse response of the echo
signal path int~ the span or interval of the delay line
internal to circuit 2~0. Accordingly, circuit 200 is
considerably less complex than if it were used without the
cooperation of circuit 300.
Although the circuit operation described thus far
; - is capable of providing echo cancellation, it does not provide
a clear signal path from circuit 116 to circuit 113. This
is primarily due to the operation of circuit 300 which modifies
the echo return signal in the
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process of effecting echo cancellation. Accordingly,
the output of combiner 121 is applied to the slaved
circuit 400, which is a recursive circuit that has the
reciprocal transfer function of circuit 300. Therefore,
any linear signal distortion introduced by circuit 300
is compensated by circuit 400 since it provides the inverse
signal operation of circuit 300. The output of circuit 400
is normally applied by switch 126 to converter 119. This
completes the clear~signal path so that signals present
on two-way circuit 111 pass through the echo cancellation
apparatus of FIG. 1 unimpaired onto circuit 113.
Signals originating from two-way circuit 111
will also affect the operation of the echo cancelling
apparatus, but this effect is deleterious. Accordingly,
inhibit detector 127 is connected to analog circuits 112
and 116 to detect signals orlglnating from clrcuit 111
in the presense or absence of signals from circuit 112.
If the operation of the echo cancelling apparatus were
allowed to proceed in the presence of signals from
circuit 111, the signals on circuit 116 produced by
original signals on clrcuit 111 would tend to cause a
devergence rather than a convergence to a point for effecting
echo cancellation. Inhibit detector 127 thus opens
switch 122 so that the control loop is opened and convergence
is prevented when signals on circuit 116 are produced by
, signals emanating from circuit 111. It should be pointed
~ out that switch 126 is also controlled by inhibit detector 127.
, The main purpose of switch 126 is optional in that slightly
better echo cancellation is achieved by returning the output
of combiner 121 directly
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to circuit 113 via converter 119. Of course, it is to
be understood that this latter signal path cannot be used
during periods of double-talking or when signals are
originating on two-way circuit 111. At these times the
clear signal path should be utilized to provide an undistorted
transmission signal on circuit 113.
FIGS. 2 and 3 are diagrams of adaptive transversal
filters serving as adjustable signal processing networks in
FIG. 1. Both circuits are shown implemented in digital
form with tapped delay lines. These basic circuit configurations
and the components therein are generally well known in the
art and FIG. 2, per se, does not constitute any part of
this invention. In FIG. 2, delay elements 201-1 through
201-N com~rise a tapped delay line. Each element of the
tapped delay line imparts a delay of T seconds e~ual to the
interval between dlgital words produced by converter 117
of FIG. 1. When a glven digital word is present on the input
of each delay unit, the immediately preceding digital word
is at its output; thus successive words are available
from the outputs of successive delay units or taps of the
tapped delay line. Individual digital words produced at the
taps of the delày line are adjusted in gain by means of
multiplier networks 202-0 through 202-N through which they
are directed, and are combined in summing network 220.
Network 220 producesthe output of the circuit.
Each of the multiplier networks 202 comprises
digital multipliers 203 and 204 which produce a changeable
amount of gain (including gain less than, or greater than,
unity which may be either positive or negative) between
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its two inputs and its output. The gain coefficient of
each of multipliers 203 is set in accordance with the
encoded polarity and magnitude provided by its respective
delay unit 205 and associated adder 206, which form an
accumulator The adaptive control signal of FIG. 1
from amplifier 123 is applied to each of multipliers 204.
This arrangment provides incremental changes in the gain
coefficients of multipliers 203. While switch 126 is
closed, multiplier networks 202-0 through 202-N in the
-- 10 adaptive control loop simultaneously converge to a point
of maximum effective echo cancellation, i.e., minimum
. mean-square residual echo, in accordance with the output
of combiner 121 of FIG. 1. During intervals when switch
126 is open, the accumulators of elements 205 and 206
store the previou~ gain coefficient settings enabling
circuit 200 to maintain its unction.
The circuit of FIG. 3 is primarily the same as
' the circuit of FIG. 2 so that detailed discussion of each
element therein is not warranted. Reference numerals in
FIG. 3 of elements identical to that of FIG. 2 are
increased by a hundred. FIG. 3 has additional outputs for
-~ each of the gain coefficients of multiplier networks 302-1
thrQugh 302-L which are appplied in FIG. 1 to the recursive
filter circuit 400. Another difference is that the
coefficient of bo is forced to unity, thereby eliminating
the requirement of multiplier network 302-0 (not shown
in FIG. 3). This prevents the arrar.gement of FIG. 1 from
converging to an operating point wherein all the gain
coefficients of the multipliers in circuits 200 and 300
are zero.
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In FIG. 4, the nucleus of the circuit is a
duplication of the circuit of FIG. 3 and its peripheral
portion is arranged in a feedback or recursive circuit
with signal combiner 410. The external input signal to
comblner 410 ls supplied by combiner 121 of FIG. 1.
Signal combiner 420 supplies the internal input or feedback
input to combiner 410. The output of combiner 410 is applied
to a tap delay line comprised of elements 401-l through 401-L.
Each of delay elements 401 provides an output or a tap in
the delay line for a different one of multipliers 403,
whose outputs are delivered to combiner 420. The gain coefficient
outputs of circuit 300 of FIG. 3, labeled bl, b2 through bL, ,'
have their encoded signs inverted by digital sign inverters ''
415 before application to each one of multipliers 403. In
other words, the magnltude of the respective gain
coefficients of the multipliers in FIGS. 3 and 4 is the
same, but the signs are opposite. If one disregards
for the moment the sign change and the recur,sive connection,
the direct slaving interconnection between the circuits of
FIGS. 3 and 4 in FIG. l allows a single multiplier in the
latter to duplicate the same operation as a multiplier
network in the former. However, the overall operation of
the circuit of FIG. 4 is the inverse of the operation of
the circuit of FIG. 3 in providing a modified echo return
signal. Since circuits 300 and 400 are serially disposed
in the same signal path and perform inverse signal operations
on the same signal, they provide a clear signal path essentially
free of the linear distortion produced by circuit 300. The
previously mentioned selection of the bo coefficient as unity in
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Gitlin-Thompson 3-4
l circuit 300 is compensated by circuit 400 without utilizing
2 a mult~plier on the output of the latter. The clear
3 s~gnal output is provided by combiner 410. An important
4 dlstinction between circuits 300 and 400 is that w~hile the
former is in the control loop, the latter is outside of it.
6 Thus, the aforement~oned adaptability problem of utilizing
7 a recursive filter in an adaptive echo cancelling
8 arrangement is avoided as the recursive filter is slaved
9 to the operation of the control loop.
1~ 1
12 FIG. 5 is an alternative arrangement ~ FIG. l wh~-rein
13 the echo cancelling apparatus 500 provides a more direct
14 clear signal path than FIG. l. Reference numerals of
elements in FIG. 5 with the same last two digits as
16 those ~n FIG, l are identical in structure and fùnction in
17 both ~igures. The adjustab1e signal processing networks
18 200, 300 and 400 represent those re;pectively shown in FIGS.
l9 2, 3 and 4. The configuration and operation of the
control loop of FIG. 5 which includes elements 200, 300, 52l-
21 524 iS identical to that of FIG. l and further explanation
22 of its operation is not warranted.
23 The essential difference is that recursive fi~ter circuit
24 400 which is controlled by transversal filter 300 is used to
complete the synthesis of the replica of the echo signal
26 rather than as, in FIG. l, a means of compensating for
27 circuit 300. Accordingly, the signal input to circuit
28 400 is the partial replica produced by 200. When the control
29 loop of FIG. 5 converges, circuit 400 modifies the p~tial
replica to provide a complete and highly accurate
3l replica for signal combiner 525. ~he other input
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to combiner 525 is the output of converter 518, which is
the signal path containing the echo signal. The output of
combiner 525 is applied to switch 526. This output, of course,
ls essentially free of residual echo when the control loop
of FIG. 5 converges. Switch 526 selects the input for
converter 519. The optional nature of switch 126 in FIG.
1 also pertains to switch 526. Converter 519 provides the
analog return signal for circuit 513.
The advantage of this arrangement is that the
replica is synthesized by the combined processing of circuits
200 and 400 to provide a recursive structure able to compensate
for both transmission poles and zeros in the echo return path.
~; As in FIG. 1, the operation of circuit 400 is slaved to circuit
; 300 although it is removed from the control loop of FIG. 5
to accrue the same advantages as that of FIG. 1. The
synthe~ized repllca is then directly combined with the echo
return signal to effect echo cancellation. Since circuit
400 performs a signal processing function rather than a
compensating function as in FIG. 1, the circuit of FIG. 5
is less susceptible to the relative inaccuracies between
circuits 300 and 400 and at~endant tracking error which
may result in less than total compensation in providing
the clear signal path of FIG. 1.
In the foregoing discussion, design details have
purposely not been specified because the adaptive algorithm
controlling the operation of the control loop of FIGS. 1
and 5 is not peculiar in any respect, an is subject to
, the same design considerations as similar adaptive
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minimum mean-square control loops which are well known
in the art. This operational characteristic is, indeed, an
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advantageous feature since either of the arrangements in
FIGS. 1 and 5 is able to provide recursive-like echo
cancellation and attendant hardware simplification. In
various simulations which duplicate a variety of trans-
mission environments, eight taps and associated multiplier
networks for adjustable weightings in circuit 300, which
are partially duplicated in circuit 400, and thirty-two
adiustable tap weights in circuit 200 provided superior
echo cancellation for each simulation over conventional
transversal filter echo cancellers of equivalent overall
circuit complexity.
- For a general discussion of the effect of the gain
factor in the control loop (i.e., al and a2 of respective
amplifiers 123 and 124 in FIG. 1 and equivalent of FIG. 5)
on rate of convergence of the loop, ~ee an article entitled
"An Adaptive Echo Canceller" by M.M. Sondhi, in the
Bell System Technical Journal, Vol. 46, No. 3, March 1967,
pp. 497-511. Intermediate values are typically chosen for
al and a2 since small values slow down the convergence to
effect echo cancellation while large values converge fast
~ but limit the accuracy of the convergence. Although
; FIGS. 1 and 5 imply that the value of al is different from
a2, the values are not critical and they may be the same.
This would, of course, eliminate the use of one of loop
gain amplifiers 123 and 124 in FIG. 1. A more detailed
description of control loops, and particularly the
estimated-gradient algorithm inherent to the operation of
multiplier networks 202 and 203 of FIGS. 2 and 3 as
utilized in the control loops of FIGS. 1 and 5 is presented
in "On the Design of Gradient Algorithms for Digitally
- Implemented Adaptiv~ Filters" by R.D. Gitlin, J.E. Mazo
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and M.G. Taylor, in the IEEE Trans. on Circuit Theory, Vol. CT-20,
No. 2r March 1973, at pp. 125-136. Notwithstanding that
the specific application of the foregoing paper is adaptive
digital equalizers, the type of circuitry employed and various
considerations are readily applicable to the control loops
of adaptive digital echo cancellers.
Although the apparatus for effecting echo cancellation
has been illustrated by means of digital apparatus, it will
be evident to those skilled in the art that equivalent
analog circuit techniques may also be employed to advantage.
Even in digital apparatus, the arithmetic functions in the
signal processing networks may be time-shared to provide
a further reduction in implementing apparatus, thereby
~ er~ploiting the high speed capability of digital apparatus
- such as, or example, digital multipliers. In other words,
time-divlsion multiplexing will achieve further circuit
economies, particularly in view of the relatively slow word
rate required for encoded speech. One or more of these
illustrated echo cancellers may also be time-division multi-
;. 20 plexed to serve a plurality of transmission channels
providing system economies. Furthermore, it is to be
understood that the arrangements described in the foregoing
are merel~ an illustrative application of the principles
` of the present invention. Numerous and varied other
arrangements may be utilized by those skilled in the art
without departing from the spirit and scope of the invention.
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