A New Active Matrix Decoder for Surround Sound

Kenneth GundryDolby Laboratories Inc.

San Francisco, California 94103, U.S.A.

The decoder employs control signals derived from the signal outputs rather than the inputs, that is, using feedback analogous to an output-controlled limiter. This leads to tighter tolerances, excellent crosstalk figures and improved dynamics. It gives good performance on matrix-encoded sources but also very pleasing results on un-encoded two-channel material. The paper discusses the principles and their benefits.

BACKGROUNDMatrix decoders receiving two channels and delivering feeds forthree, four or more loudspeakers have been known for more than25 years. Early active decoders, for instance for CBS SQ (1) andSansui QS (2), were not successful for both technical andmarketing reasons; they did not work very well, in the author'sview partly because they were too ambitious. The development ofstereo optical soundtracks on 35 mm film, and of a "diamond"matrix with a very definite priority to front performance (left,center, right, surround) instead of a "square" matrix (left front,right front, left back, right back), led to active circuits thatperformed much better. They became very popular in the cinemaand later appeared on the home market under the name Dolby ProLogic (3).

However, such decoders were designed for and are most successfulin processing signals that have been deliberately encoded forsurround reproduction. The preparation of surround-encodedmaterial generally involves monitoring the result via a decoderequivalent to that which will be used in the eventual reproduction.Thus, most movies are mixed while listening via a Pro Logicdecoder, the design most commonly employed in cinemas and inhome theatre systems. This ensures that the result will be similarto that intended by the sound mixer.

With increasing interest in multichannel sound, but an obviousdearth of 5.1 channel recordings, a device capable of givingpleasing surround sound from existing two-channel material wouldbe very attractive. In recent years, several such devices have beendeveloped to improve the subjective impression of un-encodedmusic recordings by spreading the sound around the room.Unfortunately, many of these have led to undesired anomalouseffects, whereby instruments wander in position or level, and inaddition, most of these simulators do not perform satisfactorily onsurround-encoded material.

Jim Fosgate has been prominent among workers in the field ofactive matrix decoders. Some years ago it occurred to him that itwas more logical to derive the control signals from the outputs,that is, to employ negative feedback. The result of this work is ProLogic II, developed by Fosgate and brought to market by DolbyLaboratories. The new system gives good performance on matrix-encoded sources but also very pleasing results on two-channelmusic recordings that have not been matrix-encoded.

ACTIVE MATRIX SYSTEMSThe systems under discussion receive a pair of inputs,conventionally known as left total and right total (Lt, Rt), whichare subjected to a variable matrix and deliver a number of outputsto be fed to loudspeakers around the listening position. Previousactive systems, including Pro Logic, Fosgate's own previous work(4), Logic 7 (5) and Circle Surround (6), analyze Lt and Rt forrelative magnitude and phase, generating control signals withessentially only two degrees of freedom, left/right and front/back,and then use those control signals to vary the decoding matrix.With appropriate attention to keeping the apparent loudness ofsources approximately constant as the matrix coefficients changeand to appropriate dynamic behavior, such an approach can work

satisfactorily (but not all pay the required attention to thosematters).

The new system departs from previous methods in developing itscontrol signals from signal outputs rather than inputs, that is, inusing feedback in a manner analogous to an output-controlledcompressor. This leads to tighter tolerances, excellent crosstalkfigures and improved dynamic performance.

FRAME OF REFERENCE FOR ANALYSISFor the purposes of explanation, it is convenient to express Lt andRt in terms of the intended direction of a source, independent ofthe magnitude. This approach has been taken by many in the field,and avoids the need to consider how the signals were actuallyderived. Since absolute magnitude is not relevant to direction, forthe rest of this analysis the inputs to the decoder will be taken to benormalized to unity power; thus by definition, Lt2 + Rt2 = 1

The encoding can then be generalized by considering a directionparameter, α degrees, which has the value 0 for surround (rear), 90for left, 180 for center front and 270 for right, and by expressing Ltand Rt as functions of α. By inspection, we can see that therequired functions are

��

���

� −α=α290cos)(Lt and ( ) �

�

���

� −α=α2

90sinRt

Note that the 90 degrees in these expressions arises solely from thechoice of 0 at the rear (other workers have chosen other referencedirections), and that only the relative polarity is significant. If Ltand Rt were generated by a panpot that could be steered around thefull circle, these would be the relative magnitudes and polarities.For instance, when α = 90 (left), Lt = 1 and Rt = 0, when α = 180

(center), Lt = Rt =21

, and so on.

Figure 1 shows the variation of Lt and Rt as the direction α ispanned around the whole circle.

1

0 90 180 270 3601

0Lt α( )

Rt α( )

α

Figure 1. Relative amplitudes and polarities of Lt and Rt as functions of direction angle α.

GUNDRY ACTIVE MATRIX DECODER

AES 19TH INTERNATIONAL CONFERENCE

It should be noted that for α in the range 90 to 270 degrees, that is,for the front half of the circle, Lt and Rt have the same polarity.Outside that range, in the rear half, they have the opposite polarity.For reproducing matrixed surround sound, for instance via a ProLogic decoder, the loudspeakers usually have positions as shownin figure 2. The left and right front loudspeakers are 30 or 40degrees either side of the center front, and the two "surround"loudspeakers are to the side and somewhat behind the listener andreceive identical signals. The actual angle of the loudspeakerswith respect to the listener can then be considered as atransformation or systematic distortion of the directional parameterα, as illustrated in the figure. For the remainder of this paper, itwill be understood that in actual reproduction, the directional angleα will be so transformed.

In the following, the term principal direction refers to a directionwhere an output of an active matrix rises to a maximum. Hencefor a four-output matrix, the principal directions are 0, 90, 180 and270 degrees.

Figure 2. Plan view of conventional positions ofloudspeakers and relationship with angle α

DESIRED RESULT FOR A FOUR-OUTPUT ACTIVEMATRIXConsider an active matrix with four outputs, left center right andsurround (L C R S).

The center output should be zero when the source direction lies inthe rear half of the circle. In the front half, we would like thecenter output to rise from zero at 90 degrees to a maximum at 180and then to fall back to zero at 270.

Similar variations should apply to the other three outputs.Considering any one of the outputs, there should be no signal whenα is more than 90 degrees away (considering the circle ascontinuous so that 0 and 360 are equivalent), and the signal levelshould rise from zero to a maximum and fall back to zero as αvaries from –90 to +90 with respect to that output's direction.

In other words, for an output corresponding to a principaldirection, the output level should be zero at and beyond theadjacent principal directions, and should change smoothly withinthe arc bounded by those adjacent directions.

This is of course no more than a spelling out of what is generallycalled pair-wise pan-potting. A source from any arbitrary directionshould be delivered only by the two (or one) loudspeakers closestto that direction.

SERVOSFigure 3 shows a simple block diagram. The two input signals LtRt pass via voltage-controlled amplifiers (VCAs) with gains hl andhr, and are summed and differenced to deliver two outputs, labeledC and S. These will become the center front and surround outputs.In accordance with this diagram:

C = hl.Lt + hr.Rt and S = hl.Lt – hr.Rt

All the terms are of course functions of α, and thus it might seemobvious to generate control signals directly from Lt and Rt to varygains hl and hr . Previous active matrices have universally derivedtheir control from the inputs. However, there is another way ofconsidering the matter.

For dirsame pcome fequal, sourcespolaritithis tim

The twmagnitby an outputstoward

Now ccenter fthe maservo calso zealso, so

For a c

magnitequal, bvalue.

conditi

value u

deliver

left andexpect.

In pracmaximafter. smallerto be eq

0

90

180

270

hl hl.Lt

+ +

Lt

C S

2

ections in the front half of the circle, Lt and Rt have theolarities, and S should be zero. Thus for signals intended torom somewhere in the front half, hl.Lt and hr.Rt must beso that the subtraction can yield no output. Similarly for in the rear half of the circle, Lt and Rt have oppositees and C should be zero, leading to a similar requirement,e that hl.Lt and minus hr.Rt must be equal.

o requirements become the same if we say that theudes of hl.Lt and hr.Rt must be equal. This can be achievedactive servo that measures the magnitudes of the VCA and drives the VCA gains to urge those magnitudess equality.

onsider what happens within the half-circle containingront. For a left only source, α = 90, Lt =1 and Rt = 0. Thusgnitude of hr.Rt is inherently zero and the only way thean force equal magnitudes is to make hl zero, so that hl.Lt isro. If hl.Lt and hr.Rt are both zero, clearly their sum is zero there is no output from C, as desired.

enter front source, α = 180, Lt = Rt =21

. For the equal

ude requirement, the servo must force gains hl and hr to beut the absolute value is undefined. Here we must impose a

Suppose that the circuit is designed so that under this

on the VCAs adopt gains of21

(and can never exceed that

nder any other conditions). In that case, for center front, C

s21

(Lt + Rt), a finite signal consisting of the sum of the

right total signals with equal weights, just as we might

tice, it is more convenient to consider the VCAs as havingum gains of unity, and to introduce any scaling before orIn its basic form, the servo then leaves unchanged the of its inputs, but attenuates the larger to force its magnitudeual to that of the smaller.

hrhr.Rt

+ –

Rt

Figure 3. Lt Rt via VCAs andthen summed and differenced

to give C and S.

GUNDRY ACTIVE MATRIX DECODER

AES 19TH INTERNATIONAL CONFERENCE

Figure 4 shows the resultant C and S output levels (scaled by 21

)

as functions of α. There is no output in the opposite half-circle,and a smooth rise towards and fall from the maximum at thedesired direction.

Now consider a second identical servo whose inputs are

Ct = (Lt + Rt)/2 and St = (Lt – Rt)/2

Without much effort it can be seen that the sum and difference ofthis second servo's outputs rise to maxima at α = 90 and α = 270respectively, at which points they consist of Lt only and Rt onlyrespectively. In other words, they deliver the left and right outputsof a four-output active matrix, as shown in figure 5. (No outputscaling is necessary here).

Combining figures 4 and 5, and expressing the outputs in dB, weget figure 6.

Figure 7 presents the same information in the form of a polar plot.

0 90 18040

30

20

10

0

Left α( )

Center α( )

Right α( )

Surround α( )

α

Figure 6. L C R S out

0 90 180 270 3600

0.5

1

C α( )

S α( )

α

Figure 4. C and S outputs when servo outputs are forced to equal magnitudes.

1

3

270 360

puts in dB.

Figure 7. Four-output active matrix (front is at top).

0 90 180 270 3600

0.5L α( )

R α( )

α

Figure 5. L and R outputs when servo outputs are forced to equal magnitudes.

GUNDRY ACTIVE MATRIX DECODER

We have substantially perfect pair-wise panning with no crosstalk.

Since the directional properties of human hearing vary withfrequency, and transients often determine apparent direction, thesignals measured in the servos are in fact subjected to a frequencyweighting, effectively reducing the contributions of low and ofvery high frequencies to the control.

DYNAMICSThe next block diagram, figure 8, adds more of the servo. Theblocks labeled magnitude must be understood to contain rectifiers(absolute value) and smoothing. The plus and minus signs by theVCAs indicate the sense of gain change in response to the controlsignals. For a path containing a VCA whose gain is less thanunity, the configuration from the input to the servo output is verysimilar to that of an output-controlled audio limiter, where abovethreshold the output is forced to a reference level. However, herethe reference or limiting level is not a constant but is the magnitudeof the other servo input. Most of the normal considerations andbenefits in the design of output-controlled limiters apply.

control signal is less critical, and there are many fewer componentsrequiring tight tolerances than in an input-controlled active matrix.

OPERATING IN THE RATIO OR LOGARITHMIC DOMAINSThe servo as described above theoretically "cares" only about therelative levels of the input signals, since it merely uses themagnitude of one as the reference for the other. However, it isclear that unlike an audio limiter that by definition is alwaysdealing with large signals, an active matrix should perform itssteering operations over a wide dynamic range. The referencelevel can therefore vary over a range of tens of dB.

A servo operating in the linear domain would equate the outputmagnitudes to within a roughly constant error expressed in volts,say 10 mV for the sake of explanation. For signals with largemagnitudes, say 1 V, a 10 mV error would be negligible. Forsignals 40 dB smaller, a 10 mV error would be disastrous.

Hence a practical embodiment works better if instead of literallyservoing one magnitude to be equal to another, it servos the ratioof the magnitudes towards 1. This of course gives similar results,but means that the error is approximately a constant in dB, and it

AES 19TH INTERNATIONAL CONFERENCE

In conventional input-controlled dynamic audio processing, suchas compressors, the choice of attack and release times and thedistortion are in conflict. A processor with a smoothing time-constant that gives acceptable distortion may operate too slowly;time-constants that allow the desired speed of response may resultin excessive distortion, both harmonic and modulation. Thisproblem exists also in active matrix decoders, where in addition todistortion, rapid response may lead to unstable imaging. Some,including Pro Logic, counter the problem with program-adaptingtime-constants, but the result is still a compromise.

In an output-controlled or feedback system, the response time isshorter than the smoothing time-constant by a degree that dependson the degree of feedback. (This is exactly equivalent to theextension in frequency response resulting from applying negativefeedback to an amplifier). Hence if that degree is very large, as ina tight servo, the time-constant can be made large and distortionresulting from ripple on the control signal small, while stillmaintaining a fast response. In Pro Logic II, a response time of afew milliseconds is achieved with a smoothing time-constant in theneighborhood of 1 second.

Feed-forward systems capable of reacting in a few ms or lessgenerally respond to the peak of the waveform, at least for low andmiddle frequency signals, so that for instance brief disturbancescan take control, often inappropriately. With a long time-constant,the magnitude blocks measure the average rather than the peak ofthe waveform, giving very stable imaging and low modulationdistortion.

Another benefit of the servo method, relevant primarily to analogembodiments, is that the function in the VCAs relating gain to

allows the servo loop gain and hence its dynamic properties to bemuch less dependent on signal levels. A further refinement,especially convenient in an analog design, is to work in thelogarithmic domain and to control the VCAs so that the differencein the logs of the output magnitudes is urged towards zero.

This difference constitutes the control signal operating on the VCAgains. When it is zero, both VCA gains are unity. When it ispositive, one VCA's gain falls; when it is negative the other VCA'sgain falls.

Figure 9 fills in more of the servo block diagram.

hl

hr

Lt

Rt

+ +

+ –C S

Frequencyweighting

Frequencyweighting Magnitude

Magnitude

+

–

–

+

Comp

h less than or equal to 1

Figure 8. Block diagram of servo showing rectifiers and comparator

4

PASSIVE AND ACTIVE MATRICESConsider a minor transformation of the servo part of figure 9, asshown in figure 10. Each VCA, whose gain h could vary fromunity down to substantially zero, has been replaced by thecombination of a subtractor and a VCA whose gain g can varyfrom substantially zero up to unity. Clearly, by reversing the senseof the control signal, this can perform equivalently.

hl

hr

Lt

Rt

+ +

+ –C S

Frequencyweighting

Frequencyweighting Magnitude

Magnitude

+

–

–

+

Comp

Logarithm

Logarithm

Figure 9. Block diagram showinglog rectifiers and subtractor.

GUNDRY ACTIVE MATRIX DECODER

A

Wr

C

(Tpra

Imfr

AsopttTScaat

For the center front, figure 12 shows the passive term (Lt + Rt), the

hen the servo outputs are summed and differenced as before, theesults C and S now follow the equations

= (Lt + Rt) – gl.Lt – gr.Rt and S = (Lt – Rt) – gl.Lt + gr.Rt

Again, there may be a further scaling, omitted here for clarity).hese equations are presented in the form of the combination ofassive terms (no VCA gains) and some adaptive terms. Nowedraw the diagram to show this explicitly (figure 11). Clearly, Cnd S are unchanged by the transformation.

actual cancellation terms gl.Lt and gr.Rt, and the result ofsubtracting them from the passive term giving the center output

(the heavy solid line; this is the same as figure 4 without the 21

scaling). It is apparent from this graph that the cancellation termsare indeed exactly what are required to combine with the passiveterms to yield zero except over the range 90 to 270 degrees.

Note that the cancellation term for a left-only source rises to amaximum at 90 degrees, and similarly that the term for a right-only

gl

gr

Lt

Rt

Frequencyweighting

Frequencyweighting Magnitude

Magnitude

+

–

–

+

Comp

Logarithm

Logarithm+

–

+

–

gl.Lt

gr.Rt

Figure 10. Complete servo, with two inputs and twooutputs. The VCAs of figure 9 have been replaced by

subtractors plus VCAs.

Lt +

0 90 180 270 3600

1

2

Figure 12. C output (thick solid line) as combination of passive (dashed) and two

active terms (thin solid and dotted).

ES 19TH INTERNATIONAL CONFERENCE

t is useful to consider every output of the complete adaptiveatrix as such a combination of passive (that is, non-adaptive or

ixed) terms plus adaptive terms that cancel the output whenequired.

s a first example, consider the center front. Its passive matrix isimply (Lt + Rt). When there is a dominant signal from the leftnly, so that Lt is finite and Rt is zero, we want to add to thisassive term an additional cancellation term equal to minus Lt,hereby reducing the center output to zero. Under this condition,he servo would have forced hl to zero, so it forces gl to unity.herefore –gl.Lt is equal to –Lt and provides this cancellation.imilarly of course for a right-only source, the requiredancellation signal is –gr.Rt. Since this transformation has notltered the outputs in any way from the analysis above, clearly thedaptive cancellation terms so derived must indeed provide exactlyhe right results for all directions, not just left or right only.

souneeint

Notraof

L =

whreccan

L =

Aswesurno27

Clesin

MOThoucontramo

Fo18

Rt

C

S

+

Servo

+

+

+

––

–

Lt + Rt

Lt – Rt

gl.Lt

gr.Rt

+

–

C = (Lt + Rt) – gl.Lt – gr.RtS = (Lt – Rt) – gl.Lt + gr.Rt

Figure 11. Derivation of C and S outputs shown explicitlyas combinations of passive and active terms.

5

rce rises to a maximum at 270 degrees. No cancellation term isded for a rear source (α = 0) because the center output is

rinsically zero anyway.

w consider the left output. Using the same servonsformation, we can express the left output as the combinationpassive and cancellation terms.

Ct + St − gc.Ct − gs.St

ere gc and gs are of course the VCAs gains in the servoeiving Ct and St. In view of the definitions of Ct and St, this also be written

Lt − gc.Ct − gs.St

expected, the passive matrix for the left output is merely Lt, and have two cancellation signals that ensure that for center andround sources (α = 180 and 0 degrees), the left output deliversthing. No cancellation term is needed for a right source (α =0) because the left output is intrinsically zero anyway.

arly, the process is the same for the right and surround outputs,ce the analysis above is unchanged.

RE THAN FOUR OUTPUTSe servo system so far presented works very well for a four-tput matrix, although the cancellation approach might besidered an unnecessary complication. However, the

nsformation allows us to extend the servo method to five orre outputs, and indeed Pro Logic II provides five.

r any output with an arbitrary principal direction, not just 0, 90,0 or 270 degrees, the task is to devise an appropriate passive

GUNDRY ACTIVE MATRIX DECODER

AES 19TH INTERNATIONAL CONFERENCE

matrix, consisting of a weighted sum of Lt and Rt, and to combineit with cancellation terms which rise to a maximum for each otherprincipal direction except those where no cancellation is necessary.

As before, for an output corresponding to a principal direction, theoutput level should be zero at and beyond the adjacent principaldirections, and should change smoothly within the arc bounded bythose adjacent directions.

In Pro Logic II we retain the two servos unchanged, but have fiveoutputs: left front, center front, right front, left back and right back(L C R LB RB). The last two replace the single surround S of thefour-output case and have principal directions corresponding to α =32 and 360 – 32 degrees. This value was arrived at by extensivelistening, and other values are possible.

The center front output still has adjacent principal directions at leftand right (90 and 270 degrees) beyond which we require no output.Thus changing the number of outputs and principal directions inthe rear half of the circle makes no difference to the derivation ofcenter front, which is derived as described above.

Consider again the left output. In the four-output case, its adjacentprincipal directions were 0 and 180 degrees, and the left outputwas finite only in this arc, in accordance with the finer solid line infigure 13.

In the five-output case, the adjacent principal directions are 32 and180 degrees, so the desired output is as shown by the dotted line,where the left output is finite over the narrower arc 32 to 180degrees (with its maximum still at 90 degrees, of course). Thedifference between this and the four-output left response indicatesthe need for an extra cancellation signal (heavy dashed line), activeonly over the arc 0 to 90 degrees.

This new cancellation signal requires the generation of anadditional control signal to operate on an additional VCA. Thereare probably many ways of generating this further cancellationsignal, but the most economical seems to be to derive its controlsignal from the control signals already present in the two servos.

The control signals in the two servos are functions of the intendeddirection of a reproduced signal. The precise shape of the curvesdepends among other things on the function relating VCA gain tocontrol signal. In the present Pro Logic II, the servo controlsignals vary as shown in figure 14. Here, Vlr is the control signalin the servo receiving Lt and Rt, and Vcs is that for the servoreceiving Ct and St, inverted in this example. It is easy to derive afurther control signal, which is defined as always positive, but theless positive of the servo control signals; the heavy line shows this.It is non-zero only over the desired arc, 0 to 90 degrees, so that byapplying it to a VCA, we can obtain an output that only exists forsources in the range over which we need the new cancellationsignal.

15

0 90 1815

0

15

Vlr α( )

fcs− Vcs α( )⋅

Vy α( )

Figure 15. Control signals in the two servos, one attenua

0 90 180 270 3600

0.5

1

Figure 13. Left output for four-output (thin solid) and five-output (dotted) cases, and

difference between them (thick solid).

However, this control signal has its maximum at 45 degrees,whereas we need it at 32 degrees. The maximum occurs where thetwo servo control signals are equal (where the curves cross).Hence, by attenuating one before the less-positive operation, wecan move the position of the maximum without altering thebounds. This is illustrated in figure 15.

If this control signal operates on a VCA fed with the passivematrix LBpass corresponding to left back (see below), we cangenerate a left back cancellation signal LBV where

LBV = glb.LBpass (glb is the gain of the VCA)

This is in the form required to produce the new left output, as infigure 13.

The new cancellation signal can also be added in appropriate

0 90 180 270 36015

0

Vlr α( )

Vcs α( )−

Vx α( )

α

Figure 14. Control signals in servos and possible derived control signal

6

0 270 360

α

ted, and derived left back control signal.

GUNDRY ACTIVE MATRIX DECODER

AES 19TH IN

proportions to other outputs which might deliver unwanted signalswhen the source is in the neighborhood of left back.

Exactly the same process is used for the right output, whichrequires a right back cancellation signal, RBV.

Now consider the left back output. Its α is 32 degrees, and

875.02

9032cos =��

���

� − 485.02

9032sin −=��

���

� −

so the passive matrix for left back is LBpass = 0.875.Lt – 0.485.Rt.This is the signal fed to the left back VCA to derive the left backcancellation signal discussed above.

The left back output can be generated by combining this passivematrix with cancellation terms for each of the other four principaldirections (that is, for left, center, right and right back). The resultis as in figure 16.

Unlike the four-output case, which theoretically can be perfect, thecancellation is not complete, but in practice it is not difficult toreduce unwanted crosstalk to about –40 dB, more than adequate inreal listening conditions.

The right-back output is derived in exactly the same manner.

COMPLETE SYSTEMEach of the five outputs consists of the combination of fixed terms,that is, the passive matrix, and cancellation terms, which are

combinations of the inputs via VCAs. For the directional angles 0,90, 180 and 270, the cancellation terms are derived withinfeedback servos. For the extension to include left back and rightback, they are derived using control signals generated from thecontrol signals of the servos.

Figure 17 shows one way of presenting a block diagram of thecomplete system, omitting the intricacies of the servos and controlsignal generation. The block on the left generates the passivematrix. The results pass through VCAs to generate sixcancellation signals, one for each principal direction plus one forcenter rear; each is designated with a V to indicate that it is theoutput of one of the VCAs. Thus for instance LV = gl.Lt, CV =gc.Ct, LBV = glb.LBpass, etc. The summers on the right combinethe passive matrix signals with the cancellation signals.Obviously, the novelty and most of the improved performance liein the manner of generating those cancellation signals usingfeedback servos.

Figures 18 and 19 show the results.

0

Lt

Rt

R

LB

Servo

Passivematrix Servo

L

C

CVSV

LBV

LV

CVSV

RBV

RV

RB

Lt

Rt

Ct

St

LV

RV

CV

SV

LBV

RBV

RV

RVLV

LV

CV

CVRBV

LBV

LBpass

RBpass

Figure 17. Overall block diagram.

0 90 180 270 3600

0.5

1

Figure 16. Left back output derived by combining the passive matrix LBpass with left,

center, right and right back cancellation signals.

TERNATIONAL CONFERENCE

0 9040

30

20

10Left5 α( )

Center α( )

Right5 α( )

Leftback α( )

Rightback α( )

Figure 18. L C R LB

7

180 270 360

α

RB outputs in dB.

GUNDRY ACTIVE MATRIX DECODER

A

A(Pcctah"acdmbpe

DTfurapT

Tdrsiwt

Iaadb

Ip

aco

b) Control signals can be generated at a sub-sampled rate. In thepresent realization of the new system, this is 1/8th of the audio

ES 19TH INTERNATIONAL CONFERENCE 8

n important feature of this system, inherent in the configurationalthough not unique to it, in that some previous systems, includingro Logic, have the same property), is that when the input is moreomplex than a single source from a single direction, theancellation signals adopt smaller magnitudes and the system tendsowards the passive matrix. In the extreme case where Lt and Rtre totally uncorrelated, all VCA gains are close to zero and weave the "pure" passive matrix. In other words, the degree ofsteering" or hardening of reproduced images can vary smoothlynd continuously from full to none in accordance with theorrelation of the inputs. The designers of some other recent activeecoders have abandoned the principle of reverting to a passiveatrix when the steering is faced with little or no correlation

etween the input signals; the result is level modulation effects,articularly on un-encoded two-channel stereo sources. Suchffects are largely absent in Pro Logic II.

IGITAL EMBODIMENThe system employs four cancellation signals generated via two

eedback servos, and two further cancellation signals generatedsing control signals derived from those servos. Each servoequires two weighting filters, two sets of smoothing componentsnd two VCAs. In short, the complexity of an analog realizationrobably makes it uneconomic for the mass consumer market.hus the system was an obvious candidate for a digital realization.

he feedback servos are fundamental to the operation. An exactigital equivalent of the analog feedback servo would requireecursion with, for each sample period, a repetitive process ofuccessive approximation to arrive at an equilibrium. A change innput condition would lead to a change in the control signal whichould command a change in the VCA gains which would change

he control signal which would change the gains … and so on.

n most dynamic audio processing, including compressors, limitersnd the servos of Pro Logic II, it is necessary to ensure that theudio is not modified so rapidly that we get audible modulationistortion. Hence, control signals typically have much narrowerandwidth than the audio being controlled.

n a digital decoder, the narrow bandwidth of the control signalsermits two economies in digital signal processing.

) Repetitive approximation can be avoided. A change in theontrol voltage is applied not to the current sample but to the nextne, leading to a lag of a sample period.

sampling frequency.

Figure 20 shows a rearrangement of the servo elements allowingmost of it to operate at the lower sampling rate (the part within thedashed box). The frequency weighting has been removed from theservo, and instead precedes it, and the VCAs, now multipliers,operate on the absolute values. This configuration leads to asignificant economy, at the expense of a lag of between 8 and 16samples (for 48 kHz sampling rate, roughly 250 µs); however, thisdelay is small compared with the lag already inherent in the signalmeasurement in the servos.

Unfortunately, deliberately slowed response to avoid modulationdistortion leads to transient imperfections. In limiters, these takethe form of overshoots, and it is known to employ delays toeliminate them, even in the context of an output-controlled device(7). In an exactly equivalent way, the delay in generating controlsignals in a digital surround decoder can be compensated by adelay in the audio paths, providing an effective look-ahead.

See figure 21 for a complete digital realization. There are twodistinct regions. The lower two-thirds of the diagram shows thegeneration of control signals (strictly, VCA gains) using feedbackservos operating at 1/8th of the input sampling frequency. Theupper one-third operates on the audio to deliver the requiredoutputs. Note that the inputs to the upper block are delayed byabout 5 ms. This delay compensates both for the "attack" time inthe servos and for the lag due to sub-sampling and lack ofrepetitive recursion. The precise delay is not critical, but waschosen to ensure that a listener receives a proper subjectiveimpression of a sudden change of direction. If the delay is less,then transients occasionally come from the wrong direction (likeprevious active matrix decoders, including Pro Logic); if more,then sometimes it is possible to perceive movement just prior tothe onset of a new sound from a new direction. (A 5 ms delay isnot enough to disturb the subjective synchronism between soundand picture).

In the analog circuit each output consists of the passive matrix plusa number of cancellation signals, but at any one instant, eachoutput is merely a weighted sum of the inputs. It can be written

output = a.Lt + b.Rt

For each value of the four control signals (or equivalently, the sixVCA gains, gl gr gc gs glb grb), there are corresponding values forthe multipliers a and b. In the digital embodiment, thetransformation from control signals to multipliers is performed bya look-up table that models the combinations of passive and activeterms, and operates at the sub-sampled rate. The table outputs are

Lt

Rt

+

–

Frequencyweighting

Frequencyweighting

Absolutevalue

Absolutevalue +

–

Antilog

Antilog inv

Smoothing

Smoothing

Log

Log

+

–Comp

gl

gr

Figure 20. Rearrangement of L/R servoto permit sub-sampling.

Figure 19. Five-output active matrix (front is at top).

GUNDRY ACTIVE MATRIX DECODER

AES 19TH INTERNATIONAL CONFERENCE 9

then "up-sampled" or interpolated to produce coefficients for theadaptive matrix at the full audio sampling rate; this interpolationsmoothes the changes in gain.

The result is a digital decoder whose performance under steady-state conditions is substantially identical to that of the analogprototype, but whose dynamic performance is occasionally audiblysuperior due to the look-ahead.

CONCLUSIONIn an active matrix decoder, feedback servos derive terms that willbe combined to form the outputs, leading to more accurateoperation and superior dynamic behavior. In the digitalembodiment, the system is further refined to reduce the DSPdemands and to allow look-ahead. The result is a circuit that givesexcellent performance on surround-encoded material but also verypleasing results on conventional un-encoded stereo program,without the anomalous steering and pumping effects common fromsurround simulators.

REFERENCES1. Benjamin B. Bauer, Richard G. Allen, Gerald A. Budelman,Daniel W. Gravereux. "Quadraphonic Matrix Perspective -Advances in SQ Encoding and Decoding Technology". J. AudioEng. Soc. vol. 21 pp. 342-350 (June 1973).

2. R. Itoh, S. Takahashi. "Characteristics of the Sansui QS Vario-Matrix Based on a Psychoacoustic Study of the Localization ofSound in Four-Channel Stereo". Presented at the 43rd Conventionof the Audio Engineering Society, New York, September 1972(preprint 904).

3. Roger Dressler. "Dolby Pro Logic Surround Decoder, Principlesof Operation" (www.Dolby.com).

4. James W. Fosgate. U.S.patent number 5,644,640, "Surroundsound processor with improved control voltage generator".

5. David Griesinger. "Multichannel Matrix Surround Decoders forTwo-Eared Listeners" Presented at the 101st Convention of theAudio Engineering Society, 1996 Nov. 8-11 (preprint 4402).

6. James K. Waller, Jr. White Paper "The Circle Surround 5.2.5 5-Channel Surround System"(www.analog.com/publications/whitepapers/products/circle/circle.html).

7. Shorter, D.E. L., Manson, W.I. and Stebbings, D.W. "Thedynamic characteristics of limiters for sound programme circuits"BBC Engineering Monograph No.70, October 1967.

FrequencyweightingFrequencyweighting

Sum/diff

5 msdelay

5 msdelay

Lt

Rt

R

L

C

LB

RB

Servo

Servo

Backcontrol

Look-uptable

Up-sampling(interpolation)

Adaptivematrix

gl

glbgr

gs

gc grb

Operates at 1/8 samplingfrequency

10 coefficientsadapting at 1/8sampling rate

10 coefficientsadapting at fullsampling rate

Figure 21. Complete digital realization.