Pro Logic II AES Paper by Ty chamberlain

A New Active Matrix Decoder for Surround Sound Kenneth Gundry Dolby 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 outputcontrolled limiter. This leads to tighter tolerances, excellent crosstalk figures and improved dynamics. It gives good performance on matrixencoded sources but also very pleasing results on un-encoded two-channel material. The paper discusses the principles and their benefits. BACKGROUND Matrix decoders receiving two channels and delivering feeds for three, four or more loudspeakers have been known for more than 25 years. Early active decoders, for instance for CBS SQ (1) and Sansui QS (2), were not successful for both technical and marketing reasons; they did not work very well, in the author's view partly because they were too ambitious. The development of stereo 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 that performed much better. They became very popular in the cinema and later appeared on the home market under the name Dolby Pro Logic (3). However, such decoders were designed for and are most successful in processing signals that have been deliberately encoded for surround reproduction. The preparation of surround-encoded material generally involves monitoring the result via a decoder equivalent to that which will be used in the eventual reproduction. Thus, most movies are mixed while listening via a Pro Logic decoder, the design most commonly employed in cinemas and in home theatre systems. This ensures that the result will be similar to that intended by the sound mixer. With increasing interest in multichannel sound, but an obvious dearth of 5.1 channel recordings, a device capable of giving pleasing surround sound from existing two-channel material would be very attractive. In recent years, several such devices have been developed to improve the subjective impression of un-encoded music recordings by spreading the sound around the room. Unfortunately, many of these have led to undesired anomalous effects, whereby instruments wander in position or level, and in addition, most of these simulators do not perform satisfactorily on surround-encoded material. Jim Fosgate has been prominent among workers in the field of active matrix decoders. Some years ago it occurred to him that it was more logical to derive the control signals from the outputs, that is, to employ negative feedback. The result of this work is Pro Logic II, developed by Fosgate and brought to market by Dolby Laboratories. The new system gives good performance on matrixencoded sources but also very pleasing results on two-channel music recordings that have not been matrix-encoded. ACTIVE MATRIX SYSTEMS The systems under discussion receive a pair of inputs, conventionally known as left total and right total (Lt, Rt), which are subjected to a variable matrix and deliver a number of outputs to be fed to loudspeakers around the listening position. Previous active systems, including Pro Logic, Fosgate's own previous work (4), Logic 7 (5) and Circle Surround (6), analyze Lt and Rt for relative magnitude and phase, generating control signals with essentially 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 of sources approximately constant as the matrix coefficients change and to appropriate dynamic behavior, such an approach can work

satisfactorily (but not all pay the required attention to those matters). The new system departs from previous methods in developing its control signals from signal outputs rather than inputs, that is, in using feedback in a manner analogous to an output-controlled compressor. This leads to tighter tolerances, excellent crosstalk figures and improved dynamic performance. FRAME OF REFERENCE FOR ANALYSIS For the purposes of explanation, it is convenient to express Lt and Rt in terms of the intended direction of a source, independent of the magnitude. This approach has been taken by many in the field, and avoids the need to consider how the signals were actually derived. Since absolute magnitude is not relevant to direction, for the rest of this analysis the inputs to the decoder will be taken to be normalized to unity power; thus by definition, Lt2 + Rt2 = 1 The encoding can then be generalized by considering a direction parameter, α degrees, which has the value 0 for surround (rear), 90 for left, 180 for center front and 270 for right, and by expressing Lt and Rt as functions of α. By inspection, we can see that the required functions are æ α − 90 ö æ α − 90 ö and Lt (α) = cosç Rt (α ) = sin ç ÷ ÷ è 2 ø è 2 ø Note that the 90 degrees in these expressions arises solely from the choice of 0 at the rear (other workers have chosen other reference directions), and that only the relative polarity is significant. If Lt and Rt were generated by a panpot that could be steered around the full circle, these would be the relative magnitudes and polarities. For instance, when α = 90 (left), Lt = 1 and Rt = 0, when α = 180 1 , and so on. (center), Lt = Rt = 2 Figure 1 shows the variation of Lt and Rt as the direction α is panned around the whole circle. 1

Lt( α ) Rt ( α )

180

270

360

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

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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 Pro Logic decoder, the loudspeakers usually have positions as shown in figure 2. The left and right front loudspeakers are 30 or 40 degrees either side of the center front, and the two "surround" loudspeakers are to the side and somewhat behind the listener and receive identical signals. The actual angle of the loudspeakers with respect to the listener can then be considered as a transformation or systematic distortion of the directional parameter α, as illustrated in the figure. For the remainder of this paper, it will be understood that in actual reproduction, the directional angle α will be so transformed. In the following, the term principal direction refers to a direction where an output of an active matrix rises to a maximum. Hence for a four-output matrix, the principal directions are 0, 90, 180 and 270 degrees.

SERVOS Figure 3 shows a simple block diagram. The two input signals Lt Rt pass via voltage-controlled amplifiers (VCAs) with gains hl and hr, and are summed and differenced to deliver two outputs, labeled C 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 seem obvious to generate control signals directly from Lt and Rt to vary gains hl and hr . Previous active matrices have universally derived their control from the inputs. However, there is another way of considering the matter.

hl.Lt +

+ S

180

+ Rt

– hr.Rt

Figure 3. Lt Rt via VCAs and then summed and differenced to give C and S.

270

Figure 2. Plan view of conventional positions of loudspeakers and relationship with angle α DESIRED RESULT FOR A FOUR-OUTPUT ACTIVE MATRIX Consider an active matrix with four outputs, left center right and surround (L C R S). The center output should be zero when the source direction lies in the rear half of the circle. In the front half, we would like the center output to rise from zero at 90 degrees to a maximum at 180 and 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 when α is more than 90 degrees away (considering the circle as continuous so that 0 and 360 are equivalent), and the signal level should rise from zero to a maximum and fall back to zero as α varies from –90 to +90 with respect to that output's direction. In other words, for an output corresponding to a principal direction, the output level should be zero at and beyond the adjacent principal directions, and should change smoothly within the arc bounded by those adjacent directions. This is of course no more than a spelling out of what is generally called pair-wise pan-potting. A source from any arbitrary direction should be delivered only by the two (or one) loudspeakers closest to that direction.

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For directions in the front half of the circle, Lt and Rt have the same polarities, and S should be zero. Thus for signals intended to come from somewhere in the front half, hl.Lt and hr.Rt must be equal, so that the subtraction can yield no output. Similarly for sources in the rear half of the circle, Lt and Rt have opposite polarities and C should be zero, leading to a similar requirement, this time that hl.Lt and minus hr.Rt must be equal. The two requirements become the same if we say that the magnitudes of hl.Lt and hr.Rt must be equal. This can be achieved by an active servo that measures the magnitudes of the VCA outputs and drives the VCA gains to urge those magnitudes towards equality. Now consider what happens within the half-circle containing center front. For a left only source, α = 90, Lt =1 and Rt = 0. Thus the magnitude of hr.Rt is inherently zero and the only way the servo can force equal magnitudes is to make hl zero, so that hl.Lt is also zero. If hl.Lt and hr.Rt are both zero, clearly their sum is zero also, so there is no output from C, as desired. 1 . For the equal For a center front source, α = 180, Lt = Rt = 2 magnitude requirement, the servo must force gains hl and hr to be equal, but the absolute value is undefined. Here we must impose a value. Suppose that the circuit is designed so that under this 1 (and can never exceed that condition the VCAs adopt gains of 2 value under any other conditions). In that case, for center front, C 1 (Lt + Rt), a finite signal consisting of the sum of the delivers 2 left and right total signals with equal weights, just as we might expect. In practice, it is more convenient to consider the VCAs as having maximum gains of unity, and to introduce any scaling before or after. In its basic form, the servo then leaves unchanged the smaller of its inputs, but attenuates the larger to force its magnitude to be equal to that of the smaller.

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

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

L( α ) R( α )

0.5

C( α ) S( α )

0.5

180

270

360

Figure 5. L and R outputs when servo outputs are forced to equal magnitudes. 0

180

270

360

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

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 of this second servo's outputs rise to maxima at α = 90 and α = 270 respectively, at which points they consist of Lt only and Rt only respectively. In other words, they deliver the left and right outputs of a four-output active matrix, as shown in figure 5. (No output scaling is necessary here). Combining figures 4 and 5, and expressing the outputs in dB, we get figure 6. Figure 7 presents the same information in the form of a polar plot.

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

10 Left( α ) Center( α ) Right ( α )

Surround( α ) 30

180

270

360

Figure 6. L C R S outputs in dB.

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We have substantially perfect pair-wise panning with no crosstalk. Since the directional properties of human hearing vary with frequency, and transients often determine apparent direction, the signals measured in the servos are in fact subjected to a frequency weighting, effectively reducing the contributions of low and of very high frequencies to the control. DYNAMICS The next block diagram, figure 8, adds more of the servo. The blocks labeled magnitude must be understood to contain rectifiers (absolute value) and smoothing. The plus and minus signs by the VCAs indicate the sense of gain change in response to the control signals. For a path containing a VCA whose gain is less than unity, the configuration from the input to the servo output is very similar to that of an output-controlled audio limiter, where above threshold the output is forced to a reference level. However, here the reference or limiting level is not a constant but is the magnitude of the other servo input. Most of the normal considerations and benefits in the design of output-controlled limiters apply. Lt

hl –

Frequency weighting

Magnitude + Comp –

+ Rt

Frequency weighting

+ C

S –

Magnitude

control signal is less critical, and there are many fewer components requiring tight tolerances than in an input-controlled active matrix. OPERATING IN THE RATIO OR LOGARITHMIC DOMAINS The servo as described above theoretically "cares" only about the relative levels of the input signals, since it merely uses the magnitude of one as the reference for the other. However, it is clear that unlike an audio limiter that by definition is always dealing with large signals, an active matrix should perform its steering operations over a wide dynamic range. The reference level can therefore vary over a range of tens of dB.

A servo operating in the linear domain would equate the output magnitudes to within a roughly constant error expressed in volts, say 10 mV for the sake of explanation. For signals with large magnitudes, say 1 V, a 10 mV error would be negligible. For signals 40 dB smaller, a 10 mV error would be disastrous. Hence a practical embodiment works better if instead of literally servoing one magnitude to be equal to another, it servos the ratio of the magnitudes towards 1. This of course gives similar results, but means that the error is approximately a constant in dB, and it allows the servo loop gain and hence its dynamic properties to be much less dependent on signal levels. A further refinement, especially convenient in an analog design, is to work in the logarithmic domain and to control the VCAs so that the difference in the logs of the output magnitudes is urged towards zero. This difference constitutes the control signal operating on the VCA gains. When it is zero, both VCA gains are unity. When it is positive, one VCA's gain falls; when it is negative the other VCA's gain falls.

h less than or equal to 1

Figure 9 fills in more of the servo block diagram. Figure 8. Block diagram of servo showing rectifiers and comparator

In conventional input-controlled dynamic audio processing, such as compressors, the choice of attack and release times and the distortion are in conflict. A processor with a smoothing timeconstant that gives acceptable distortion may operate too slowly; time-constants that allow the desired speed of response may result in excessive distortion, both harmonic and modulation. This problem exists also in active matrix decoders, where in addition to distortion, rapid response may lead to unstable imaging. Some, including Pro Logic, counter the problem with program-adapting time-constants, but the result is still a compromise. In an output-controlled or feedback system, the response time is shorter than the smoothing time-constant by a degree that depends on the degree of feedback. (This is exactly equivalent to the extension in frequency response resulting from applying negative feedback to an amplifier). Hence if that degree is very large, as in a tight servo, the time-constant can be made large and distortion resulting from ripple on the control signal small, while still maintaining a fast response. In Pro Logic II, a response time of a few milliseconds is achieved with a smoothing time-constant in the neighborhood of 1 second.

hl –

Frequency weighting

Magnitude

Logarithm + Comp –

+ Rt

Frequency weighting

Magnitude

+ C

Logarithm

hr Figure 9. Block diagram showing log rectifiers and subtractor.

PASSIVE AND ACTIVE MATRICES Consider a minor transformation of the servo part of figure 9, as shown in figure 10. Each VCA, whose gain h could vary from unity down to substantially zero, has been replaced by the combination of a subtractor and a VCA whose gain g can vary from substantially zero up to unity. Clearly, by reversing the sense of the control signal, this can perform equivalently.

Feed-forward systems capable of reacting in a few ms or less generally respond to the peak of the waveform, at least for low and middle frequency signals, so that for instance brief disturbances can take control, often inappropriately. With a long time-constant, the magnitude blocks measure the average rather than the peak of the waveform, giving very stable imaging and low modulation distortion. Another benefit of the servo method, relevant primarily to analog embodiments, is that the function in the VCAs relating gain to

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S –

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For the center front, figure 12 shows the passive term (Lt + Rt), the actual cancellation terms gl.Lt and gr.Rt, and the result of subtracting them from the passive term giving the center output 1 (the heavy solid line; this is the same as figure 4 without the 2 scaling). It is apparent from this graph that the cancellation terms are indeed exactly what are required to combine with the passive terms to yield zero except over the range 90 to 270 degrees.

gl.Lt + – +

Frequency weighting

Magnitude

Logarithm + Comp –

+ –

Frequency weighting

Magnitude

Logarithm

– Rt

gr.Rt

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

When the servo outputs are summed and differenced as before, the results C and S now follow the equations C = (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). These equations are presented in the form of the combination of passive terms (no VCA gains) and some adaptive terms. Now redraw the diagram to show this explicitly (figure 11). Clearly, C and S are unchanged by the transformation. Lt

Lt + Rt +

– gl.Lt

C –

–

– +

S +

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

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

It is useful to consider every output of the complete adaptive matrix as such a combination of passive (that is, non-adaptive or fixed) terms plus adaptive terms that cancel the output when required. As a first example, consider the center front. Its passive matrix is simply (Lt + Rt). When there is a dominant signal from the left only, so that Lt is finite and Rt is zero, we want to add to this passive term an additional cancellation term equal to minus Lt, thereby reducing the center output to zero. Under this condition, the servo would have forced hl to zero, so it forces gl to unity. Therefore –gl.Lt is equal to –Lt and provides this cancellation. Similarly of course for a right-only source, the required cancellation signal is –gr.Rt. Since this transformation has not altered the outputs in any way from the analysis above, clearly the adaptive cancellation terms so derived must indeed provide exactly the right results for all directions, not just left or right only.

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180

270

360

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

Note that the cancellation term for a left-only source rises to a maximum at 90 degrees, and similarly that the term for a right-only source rises to a maximum at 270 degrees. No cancellation term is needed for a rear source (α = 0) because the center output is intrinsically zero anyway. Now consider the left output. Using the same servo transformation, we can express the left output as the combination of passive and cancellation terms.

Servo gr.Rt

L = Ct + St − gc.Ct − gs.St where gc and gs are of course the VCAs gains in the servo receiving Ct and St. In view of the definitions of Ct and St, this can also be written L = Lt − gc.Ct − gs.St As expected, the passive matrix for the left output is merely Lt, and we have two cancellation signals that ensure that for center and surround sources (α = 180 and 0 degrees), the left output delivers nothing. No cancellation term is needed for a right source (α = 270) because the left output is intrinsically zero anyway. Clearly, the process is the same for the right and surround outputs, since the analysis above is unchanged. MORE THAN FOUR OUTPUTS The servo system so far presented works very well for a fouroutput matrix, although the cancellation approach might be considered an unnecessary complication. However, the transformation allows us to extend the servo method to five or more outputs, and indeed Pro Logic II provides five.

For any output with an arbitrary principal direction, not just 0, 90, 180 or 270 degrees, the task is to devise an appropriate passive

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

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

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

The control signals in the two servos are functions of the intended direction of a reproduced signal. The precise shape of the curves depends among other things on the function relating VCA gain to control signal. In the present Pro Logic II, the servo control signals vary as shown in figure 14. Here, Vlr is the control signal in the servo receiving Lt and Rt, and Vcs is that for the servo receiving Ct and St, inverted in this example. It is easy to derive a further control signal, which is defined as always positive, but the less 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 by applying it to a VCA, we can obtain an output that only exists for sources in the range over which we need the new cancellation signal.

In Pro Logic II we retain the two servos unchanged, but have five outputs: 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 the four-output case and have principal directions corresponding to α = 32 and 360 – 32 degrees. This value was arrived at by extensive listening, and other values are possible. The center front output still has adjacent principal directions at left and right (90 and 270 degrees) beyond which we require no output. Thus changing the number of outputs and principal directions in the rear half of the circle makes no difference to the derivation of center front, which is derived as described above.

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

Vlr( α ) − Vcs( α )

Vx( α )

180

270

360

0.5

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

180

270

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

360

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

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

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

LBV = glb.LBpass

(glb is the gain of the VCA)

This is in the form required to produce the new left output, as in figure 13. The new cancellation signal can also be added in appropriate

Vlr ( α ) − fcs⋅Vcs ( α )

Vy ( α )

180

270

360

Figure 15. Control signals in the two servos, one attenuated, and derived left back control signal.

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proportions to other outputs which might deliver unwanted signals when the source is in the neighborhood of left back. Exactly the same process is used for the right output, which requires a right back cancellation signal, RBV. Now consider the left back output. Its α is 32 degrees, and æ 32 − 90 ö sin ç ÷ = −0.485 è 2 ø

æ 32 − 90 ö cosç ÷ = 0.875 è 2 ø

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 back cancellation signal discussed above. The left back output can be generated by combining this passive matrix with cancellation terms for each of the other four principal directions (that is, for left, center, right and right back). The result is as in figure 16.

combinations of the inputs via VCAs. For the directional angles 0, 90, 180 and 270, the cancellation terms are derived within feedback servos. For the extension to include left back and right back, they are derived using control signals generated from the control signals of the servos. Figure 17 shows one way of presenting a block diagram of the complete system, omitting the intricacies of the servos and control signal generation. The block on the left generates the passive matrix. The results pass through VCAs to generate six cancellation signals, one for each principal direction plus one for center rear; each is designated with a V to indicate that it is the output of one of the VCAs. Thus for instance LV = gl.Lt, CV = gc.Ct, LBV = glb.LBpass, etc. The summers on the right combine the passive matrix signals with the cancellation signals. Obviously, the novelty and most of the improved performance lie in the manner of generating those cancellation signals using feedback servos. CV SV

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

Servo

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

LV RV

CV SV

RBV

Servo

Ct Passive matrix

LBV

CV SV

0.5

LBpass

180

270

360

Figure 16. Left back output derived by combining the passive matrix LBpass with left, center, right and right back cancellation signals.

RV LV

LBV

CV RBV

RBV

LV RV

RBpass

CV LBV

Figure 17. Overall block diagram.

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

Figures 18 and 19 show the results.

Left5( α )

Center( α ) Right5 ( α )

Leftback( α ) Rightback( α )

180

270

360

Figure 18. L C R LB RB outputs in dB.

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b) Control signals can be generated at a sub-sampled rate. In the present realization of the new system, this is 1/8th of the audio sampling frequency. Figure 20 shows a rearrangement of the servo elements allowing most of it to operate at the lower sampling rate (the part within the dashed box). The frequency weighting has been removed from the servo, and instead precedes it, and the VCAs, now multipliers, operate on the absolute values. This configuration leads to a significant economy, at the expense of a lag of between 8 and 16 samples (for 48 kHz sampling rate, roughly 250 µs); however, this delay is small compared with the lag already inherent in the signal measurement in the servos.

Frequency weighting

Absolute value

Figure 19. Five-output active matrix (front is at top). An important feature of this system, inherent in the configuration (although not unique to it, in that some previous systems, including Pro Logic, have the same property), is that when the input is more complex than a single source from a single direction, the cancellation signals adopt smaller magnitudes and the system tends towards the passive matrix. In the extreme case where Lt and Rt are totally uncorrelated, all VCA gains are close to zero and we have the "pure" passive matrix. In other words, the degree of "steering" or hardening of reproduced images can vary smoothly and continuously from full to none in accordance with the correlation of the inputs. The designers of some other recent active decoders have abandoned the principle of reverting to a passive matrix when the steering is faced with little or no correlation between the input signals; the result is level modulation effects, particularly on un-encoded two-channel stereo sources. Such effects are largely absent in Pro Logic II. DIGITAL EMBODIMENT The system employs four cancellation signals generated via two feedback servos, and two further cancellation signals generated using control signals derived from those servos. Each servo requires two weighting filters, two sets of smoothing components and two VCAs. In short, the complexity of an analog realization probably makes it uneconomic for the mass consumer market. Thus the system was an obvious candidate for a digital realization.

The feedback servos are fundamental to the operation. An exact digital equivalent of the analog feedback servo would require recursion with, for each sample period, a repetitive process of successive approximation to arrive at an equilibrium. A change in input condition would lead to a change in the control signal which would command a change in the VCA gains which would change the control signal which would change the gains … and so on. In most dynamic audio processing, including compressors, limiters and the servos of Pro Logic II, it is necessary to ensure that the audio is not modified so rapidly that we get audible modulation distortion. Hence, control signals typically have much narrower bandwidth than the audio being controlled.

Frequency weighting

Smoothing

Antilog

Absolute value

Log

–

inv

+ Comp –

– Smoothing

Log

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

Unfortunately, deliberately slowed response to avoid modulation distortion leads to transient imperfections. In limiters, these take the form of overshoots, and it is known to employ delays to eliminate them, even in the context of an output-controlled device (7). In an exactly equivalent way, the delay in generating control signals in a digital surround decoder can be compensated by a delay in the audio paths, providing an effective look-ahead. See figure 21 for a complete digital realization. There are two distinct regions. The lower two-thirds of the diagram shows the generation of control signals (strictly, VCA gains) using feedback servos operating at 1/8th of the input sampling frequency. The upper one-third operates on the audio to deliver the required outputs. Note that the inputs to the upper block are delayed by about 5 ms. This delay compensates both for the "attack" time in the servos and for the lag due to sub-sampling and lack of repetitive recursion. The precise delay is not critical, but was chosen to ensure that a listener receives a proper subjective impression of a sudden change of direction. If the delay is less, then transients occasionally come from the wrong direction (like previous active matrix decoders, including Pro Logic); if more, then sometimes it is possible to perceive movement just prior to the onset of a new sound from a new direction. (A 5 ms delay is not enough to disturb the subjective synchronism between sound and picture). In the analog circuit each output consists of the passive matrix plus a number of cancellation signals, but at any one instant, each output is merely a weighted sum of the inputs. It can be written output = a.Lt + b.Rt

In a digital decoder, the narrow bandwidth of the control signals permits two economies in digital signal processing. a) Repetitive approximation can be avoided. A change in the control voltage is applied not to the current sample but to the next one, leading to a lag of a sample period.

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

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L 5 ms delay

C Adaptive matrix

5 ms delay

R LB RB

10 coefficients adapting at full sampling rate

Frequency weighting Frequency weighting

Look-up table

Servo

gl gr

Sum/ diff

6. James K. Waller, Jr. White Paper "The Circle Surround 5.2.5 5Channel Surround System" (www.analog.com/publications/whitepapers/products/circle/ circle.html). 7. Shorter, D.E. L., Manson, W.I. and Stebbings, D.W. "The dynamic characteristics of limiters for sound programme circuits" BBC Engineering Monograph No.70, October 1967.

Up-sampling (interpolation)

10 coefficients adapting at 1/8 sampling rate

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

Servo

Back glb control gc

grb

gs Operates at 1/8 sampling frequency Figure 21. Complete digital realization.

then "up-sampled" or interpolated to produce coefficients for the adaptive matrix at the full audio sampling rate; this interpolation smoothes the changes in gain. The result is a digital decoder whose performance under steadystate conditions is substantially identical to that of the analog prototype, but whose dynamic performance is occasionally audibly superior due to the look-ahead. CONCLUSION In an active matrix decoder, feedback servos derive terms that will be combined to form the outputs, leading to more accurate operation and superior dynamic behavior. In the digital embodiment, the system is further refined to reduce the DSP demands and to allow look-ahead. The result is a circuit that gives excellent performance on surround-encoded material but also very pleasing results on conventional un-encoded stereo program, without the anomalous steering and pumping effects common from surround simulators. REFERENCES 1. Benjamin B. Bauer, Richard G. Allen, Gerald A. Budelman, Daniel W. Gravereux. "Quadraphonic Matrix Perspective Advances in SQ Encoding and Decoding Technology". J. Audio Eng. Soc. vol. 21 pp. 342-350 (June 1973).

2. R. Itoh, S. Takahashi. "Characteristics of the Sansui QS VarioMatrix Based on a Psychoacoustic Study of the Localization of Sound in Four-Channel Stereo". Presented at the 43rd Convention of the Audio Engineering Society, New York, September 1972 (preprint 904). 3. Roger Dressler. "Dolby Pro Logic Surround Decoder, Principles of Operation" (www.Dolby.com). 4. James W. Fosgate. U.S.patent number 5,644,640, "Surround sound processor with improved control voltage generator".

AES 19TH INTERNATIONAL CONFERENCE