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Lexicon 5-2-5 Matrix Systems Manual

Progress in 5-2-5 matrix systems
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Progress in 5-2-5 Matrix Systems
David Griesinger
Lexicon
3 Oak Park
Bedford MA 01730
Abstract
A high quality 5-2-5 matrix encoder and decoder system offers the prospect of
inexpensive compatible media for multichannel sound. The advantages to the consumer,
music and film producers, and broadcasters, are obvious. This paper reports on a system
which offers excellent 5-2-5 codec performance, while preserving or improving the
balance, frontal perspective, and spaciousness of standard stereo recordings. The decoder
provides two or four independent rear outputs, which are capable of complete separation
from the other outputs for a single steered sound effect, and which preserve full left/right
separation during music. Decorrelated signals such as music can be panned forward and
back with full left/right separation. Frontal perspective and the balance between center
material such as dialog and vocals and other material is preserved through careful control
of the center channel level as a function of the center content of the input signal. This
paper will present a mathematical description of the matrix elements of the new decoder,
and discuss some of the psychoacoustic data on which it is based.
Introduction
Although initially developed for multichannel music reproduction, matrix systems have
been relegated to film sound. They are capable of much more. A preliminary design for a
new matrix topology has been tested by the IRT in Munich as a 5-2-5 codec, with
excellent results on a wide range of broadcast material. Although there were audible
differences, the differences were perceived as small changes in localization – and were
sometimes preferred to the original. We have extensively tested the new matrix with
ordinary stereo music material. In almost every case the multichannel matrix
reproduction of the material is preferable to a two-channel presentation. This is a
wonderful way to hear new sounds from your favorite recordings, and amazing sounds
from recordings which have been remixed for 5.1 channels. A high quality 5-2-5 matrix
offers a Rosetta stone for audio reproduction. A single inexpensive circuit can play both
encoded and unencoded music, films, and broadcast material. The advantage to the
consumer is obvious – high quality multichannel recordings available on compatible
CD's, cassettes, videotapes, etc. The recordings can be played anywhere the consumer
has a player, and yet on a multichannel system true multichannel audio results. Who
wouldn't want to hear multichannel broadcasts in an automobile?
Why do we need more than two loudspeakers? Research into the spatial acoustics of
small rooms shows that reproduction of stereo music through two speakers is not an
optimal solution, even when the listener is ideally situated. Additional loudspeakers,
driven with signals that provide audible spatial components, can significantly increase the

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Summary of Contents for Lexicon 5-2-5 Matrix Systems

  • Page 1 Progress in 5-2-5 Matrix Systems David Griesinger Lexicon 3 Oak Park Bedford MA 01730 Abstract A high quality 5-2-5 matrix encoder and decoder system offers the prospect of inexpensive compatible media for multichannel sound. The advantages to the consumer, music and film producers, and broadcasters, are obvious. This paper reports on a system which offers excellent 5-2-5 codec performance, while preserving or improving the balance, frontal perspective, and spaciousness of standard stereo recordings.
  • Page 2 pleasantness of the sound field, and enlarge the listening area. This is particularly true when speakers are placed along the sides of the room. The primary improvement is in the perception of spaciousness. To see how multiple speakers can help, we can look at the perceptual origin of spaciousness. Spaciousness in concert halls and in small rooms is primarily determined by the spatial diffusion of sounds that arrive at least 160ms after the ends of strong foreground sound events.
  • Page 3 from the sum of the left and right input signals. However this sum contains not only the original center channel information, but the left and right stereo material as well. Reproducing the sum through the center loudspeaker must inevitably cause instruments located to the left and the right of the stereo image to move toward the center.
  • Page 4 of the amplitudes of the sum and the difference of the input channels. We will not discuss the method for determining these steering directions in this paper, although Logic7 differs from standard decoders significantly in how this is done. These issues will be covered in another paper.
  • Page 5 In this paper we contrast the several different versions of the matrix elements. The earliest are elements from our 1989 patent. These elements were used in our first surround processor, and are identical to the elements of a standard surround processor in the left, center, and right channels.
  • Page 6 The function G(x) is described in the 89 patent, and specified in the ’91 patent. It varies from 0 to one as x varies from 0 to 45 degrees. When steering is in the left front quadrant (lr and cs are both positive) G(x) can be shown to be equal to 1-|r|/|l| where |r| and |l| are the right and...
  • Page 7 The 1996 AES paper corrected the amplitude errors in figure 3 by replacing the function G(x) in the matrix equations with sines and cosines: See Figure 4. For the left front quadrant LFL = cos(cs) + .41*G(lr) LFR = -sin(cs) Figure 3: the square root of the sum of the squares of lfl and lfr For the right front quadrant from the ’89 patent, scaled so the maximum value is one.
  • Page 8 Improvements to the left front matrix elements In March of 1996 we made several changes to these matrix elements. We kept the basic functional dependence, but added an additional boost along the cs axis in the front, and added a cut along the cs axis in the rear. The reason for the boost was to improve the performance with stereo music that was panned forward.
  • Page 9 for x = 1:24; % x has values of 1 to 24 corr(x) = 10^(3*(x-1)/(23*20)); % go up 3dB over this range corr1(x) = corr(x); for x = 25:46 % go back down for corr1 over this range corr(x) = 1.41; corr1(x) = corr(48-x);...
  • Page 10 The boost is only needed along the lr=0 axis. When lr is non zero the matrix element should not be boosted. This problem can be solved by using an additive term to the matrix elements, instead of a multiply. We define a new steering index, the boundary limited cs value with the following Matlab code: Assume both lr and cs >...
  • Page 11 % now define the sine and cosine tables, as well as the boost tables for the front sin_tbl = sin(a1); cos_tbl = cos(a1); cos_tbl_plus = cos(a1).*corr1(a+1); cos_tbl_plus = cos_tbl_plus-cos_tbl; % this is the one we use cos_tbl_minus = cos(a1)./corr(a+1); sin_tbl_plus = sin(a1).*corr1(a+1); sin_tbl_plus = sin_tbl_plus-sin_tbl;...
  • Page 12 These matrix elements are very nearly identical to the elements in the ’89 patent. Consider the case when a strong signal pans from left to rear. The ‘89 elements were designed so that there is complete cancellation of the output from the front left output only when this signal is fully to the rear (cs = -45, lr = 0).
  • Page 13 A linear interpolation could be used. In the processor used in Lexicon products, where multiplies are expensive, a better strategy is to define a new variable – the minimum of lr and cs: % new - find the boundary parameter bp = x;...
  • Page 14 we then define lfl and lfr in this quadrant as: LFL = cos(cs)/(cos(cs)+sin(cs)) – front_boundary_table(bp) + .41*G(lr) LFR = sin(cs)/(cos(cs)+sin(cs)) + front_boundary_table(bp) Note the correction of cos(cs)+sin(cs). When we divide cos(cs) by this factor we get the function 1-0.5*G(cs), which is the same as the Dolby matrix in this quadrant. In the right rear quadrant LFL = cos(cs)/(cos(cs)+sin(cs)) LFR = sin(cs)/(cos(cs)+sin(cs))
  • Page 15 One of the major design goals of the design of the Logic 7 matrix is that the loudness in any given output of unsteered material presented to the inputs of the decoder should be constant, regardless of the direction of a steered signal which is present at the same time. As explained previously, this means that the sum of the squares of the matrix elements for each output should be one, regardless of the steering direction.
  • Page 16 LRL = .71 – .71*G(lr) + .41*.71*G(cs) LRR = -.71 + .41*.71*G(cs) For the rear left LRL = .71*(1 - G(lr)+.41*G(-cs)) LRR = .71*(1 + .41*G(-cs)) (the right half of the plane is identical but switches lrl and lrr.) The rear matrix elements in the Dolby Pro-Logic are For the front left quadrant LRL = .71*(1 –...
  • Page 17 The lack of a level boost in the rear direction in the Dolby decoder means that during the calibration procedure the gain of the rear outputs will be raised by 3dB relative to the other outputs. In fact, for the Dolby decoder in practice: LRL = 1 –...
  • Page 18 When Ain and Bin are played through a conventional stereo system, the sound power in the room will be proportional to Lin^2 + Rin^2 + Cin^2. If all three components have roughly equal amplitudes, the power ratio of the center component to the left plus right component will be 1:2.
  • Page 19 These two figures show something mix engineers are often aware of – namely that a mix prepared for playback on a Dolby Pro-Logic system can need more center loudness than a mix prepared for playback in stereo. Conversely, a mix prepared for stereo will lose vocal clarity when played over a Pro-Logic decoder.
  • Page 20 For the right front quadrant the matrix elements are identical to the rear elements in the ’89 patent. The corrected elements as in the AES paper were used in the version of March 1997. First consider the dip in the sum of the squares along the cs=0 axis. This dip exists because of the use of G(lr) in LRR.
  • Page 21 % find the minimum of x or y xymin = x; if (xymin > y) xymin = y; if (xymin > 23) xymin = 23; note that xymin varies from zero to 22.5 degrees. If we multiply it by four, it will vary from zero to 90 degrees, and can be used below.
  • Page 22 As explained in the previous paper, these elements are additionally multiplied by the "tv matrix" correction, which reduces the amplitude when the steering in near the middle. This factor shows up in the figure below as a valley centered on zero steering. As of 7/31/97 the "tv matrix"...
  • Page 23 LRR = sin(-cs) = sric(-cs) To complete LRL and LRR over the range of cs = 0 to -22.5 we must add a gain reduction for the "TV MATRX" mode. Once again in the "TV matrix" mode we desire 3dB less output when steering is neutral, but rising to full value when the steering is more than 22.5 degrees to the rear.
  • Page 24 On the rear side the function given by the AES paper has the same end points, but is different in-between. The mathematical method in the AES paper provides the following equations for the Left Rear matrix elements over the range 22.5 < lr < 45: (remember that t = 45-lr) LRL = cos(45-lr)*sin(4*(45-lr))-sin(45-lr)*cos(4*(45-lr)) = sra(lr) LRR = -(sin(45-lr).*sin(4*(45-lr))+cos(45-lr).*cos(4*(45-lr))) = -srac(lr) If cs <= 22.5, lr can still vary from 0 to 45.
  • Page 25 The important point about this method is that it works when lr < 22.5, but it does not work when lr is larger. A better technique, which is used in the newest versions, is the interpolation technique, which is used for LRR. The March 1997 version uses an interpolation technique to find LRR.
  • Page 26 In the new system LRL is computed with interpolation, just as LRR for cs = 0 to 15 LRL = ((sra(lr) + (sra(lr)-GS(lr))*(15-cs)/15) + sri(-cs))*tvcorr(|lr|+|cs|); for cs = 15 to 22.5 LRL = (sra(lr) + sri(-cs))*tvcorr(|lr|+|cs|); Rear outputs during steering from Left Rear to Full Rear As the steering goes from left rear to full rear the elements follow the ones given in the AES paper, with the addition of the corrections for rear loudness.
  • Page 27 Since the matrix elements have symmetry about the left/right axis, the values of CL and CR for right steering can be found by swapping CL and CR. See Figure 17. Figure 17: The Center Left matrix element in the ’89 Patent (and Pro- Logic).
  • Page 28 The output of the center channel is thus 4.5dB less than the old output when steering in neutral, but rises to the old value when the steering is fully to the center. See Figure 18. Figure 18: The Center Left matrix element in the March 1997 version of Logic 7.
  • Page 29 However, if the input to the decoder consists of uncorrelated left and right channels to which an unrelated center channel has been added Ain = Lin + .71*Cin Bin = Rin + .71*Cin then as the level of Cin increases relative to Lin and Rin the C component of the L and R front outputs of the decoder is not completely eliminated unless Cin is large compared to Lin and Rin.
  • Page 30 We previously gave graphs showing the energy relations for a Dolby Pro- Logic decoder under various conditions. The Pro-Logic decoder is not optimal. We can do the same for our new decoder. See Figure 19 Figure 19; Solid curve - the center output channel attenuation needed for the new LFL and LFR if the energy of the center component of the input signal is to be preserved in the front three channels as steering increases toward the...
  • Page 31 Lets assume the center channel is reduced in level by 4.5 dB below the level in our ’89 decoder, or –7.5dB total attenuation. –7.5dB equals 0.42. The matrix elements for the center can be multiplied by this factor, and a new center boost function (GC) can be defined.
  • Page 32 gc(cs+1) = center_max; else gc(cs+1) = center_max*10^((cs-29)*center_rate2/(20)); if (gc(cs+1) > center_max2) gc(cs+1) = center_max2; This function is plotted in Figure 20. We can solve for the needed function for LFR if we assume functions for LFL, LRL, and LRR. We want to solve for the rate that the Cin component in the left and right outputs should decrease, and then design matrix elements, which...
  • Page 33 Power from the center PC = GC^2*(Lin^2+Rin^2) + 2*GC^2*Cin^2 Power from the rears depends on the matrix elements we use. We will assume the rear channels are attenuated by three dB during forward steering, and that LRL is cos(cs) and LRR is sin(cs).
  • Page 34 GP = LFL as before we can see the result in Figure 21. Figure 21: Solid curve - graph of GF needed for constant energy ratios with new center attenuation GC. Dashed curve is sin(cs)*corr1 (the previous LFR element). Dotted curve is sin(cs). Note that GF is close to zero until cs reaches 30 degrees, and then increases sharply.
  • Page 35 bcs = y-(x-1); if (bcs<1) % this limits the maximum value bcs = 1; else bcs = 47-y-(x-1); if (bcs <1) %> 46) bcs = 1; %46; The LFR element can now be written: % this neat trick does an interpolation to the boundary % the cost, of course, is a divide!!! if (y <...
  • Page 36 Panning error in the center output Figure 23 shows the new center left matrix element, using the new value of GC(cs). As it turns out, the new center function if we write it this way: CL = .42 - .42*G(lr) + GC(cs) CR = .42 + GC(cs) Figure 23: the center left matrix element with the new center boost function.
  • Page 37 Technical details of the encoder There are two major goals of the Logic 7 encoder. First, it should be able to encode a 5.1 channel tape in a way that allows the encoded version to be decoded by a Logic 7 decoder with minimal loss.
  • Page 38 With extensive listening several small problems with the first encoder were discovered. Many (but not all) of these problems have been addressed in the new encoder. For example, when stereo signals are applied to both the front and the rear terminals of the encoder at the same time, the resulting encoder output is biased too far to the front.
  • Page 39 shifted path for the rear channels is a 90 degree phase difference between the output channels A and B. This results in an unsteered signal, which is what we want. In discussions at the IRT Munich I discovered that there is a European standard surround encoder.
  • Page 40 Future improvements to the encoder are likely to include a feature similar to feature 2 above for the front channels. In the current encoder when the two front channels are out of phase the encoding will cause the decoder to place the sound in the rear. We intend to detect this condition and make the resulting output unsteered.
  • Page 41 References Patent # 4,862,502 – A four channel matrix surround decoder – David Griesinger, Inventor 1989 Patent # 5,046,098 – A four channel matrix surround decoder – Douglas Mandel, Inventor Patent # 5,109,419 – A six channel matrix surround decoder – David Griesinger, Inventor, 1992 Multichannel Matrix Surround Decoders for Two-Eared Listeners –...