How to Obtain a Good Stereo Sound Stage in Cars

Transcription

1 Page 1 How to Obtain a Good Stereo Sound Stage in Cars Author: Lars-Johan Brännmark, Chief Scientist, Dirac Research First Published: November 2017 Latest Update: November 2017 Designing a sound system for a car has a different success formula than designing a sound system for a living room. In a car, neither the loudspeakers or the people listening to them can be placed precisely according to the standard. Consequently, when listening to a recording, the stereo information is likely to be lost or, at least, severely distorted. Here we will discuss the motivation and basic principles behind a Dirac technology called Dirac Virtual Center, which was developed to solve one of the classic problems in automotive sound system tuning: the near-side bias problem. First we will take a look at the basic theory, along with a classical solution known from audio literature. We will then explore some practical limitations of the classical approach, and give an outline of what Dirac Virtual Center can do to make things work better.

2 Page 2 Stereo reproduction and the near-side bias problem For a stereo recording to be perceived as intended, it needs to be played back over a sound system that correctly reproduces the spatial information encoded in the stereo signal. In short, stereo recordings rely on a psychoacoustic principle called summing localization. This means that, when superimposed at the entrance of our ear canals, sound emitted by two loudspeakers can be perceived as coming from points in space where no actual sound source is located (so-called phantom sources). In particular, a mono signal which is equal in the left and right loudspeaker channels will be perceived as coming from a point in the center, directly in front of the listener. This is often referred to as the phantom center effect. In order for summing localization to work properly, it is required that the listener is located somewhere along a center axis between two identical loudspeakers with equal distance to both, as shown in Fig. 1. This requirement poses a problem in automotive sound system design since, in a car, neither the listeners or the loudspeakers can be placed exactly as dictated by the standard. Consequently, when a recording is listened to in a car, the stereo information will be lost or, at least, severely distorted. Figure 1: A listener located along a center axis between two identical loudspeakers with equal distance to both.

3 Page 3 For example, if a listener sits closer to left loudspeaker, the sound from the left loudspeaker will arrive at the listener slightly before the sound from the right loudspeaker. The resulting time difference between the left and right loudspeakers causes the perceived direction of sound to be heavily biased towards the left loudspeaker (see Fig. 2). Consequently, the mono component of the stereo signal will not be perceived as coming from straight in front of the listener, but almost solely from the left speaker. This collapse of the stereo panorama into the loudspeaker closest to the listener is often referred to as near-side bias. Figure 2: A listener sitting closer to the left loudspeaker, resulting in the sound from the left loudspeaker arriving at the listener slightly before the sound from the right loudspeaker. In an automobile, the listener is sitting either to the left or the right of the center axis. A simplified view of this case is shown in Fig. 3, where Listener 1 sits closer to the left loudspeaker, and Listener 2 sits closer to the right loudspeaker. In this example, a sound intended to be reproduced as coming from a point straight ahead of the listener will be experienced by Listener 1 as coming from the left side, and by Listener 2 as coming from the right side.

4 Page 4 Figure 3: Two listeners in an automobile, sitting to the left and the right of the center axis. In the case of a single listener located off from the center axis, the near-side bias problem can be solved by simply adding a delay to the signal path of the loudspeaker closest to the listener, so that the left and right signals arrive at the listener with equal delay. However, whenever there are two or more listeners, and the listeners are spread out relative to the center axis, adding a delay to one channel cannot solve the near-side bias problem for all listeners simultaneously. For example, if listeners are located according to Fig. 3, then adding a delay in the left channel may solve the near-side bias problem for the left listener. However, the right listener will then experience an even worse bias to the right side. Thus, it seems that the near-side bias problem has no solution in a multiple-listener scenario; that true stereo reproduction can be delivered, at most, to one listener at a time. Fortunately, it turns out that this is not true: A quite effective solution can actually be found, at least in theory, if we look at the problem in the frequency domain.

5 Page 5 Delay difference along the frequency axis: The IDP How does a delay between two signals manifest itself along the frequency axis? The delay difference between two channels of an audio system, experienced at a spatial position, can be described in the frequency domain by a phase difference function which is called the inter-loudspeaker differential phase (IDP), taking values between -180 and +180 degrees. An example of an IDP is shown in Fig. 4. The black line represents the IDP of a constant time delay that results in a position where the listener is 35.6 cm closer to the left loudspeaker than the right loudspeaker. A sound wave from the right loudspeaker then arrives with a delay of milliseconds, compared to if the same sound wave were emitted from the left loudspeaker. Figure 4: An example of Inter-loudspeaker Differential Phase (IDP). In order to understand why the IDP in Fig. 4 looks as it does, one needs to understand the concepts of phase and frequency, as explained by the following argument: At a single frequency, sound is by definition a sine wave and its location in

6 Page 6 time is determined by the phase lag in degrees, where 360 degrees corresponds to one full cycle of the wave. In Fig. 5, the thick blue curve illustrates a 440 Hz sine wave. The red curve has zero-degree phase lag relative to the blue curve (although its amplitude is half of that of the blue curve). The red and blue curves are therefore said to be in-phase. The green curve (which has the same amplitude as the blue) has a 180-degree phase lag relative to the blue curve, which also means they are the exact opposites of one another and are said to be out-of-phase. Finally, the black curve in Fig. 5 has a phase lag of 90 degrees, which is exactly between the phase lags of the red and green curves. It is thus neither fully in-phase or fully out-of-phase with the blue curve. Two sine waves can be said to be either predominantly in-phase or predominantly out-of-phase, if their relative phase lag is either within or outside the +/- 90 degree interval. Figure 5: Illustration of phase lag: The red, black and green curves have phase lags of 0, 90 and 180 degrees, respectively, relative to the blue curve. The frequency of a sinusoidal wave is the number of completed cycles per second, and for a 440 Hz sine wave it takes 1/440 s = 2.3 ms to complete one full cycle. A time delay of 2.3 ms is therefore equal to a phase lag of 360 degrees at 440 Hz. At 880 Hz, however, a 2.3 ms delay corresponds to two full cycles which implies a phase lag of 720 degrees. By the same argument, a 2.3 ms delay is equal to a phase lag of only 180 degrees if the frequency is 220 Hz.

7 Page 7 Thus, a constant time delay corresponds to a phase lag that is linearly proportional to frequency. Moreover, since a phase lag of 181 degrees is indistinguishable from a phase lag of 179 degrees, it can always be specified as a value between 180 and +180 degrees. A linearly increasing phase lag therefore contains jumps of 360 degrees with regular intervals. The above argument explains the behavior of the IDP in Fig. 4: The constant delay of ms between the left and right channels corresponds to an IDP that increases linearly with frequency, and every time it reaches +180 degrees it jumps down to -180 degrees. The IDP for two listeners in a car Let us now look again at the situation illustrated by Fig. 3, where two listeners are sitting in a car at each side of the center axis. Both listeners will experience a time delay between the loudspeaker channels, but in opposite order: Sound from the right channel reaches Listener 1 with a delay of ms relative to the sound from the left channel, and vice versa for Listener 2. The IDPs that describe this situation are shown in Fig. 6, where the black line is the IDP for Listener 1 and the gray line is the IDP for Listener 2. Figure 6: The IDPs for two listeners sitting in a car on either side of the center axis.

8 Page 8 The two IDP curves in Fig. 6 illustrate an interesting behavior: In some frequency intervals, for example Hz, the IDP stays inside +90 degrees for both listeners simultaneously (i.e., the sound waves are predominantly in-phase). In other intervals, the IDP is outside +90 degrees for both listeners simultaneously (i.e., the sound waves are predominantly out-of-phase). Manipulating the IDP: From out-of-phase to in-phase In an ideal listening situation, such as that of Fig. 1, the IDP is strictly zero and the loudspeaker channels are 100% in-phase at all frequencies. Of course, a similar all-zero IDP would also be desired in the automobile case, but for reasons given above this can never be fulfilled for two listeners at the same time. Nevertheless, an interesting compromise can be obtained if we can get rid of the out-of-phase intervals in Fig. 6, so that the IDP stays within +90 degrees (i.e., the left and right channels become predominantly in-phase) at all frequencies for both listeners. This can be realized by applying artificial phase-shifts to the left and right channels, using so-called all-pass filters. The task of these filters is to add a phase difference of 180 degrees between the channels in the out-of-phase intervals and to do nothing in the intervals where the channels are already predominantly in-phase. This could, for example, be accomplished by a pair of filters whose phase response are as illustrated in Fig. 7: If we shift the phase by +90 degrees in one channel (black line) and by -90 degrees in the other channel, the IDP between the channels will be shifted by 180 degrees. Figure 7: Phase responses accomplished by a pair of all-pass filters. The thick black curve is the phase response of the filter applied to the left channel, and the thin gray line is the phase response of the filter applied to the right channel.

9 Page 9 Applying the filters of Fig. 7 to the left and right channels results in IDPs that stay within +90 degrees at all frequencies, as shown in Fig. 8. We have thereby managed to create a loudspeaker pair that is predominantly in-phase at all frequencies for two listeners simultaneously, and this turns out to be good enough for eliminating the near-side bias problem; the out-of-phase relations between the channels have been removed so that a mono sound from the left and right speakers adds up coherently at both listener positions. Figure 8: Applying the filters of Fig. 7 to the left and right channels results in IDPs that stay within +90 degrees at all frequencies Theory vs. practice Based on the discussion so far, it seems that the near-side bias problem can be solved very easily, simply by adding phase-shifting filters (like those in Fig. 7) to the left and right channels. However, the analysis that led us to this classical solution is based on some quite unrealistic assumptions that deserve further examination. One assumption is that the sound from the opposite-side loudspeaker is simply a delayed copy of the sound wave from the same-side loudspeaker. Since the acoustic environment in a real car is extremely complex and not at all as symmetric as the simple sketch in Fig. 3 suggests, it turns out that this assumption does

10 Page 10 not hold in practice. The neat and tidy IDP curves of Fig. 6 do not represent anything that would be encountered in reality; if one computes the IDP based on measurements in a real car, the curves will rather look like in Fig. 9. Given these measured IDPs, it is no longer obvious if and how the situation can be improved with all-pass filters. Moreover, what should be done in the cases when there are three or four listeners, and thus three or four IDP curves to consider, instead of only two? Figure 9: The IDP based on measurements in a real car Another practical aspect to consider is the side effects that may result from introducing filters with such dramatic phase shifts, as those in Fig. 7. A drawback of defining filters in the frequency domain is that we then only define how the filters respond to single stationary sinusoids, while the response to transient signals such as, e.g., a drum beat, is neglected. In fact, filters such as those in Fig. 7 generally introduce quite severe time-smearing artifacts, both backwards and forwards in time, that would be immediately audible when listening to drums or other transient sounds. In order to be of relevance to the practicing audio engineer, we must take such real-world aspects into account. This has been the ambition behind the development of Dirac Virtual Center.

11 Page 11 Dirac Virtual Center So, what is Dirac Virtual Center and what makes it different from the classical solution described above? First of all, the reason why we call this filtering algorithm Dirac Virtual Center is that it has the perceptual effect of filling in a hole in the middle of the sound stage, creating a continuous stage that covers the whole space between the left and right loudspeakers, as if an invisible extra loudspeaker were placed at the center of the dashboard of the car. Just like the classical solution, the Dirac Virtual Center algorithm treats the near-side bias problem by applying phase-shifting filters to a pair of audio channels. However, the design steps, performance criteria, and the scope of application differ considerably from the classical approach. The primary features of Dirac Virtual Center are as follows: Instead of deriving the IDPs based solely on distances between loudspeakers and listeners, Dirac Virtual Center is based on measurements in the real acoustic environment. Dirac Virtual Center filters are thus based on real data such as that in Fig. 9.

12 Page 12 The measurement-based approach allows adaptation to very complex acoustic circumstances, accommodating for asymmetric environments and different loudspeaker configurations. Virtual Center has no formal restriction on the number of listeners; filters are designed to produce the smallest possible IDP on average, for any number of listeners. Spatial robustness: The measurement positions can be selected so as to accommodate for listeners head movements, thereby preventing the over-fitting of filters to a predetermined positioning of listeners. The frequency range of operation can be selected by the tuning engineer. Cautious filters: Overly aggressive filters are avoided through constraints that limit the time-smearing artifacts to a perceptually acceptable level. Filter pre-echoes are not allowed. Flexible implementation: Dirac Virtual Center finds the best solution under given complexity constraints. It can be implemented using either low-complexity biquad filters or high-order FIR filters. In cases where computational resources are very limited, a constraint can be put on the maximum allowed number of biquad filters. The Dirac Virtual Center algorithm is currently available to customers in the automotive field. To learn more, visit dirac.com/dirac-virtual-center/