Stereo Reproduction and the Near-Side Bias Problem
Multichannel audio recordings, and in particular recordings in 2-channel stereo, rely to a great extent on the principle of summing localization [1] to be correctly perceived when played back over a pair of loudspeakers. In order for the summing localization principle to work as intended, it is required that the listener is located between two identical loudspeakers, with equal distance d to both loudspeakers, as illustrated in FIG. 1.
Such a symmetrical arrangement of loudspeakers and listener makes it possible for the listener to experience a stereo panorama, or sound image, when a stereo recording is played back through the loudspeakers (that is, when the left and right channels of the recording are played back through the left and right loudspeakers, respectively). Various components of the stereo signal are then perceived as sound sources located somewhere between the loudspeakers. In particular, a mono signal, which is equal in left and right channels, will be perceived as coming from a point in the center, straight in front of the listener. This is the so-called phantom center effect.
If the listener is not positioned along the center axis between the loudspeakers, as in FIG. 1, but is closer to one of the loudspeakers, then the stereo panorama will be incorrectly perceived. For example, if the listener's distance d1 to the left loudspeaker is shorter than the distance d2 to the right loudspeaker, then the sound from the left loudspeaker arrives at the listener with a shorter time delay than the sound from the right loudspeaker. Due to the resulting time difference between the left and right loudspeakers, the perceived direction of sound will be heavily biased towards the left loudspeaker, see FIG. 2. In particular, the mono component of the stereo signal will in such a scenario no longer be perceived as coming from straight ahead 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. The most common and well known example of near-side bias occurs when listening to stereo recordings in an automobile, where the listener is situated either to the left or to the right of the center axis. A schematic view of the automobile example is shown in FIG. 3, where Listener 1 sits closer to the left loudspeaker, and Listener 2 sits closer to the right loudspeaker. Thus, in the example of FIG. 3, a sound that is intended to be reproduced as coming from a point straight ahead of the listener will be experienced by Listener 1 as corning from the left side, and by Listener 2 as coming from the right side.
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, commonly referred to as inter-loudspeaker differential phase (IDP), taking values between −180 and +180 degrees [5], an example of which is shown in FIG. 5. The IDP allows for a more general description of the time difference between channels, in the sense that it can accommodate for time delays that are frequency dependent.
The IDP between two audio channels C1 and C2 can be determined either by using information from a single point in space, or by using information from a pair of points in space. In the first case, the IDP is obtained by comparing the acoustic transfer function of channel C1 with that of channel C2 at the same point. In the latter case, the IDP is obtained by comparing the transfer function of channel C1 in one point with the transfer function of channel C2 at another point. A listener position, for which the IDP between two channels C1 and C2 is defined, can thus be associated with either one single point or a pair of points in space.
In an ideal, theoretically constructed version of the automobile example, one assumes that the two loudspeakers and the listening environment are perfectly symmetrical, and that two listeners are positioned symmetrically on each side of the center axis, as illustrated in FIG. 4, where the left listener is a distance |d1−d2| closer to the left loudspeaker than to the right loudspeaker, and vice versa for the right listener. The delay difference between the loudspeaker channels experienced by the two listeners can then be described in the frequency domain by two IDP functions, as illustrated in FIG. 5. In the particular example shown in FIG. 5, the loudspeaker and listener positions were such that |d1−d2|=35.6 cm. It can be seen in FIG. 5 that the IDP functions in this case either increase or decrease linearly with frequency, depending on which side of the center axis the listener is situated (the black line is the phase difference at the left listener position and the grey line is the IDP at the right listener position). It should be noted that IDP functions, such as those in for example FIG. 5, may be considered to be continuous even if they appear to contain discontinuous jumps of 360 degrees at some frequencies. This is because of the ambiguity in how phase angles are represented: an angle of +190 degrees is equivalent to an angle of −170 degrees, an angle of 360 degrees is equivalent to an angle of 0 degrees, and so on. It thus makes sense to describe an IDP or a phase curve as for example linearly increasing even if it decreases by a discontinuous jump of 360 degrees at some frequencies.
It can further be seen in FIG. 5 that the frequency axis can be divided into sequential frequency bands where both listeners experience either an IDP within the interval of ±90 degrees, or an IDP of more than ±90 degrees. In particular, there are frequencies (0 Hz, 966 Hz, 1932 Hz, etc.) where the IDP is zero at both listener positions. This happens when the distance difference |d1−d2| corresponds to an integer multiple of the acoustic wavelength, so that a mono signal at that frequency, emitted by both loudspeakers, will yield a maximally constructive interference at both listener positions. Similarly, there are frequencies (483 Hz, 1449 Hz, 2415 Hz, etc.) where the distance difference |d1−d2| corresponds to an odd number of half wavelengths, in which case a mono signal will yield a maximally destructive interference at both listener positions.
At frequencies where the IDP at both listener positions is limited to between ±90 degrees, the system is said to be predominantly in-phase, and at frequencies where both IDPs are outside of the interval ±90 degrees, the system is said to be predominantly out-of-phase.
The presence of sequential in-phase and out-of-phase frequency bands described above adds an undesired spectral distortion (so-called comb filtering) to the reproduced sound which, together with the near-side bias problem, significantly deteriorates the listening experience.
Possible Remedies to Near-Side Bias
In the case of one single listener located somewhere off from the center axis, the near-side bias problem can be corrected to a great extent if a delay is added 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, similarly to the situation when the listener is located on the center axis between the loudspeakers.
However, if there are two or more listeners, and the listeners are located at separate spatial positions, then adding a delay to one channel cannot resolve the near-side bias problem for all listeners. For example, if one listener is closer to the left loudspeaker and another listener is located closer to the right loudspeaker (as in FIG. 4), then a delay in the left channel will solve the near-side bias problem for the left listener, but the right listener will experience an even worse bias to the right side.
A previously proposed solution to the near-side bias problem is based on viewing the delay differences as phase difference functions, often referred to as inter-loudspeaker differential phase (IDP) functions, in the frequency domain, as described in the previous section. The idea is then to use phase shifting filters which add a phase difference of 180 degrees to the channels, thereby changing the IDP by 180 degrees, in one or several of those frequency bands where the system is predominantly out-of-phase [2, 3, 4, 5]. The adding of a phase difference of 180 degrees to the channels can be accomplished in many different ways; for example by applying a filter that shifts the phase 180 degrees in the left channel and leaving the right channel unprocessed. Alternatively, one can add +90 degrees to one channel and −90 degrees to the other, as suggested in for example [2]. The phase responses of such filters are shown in FIG. 6, where the black line is the desired phase response of the left channel filter, and the grey line is the desired phase response for the right channel filter. For a symmetrical situation such as in FIG. 4, the IDP functions that result from applying such filters to the system are shown in FIG. 7, where the black line is the IDP at the left listener position and the grey line is the IDP at the right listener position. Comparing FIG. 5 and FIG. 7, one can observe that the system has changed from alternating between predominantly in-phase and out-of-phase in sequential frequency bands, to being predominantly in-phase for all frequencies. Since the processed system is now predominantly in-phase everywhere, the comb filtering effect is alleviated, and a mono sound from the left and right speakers will add up coherently at both listener positions. A number of publications and patents exist that in one way or another treat the near-side bias problem using methods as described above, that is, by identifying frequency bands which are classified according to whether two audio channels are predominantly in-phase or predominantly out-of-phase at both listener positions. A phase adjustment, adding a phase difference of 180 degrees to the channels, is then performed in the frequency bands where the channels are predominantly out-of-phase [2, 3, 4].
Thus, in order to solve the idealized near-side bias problem of FIG. 4, where it is assumed that listeners are positioned symmetrically off the center axis and that the IDP depends only on the delay difference between channels, it is sufficient to apply methods of prior art. That is, to realize an additional phase difference of 180 degrees between the channels, by means of applying phase shifting filters to one or both of the channels, in frequency bands where the system in predominantly out-of-phase.
In nearly all real-world cases, however, listeners may be positioned asymmetrically with respect to the center axis, and the IDP at various positions does not depend solely on the loudspeaker-listener distances but is a more complicated function of frequency.