Two-channel stereophonic sound 83
Figure 2.5 Trade-off curves of the combined ICLD and ICTD by Williams. (adapted from Williams 2013).
2.1.4 Virtual source created by interchannel time difference
As stated in Section 1.7.1, for some signals with transient characteristics, the method of interchannel time difference (ICTD) or a combination of ICTD and ICLD can be used to recreate a virtual source. The trade-off curves of the combined ICLD and ICTD are applicable to analyze the direction of the summing virtual source. Figure 2.5 illustrates an example of these curves, which were derived by Williams (1987) through interpolation of the original data obtained by Simonson (1984) and called Williams curves. The original data are measured through a localization experiment by using the stimuli of speech and maracas. The trade-off curves for standard loudspeaker configuration with 2θ0 = 60° and three target azimuths of θI = 10°, 20°, and 30° are shown in the figure.
The localization results of the combined ICLD and ICTD vary among studies. For example, Figure 1.26 indicates that the mean perceived virtual source azimuth θI measured by Simonsen for an ICLD only is larger than those in the two other curves. As stated in Section 1.7.1, the perceived virtual source azimuth depends on stimuli and other experimental conditions. The curves in Figure 2.5 are often used in practice because Simonsen’s data are measured from natural stimuli rather than artificial ones. These differences have been observed, and the trade-off curves of the combined ICLD and ICTD have been remeasured using musical stimuli in some studies (Lee, 2010).
ICTD-based summing localization in two or more loudspeakers is a psychoacoustic phenomenon, but physical interpretations or models for this phenomenon have not been developed yet.This situation is different from the case of ICLD-based summing localization. Similar to the precedence effect, a neurophysiologic experiment on cats has demonstrated that the responses of inferior colliculus neurons caused by ICTD signals match those caused by the target source at the summing localization direction (Yin, 1994).Therefore, ICTD-based summing localization may be interpreted at the level of the neurophysiology of hearing.
2.1.5 Limitation of two-channel stereophonic sound
The spatial information of sound includes the localization information of sound sources and the comprehensive spatial information of environment reflections. In two-channel stereophonic sound, the spatial information of sound is represented by the relative relationship
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between two channels or loudspeaker signals with various manners, resulting in various subjective perceptions or sensations in reproduction.
The directional localization information of the target source can be represented by the ICLD between two-channel signals. This presentation is termed amplitude stereophonic sound, level-difference stereophonic sound, or intensity stereophonic sound. The theory of amplitude stereophonic sound is relatively mature. As stated in previous sections, at low frequencies with f ≤ 0.7 kHz, the interaural phase delay difference ITDp created by in-phase loudspeaker signals with ICLD only matches with that of the target source. Within a frequency range of 0.7–1.5 kHz, ITDp created by ICLD is qualitatively consistent with but quantitatively deviates from that of the target source, resulting in frequency-dependent perceived source direction. At high frequencies (above 1.5 kHz), ICLD may result in interaural localization cues (such as ILD) that are quantitatively inconsistent with those of the target source. However, ICLD does not lead to conflicting interaural localization cues at high frequencies. For wideband stimuli with a low-frequency component below 1.5 kHz, ITDp dominates azimuthal localization. Therefore, ICLD yields an appropriate localization perception of a virtual source.
Summing localization with two loudspeakers can be further analyzed in terms of the reproduced sound field. Figure 2.6 illustrates the wave front amplitude of the superposed sound pressures created by two stereophonic loudspeakers (approximated as point sources) with identical signal amplitudes AL = AR. The distance between the loudspeakers and the origin of the coordinate is r0 = 2.5 m. The span angle between two loudspeakers is 2θ0 = 60°. Figure 2.6(a) and 2.6(b) present the results of the harmonic wave at f = 0.5 kHz and 1.5 kHz, respectively. In the regions adjacent to either of the loudspeakers, the wavefront is dominated by the spherical wave generated by the loudspeaker. Within a small region adjacent to the central line (bounded by the two dash lines in the figures), the superposed wavefront is approximated to that of a spherical wave incidence from the frontal direction θI= 0°. In the far-field distance, the superposed wavefront is further approximated to that of a plane wave incidence from the frontal direction. However, apart from the adjacent region of the central line, the superposed wavefront is no longer a plane or spherical wave. As frequency increases, the width of the region for reconstructing the plane or spherical wavefront narrows. As the receiver position moves toward the back, the span angle between two loudspeakers with respect to the receiver
(a) f = 0.5 kHz |
(b) f = 1.5 kHz |
Figure 2.6 Wavefront amplitude of the superposed sound pressures in stereophonic reproduction with identical signal amplitudes (a) f = 0.5 kHz; (b) f = 1.5 kHz.
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position reduces, and the width of the region for reconstructing the plane or spherical wavefront broadens. With an appropriate span angle between two loudspeakers and within the low-frequency range of f ≤ 0.7 kHz, the amplitude stereophonic sound can reconstruct the target plane or spherical wavefront in a region whose width matches the size of the head (Makita, 1962; Bennett et al., 1985). Therefore, the two-channel amplitude stereophonic sound is a typical example of a spatial sound based on the sound field approximation and psychoacoustics. Overall, the two-channel amplitude stereophonic sound can recreate a relatively authentic and natural virtual source between two loudspeakers.
The frequency-independent interchannel phase difference gives rise to conflicting interaural localization cues and consequently degrades the perceived quality of a virtual source or prevents localization. Two-channel out-of-phase signals may be applicable to recreate an outside-boundary virtual source and then broadens the frontal stereophonic stage. However, the resultant virtual source position is unstable as frequency varies. It is also unstable even when the listening position slightly changes (Section 2.4.2). Moreover, in some cases, twochannel out-of-phase signals may create an unnatural auditory event with an uncertain position.
For some signals with transient characteristics, the method of ICTD or a combination of ICLD and ICTD can be used to recreate a virtual source. This method has been applied to design some microphone techniques for two-channel stereophonic recording. The ICTDbased method is termed time (difference) stereophonic sound. The combination method of ICLD and ICTD is termed a combined amplitude and time stereophonic sound or intensity and time difference stereophonic sound. In Section 2.1.4, physical models for ICTD-based or a combination of ICLD–ICTD-based summing localization are unavailable. This situation is different from ICLD-based summing localization. Therefore, the time stereophonic sound and the combined amplitude and time stereophonic sound are usually designed on the basis of psychoacoustic experimental results, such as the Williams curves shown in Figure 2.5 (Williams, 1987; Wittek and Theile, 2002). Generally, the perceived quality of the virtual source created via the ICTD-based method is inferior to that created via the ICLD-based method. For practical (wideband) stimuli, the ICTD-based virtual source is blurry, with less naturalness and authenticity. The perceived direction of the virtual source also depends on the spectra and transient characteristics of the stimuli.
Overall, for any loudspeaker signal method, the two-channel stereophonic sound is unable to recreate the spatial information in the full horizontal plane, to say nothing of recreating the spatial information in a fully three-dimensional space. Generally, two-channel stereophonic sound can recreate spatial information within a frontal-horizontal sector bounded by two loudspeakers. Although the case of an outside-boundary virtual source is considered, twochannel stereophonic sound is theoretically able to recreate spatial information extending to the frontal-horizontal quadrants at most. However, the outside-boundary virtual source is usually unstable. These factors are limitations of two-channel stereophonic sound. For many practical applications, such as music reproduction or television sound, if a listener’s attention is focused to the frontal direction, two-channel stereophonic sound may meet the requirements to some extent.
The analysis in this section focuses on the methods for representing or encoding the directional information of target virtual sources in two-channel stereophonic signals. The spatial position of an actual sound source or virtual source is specified by its direction and distance. Although auditory distance perception is biased, the relative perceived distance of auditory events in spatial sound reproduction may be controlled by using some appropriate signal simulation and microphone techniques. Various possible cues for auditory distance perception discussed in Section 1.6.6 may be used to control auditory distance perception in reproduction. However, altering the ratio of direct and reflected sound energy in signals is a major
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means to control the perceived distance in two-channel stereophonic and multichannel sound reproduction. Increasing the relative proportion of reflected sound creates a more distant auditory event or perception.
In Section 1.8, early lateral reflections and late diffuse reverberation are important for the sensations of an auditory source width and listener envelopment in a concert hall. Limited by its ability, two-channel stereophonic sound is unable to recreate the spatial information of these reflections exactly. Appropriate microphone and signal simulation techniques improve the perceived performance of reflected sound in stereophonic sound reproduction to some extent. Some psychoacoustic methods are available for recreating sensations similar to those caused by the reflections in a hall. For example, the perceived virtual source width can be controlled by introducing a small interchannel phase difference between two channel signals. In Section 1.7.3, the auditory event broadens and becomes blurred because of the reduction of positive interchannel correlation.
The aforementioned methods are applicable to represent the spatial information in twochannel stereophonic signals and then recreate various target auditory perceptions or sensations in reproduction. Some methods for a two-channel stereophonic sound are not based on strict acoustic theory. Instead, they are based on psychoacoustic experimental results, relevant experience, and requirements for practical uses. This problem is dealt with in the two-channel stereophonic recording discussed in the next section and the multichannel surround sound discussed in the succeeding chapters. It is also a feature of various spatial sound techniques based on sound field approximation and psychoacoustic principles.
2.2 MICROPHONE AND SIGNAL SIMULATION TECHNIQUES FOR TWOCHANNEL STEREOPHONIC SOUND
Two-channel stereophonic sound is popular in consumer use. It is usually applied to reproduce music (including classical and pop music), speech, and other program materials. However, the ability of a two-channel stereophonic sound to transmit and reproduce the spatial information of a sound field is limited. The key is the manner by which this limited ability is utilized properly to transmit and reproduce the desired information (including the localization information of direct sound and the comprehensive information of reflections) essential for auditory perceptions as much as possible.
As the first stage in the system chain of a two-channel stereophonic system, signal recording or picking up involves using some appropriate microphone techniques to capture the spatial information of an on-site sound field. Signal simulation or synthesis is a process by which appropriate signal processing techniques are utilized to artificially create the desired spatial information of sound. In accordance with the basic principle of stereophonic sound discussed in Section 2.1, the spatial information of sound is encoded into two-channel stereophonic signals. Various techniques for stereophonic signals recording and simulation have been developed and can be roughly classified into four categories.
The first category is the coincident microphone technique. It was developed on the basis of Blumlein’s patent in the 1930s (Blumlein, 1931). A pair of spatially coincident microphones with appropriate directivity is used to capture stereophonic signals. The directivity of a microphone pair encodes the direction information of a source into two channel signals with direction-dependent ICLD only. The coincident microphone technique can be further divided into two sub-categories, i.e., XY and mid-side (MS) microphone pair techniques.