284  Spatial Sound

are applicable to the latter case (Zotter et al., 2014). The spatial extension of virtual sources can be improved by distributing the neighboring band contents into far away directions. Therefore, some constraints should be applied to the randomly spatial distribution of subband contents.

The aforementioned methods may be inappropriate for controlling the vertical spread of the perceived virtual source because the mechanisms of spatial hearing in the vertical direction are different from those in the horizontal directions. For example, changing the interchannel correlation between the signals of two loudspeakers in the median plane or other cones of confusion does not effectively alter IACC. The psychoacoustic experiment by Gribben and Lee (2018) indicated that for a pair of loudspeakers arranged at elevation ϕ = 0° and 30° in the vertical planes of θ = 0°, ±30° and ±110° respectively, the perceived virtual source spreads vertically with the decrease of interchannel correlation at frequencies around 0.5 kHz and above. The loudspeaker configuration in this experiment is basically consistent with the 9.1-channel system in Figure 6.13. Pulkki et al. (2019) experimentally examined the summing spatial auditory perception caused by a pair of loudspeakers in the median plane with uncorrelated pink noise stimuli and without head movement. The result indicated that two sources (loudspeakers) can be perceived individually when they are separated in elevation by 60° or more. When the two sources are separated by less than 60°, they are perceived inaccurately, biased, and spatially compressed but nevertheless not as point-like virtual sources. Overall, dynamic cues and spectral cues for vertical localization may also contribute to the vertical spread of the perceived virtual source, and the underlying mechanism should be further studied.

The perceived depth of an auditory event (source or scene) refers to the overall perceived front-back dimensionality or distance of this particular event. It is closely related to but different from the perceived distance of the auditory event. In practice, the perceived depth is controlled by changing the reflections in reproduction. Further studies on the mechanism of controlling the perceived depth are also needed.

7.4.3  Simulation of a moving virtual source

In the preceding discussions, virtual sources are assumed to be static or immobile. In practical program production, a moving virtual source should be stimulated on a given trajectory in some instances. Chowning (1971) first simulated a moving virtual source in a quadraphone with pair-wise amplitude panning. Similar methods are applicable to stereophonic and other multichannel loudspeaker configurations with different signal mixing methods.

Generally, a moving sound source leads to the following time-dependent changes:

1.Change in the source direction with respect to a listener

2.Change in the source distance with respect to a listener

3.Change in reflected sounds in a reflective environment

4.Doppler frequency shift of a fast-moving sound source

Accordingly, these changes should be simulated for a moving virtual source in sound reproduction.

The instantaneous position of a moving sound source is specified by its time-varying distance rS(t), azimuth θS(t), and elevation ϕS(t) with respect to a listener. The functions rS(t), θS(t), and ϕS(t) are a set of parametric equations for the trajectory of a moving sound source. Given the signal panning or mixing method in a stereophonic or multichannel sound, the functions or mapping between a target source direction and channel signals are known. The

Microphone and signal simulation techniques  285

normalized amplitudes of channel signals are changed according to time-varying θS(t) and ϕS(t) to simulate a moving virtual source in a freefield at a constant distance and instantaneous direction of θS(t) and ϕS(t). For example, the time-varying normalized amplitudes of three frontal channel signals are given by letting ϕS(t) = 0°, I S t and substituting these time-dependent parameters into Equation (7.4.2) to simulate a moving virtual source across the three frontal loudspeakers in a 5.1-channel configuration with pair-wise amplitude panning. As stated in Section 5.2.2, for a 5.1-channel loudspeaker configuration and a fixed head oriented to the front, pair-wise amplitude panning fails to recreate a stable lateral virtual source. The virtual source in the rear region is also blurry and unstable. However, in practical program production, pair-wise amplitude panning is often used to recreate a moving virtual source in lateral and rear directions. For a fast-moving virtual source, human hearing is less sensitive and thus more tolerant to jumping in a virtual source direction.

In addition to pair-wise amplitude panning, other signal mixing methods can be used to recreate a moving virtual source in various multichannel sound reproductions. For pair-wise amplitude panning, the signals of a moving virtual source are previously recreated by manually manipulating a pan-pot in a console. Currently, signals of a moving virtual source can be easily created with the software of digital signal processing in accordance with the rules of signal mixing.

Direct sound magnitude should vary with the source distance to simulate a time-varying- distance virtual source. The magnitude of direct sound from a point source is inversely proportional to the source distance with respect to a listener, and the normalized amplitude or gain of all channel signals should be scaled with a factor of 1/rS(t). For spatial sound based on sound field reconstruction, such as near-field-compensated higher-order Ambisonics discussed in Section 9.3.4, a distance-dependent curve wavefront may be simulated by manipulating the time-varying parameter rS(t) of a target distance in channel signals.

In a reflective environment, the change of a source position alters the directions, delays (distances), and magnitudes of all reflections with respect to the listener. The magnitude spectra of reflections also depend on the source position. Strictly, all these changes should be considered in the simulation of a moving virtual source. However, exactly simulating all these changes is actually difficult. For some applications requiring high accuracy, such as scientific studies on a virtual auditory environment, changes in several proceeding early discrete reflections caused by a moving sound source are simulated. That is, the instantaneous delays, directions, and power spectra of early discrete reflections are evaluated and simulated according to the geometrical acoustic model of a room (Section 7.5.5). The resultant reflected signals are fed to channels in terms of certain signal mixing rules.

In a diffused reverberation field, numerous reflections reach a listener from various directions at every instant. Human hearing is unable to detect the change in each individual reflection. In practical program production, reflections are usually approximated as a diffused field, and the change in the statistical characteristics of the sound field is simulated. For example, the direct-to-reverberant energy ratio of various source distances is evaluated with Equation (1.2.25), and the relative gain of direct sound with respect to that of artificial reverberation is changed to simulate the change in the direct-to-reverberant energy ratio caused by the variation in the source distance. This method simulates the relative change in direct and reverberant sound, providing important perceptual information on the variation in the distance of a moving virtual source.

The Doppler frequency shift should be considered in the simulation of a fast-moving virtual source in multichannel sounds. If a listener is immobile and a source moves at velocity vS, then the projections of vS to the line that connects the source and the listener are vS1. For a