5.8 Other Spatial Effects

5.8.1 Digital Versions of Classic Reverbs

In the past, before the era of digital signal processing, many systems were used to create a reverberation effect. In studios the common way was to replay the recorded signals in a reverberant room or a corridor and record it again in that particular space. In addition, plates and springs were applied to create a decaying tail to the sound. Recently, researchers have modeled the physical principles of old-school reverberators and they have proposed digital implementations of them. For example, plate reverbs have been implemented with finite difference schemes [BAC06, Bil07]. An extension to digital plate reverbs to handle objects of any shape has been made with modal synthesis methods. Thus, simulations of the vibration of many different shapes and materials can be performed in real time [Max07]. Spring reverbs have also been modeled and it seems that efficient implementation can be achieved with parallel waveguides, which include dispersive all pass filters [ABCS06].

5.8.2 Distance Effects

In digital audio effects, the control of apparent distance can be effectively introduced even in monophonic audio systems. In fact, the impression of distance of a sound source is largely controllable by insertion of artificial wall reflections or reverberant room responses.

There are not reliable cues for distance in anechoic or open spaces. Familiarity with the sound source can provide distance cues related with air absorption of high frequency. For instance, familiarity with a musical instrument tells us what is the average intensity of its sound when coming from a certain distance. The fact that timbral qualities of the instrument will change when playing loud or soft is also a cue that does help the identification of distance. These cues seem to vanish when using unfamiliar sources or synthetic stimuli that do not resemble any physical-sounding object. Conversely, in an enclosure the ratio of reverberant to direct acoustic energy has proven to be a robust distance cue [Bla97]. It is often assumed that in a small space the amplitude of the reverberant signal changes little with distance, and that in a large space it is roughly proportional to [Cho71]. The direct sound attenuates as if spherical waves are propagated.

A single reflection from a wall can be enough to provide some distance cues in many cases. The physical situation is illustrated in Figure 5.18a, together with the signal-processing circuit that reproduces it. A single delay line with two taps is enough to reproduce this basic effect. Moreover, if the virtual source is close enough to the listening point, the first tap can be taken directly from the source, thus reducing the signal-processing circuitry to a simple non-recursive comb filter. To be physically consistent, the direct sound and its reflection should be attenuated as much as the distance they travel, and the wall reflection should also introduce some additional attenuation and filtering in the reflected sound, represented by the filter Hw in Figure 5.18b. The distance attenuation coefficients of Figure 5.18b have been set in such a way that they become one when the distance goes to zero, just to avoid the divergence to infinity that would come from the physical laws of a point source.

Figure 5.18 Distance rendering via single wall reflection: (a) physical situation, (b) signal-processing scheme

From this simple situation it is easy to see how the direct sound attenuates faster than the reflected sound, as long as the source approaches the wall.3 This idea can be generalized to closed environments adding a full reverberant tail to the direct sound. An artificial yet realistic reverberant tail can be obtained just by taking an exponentially decayed gaussian noise and convolving it with the direct sound. The reverberant tail should be added to the direct sound after some delay (proportional to the size of the room) and should be attenuated with distance to a lesser extent than the direct sound. Figure 5.19 shows the signal-processing scheme for distance rendering via room reverberation.

Figure 5.19 Distance rendering via room reverberation: (a) physical situation, (b) signal-processing scheme

The following M-file allows one to experiment with the situations depicted in Figures 5.18 and 5.19, with different listener positions, provided that x is initialized with the input sound, and y, z, and w are long-enough vectors initialized to zero.

5.8.3 Doppler Effect

Movements of the sound sources are detected as changes in direction and distance cues. The Doppler effect is a further (strong) cue that intervenes whenever there is a radial component of motion between the sound source and the listener. In a closed environment, radial components of motion are likely to show up via reflections from the walls. Namely, even if a sound source is moving at constant distance from the listener, the paths taken by the sound waves via wall reflections are likely to change in length. If the source motion is sufficiently fast, in all of these cases we will have transpositions in frequency of the source sound.

The principle of the Doppler effect is illustrated in Figure 5.20, where the listener is moving toward the sound source with speed cs. If the listener meets fs wave crests per second at rest, it ends up meeting crests at the higher rate

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when the source is moving. Here c is the speed of sound in air. We usually appreciate the pitch shift due to Doppler effect in non-musical situations, such as when an ambulance or a train is passing by. The perceived cue is so strong that it can evocate the relative motion between source and listener even when other cues indicate a constant relative distance between the two. In fact, ambulance or insect sounds having a strong Doppler effect are often used to demonstrate how good a spatialization system is, thus deceiving the listener who doesn't think that much of the spatial effect is already in the monophonic recording. Research into psychoacoustics has also shown how the perception of pitch can be strongly affected by dynamic changes in intensity, as they are found in situations where the Doppler effect occurs [Neu98]. Namely, a sound source approaching the listener at constant speed produces a rapid increase in intensity when it traverses the neighborhood of the listener. On the other hand, while the frequency shift is constant and positive before passing the listener, and constant and negative after it has passed, most listeners perceive an increase in pitch shift as the source is approaching. Such apparent pitch increase is due to the simultaneous increase in loudness.

Figure 5.20 Illustration of the Doppler effect.

The Doppler effect can be faithfully reproduced by a pitch shifter (see Chapter 6) controlled by the relative velocity between source and listener. In particular, the circuit in Figure 6.13 can be used with sawtooth control signals whose slope increases with the relative speed. Figure 5.21 shows the signal used to control one of the delays in Figure 6.13 for a sound source that approaches the listening point and passes it. Before the source reaches the listener, the sound is raised in pitch, and it is lowered right after.

Figure 5.21 Control signal for simulating the Doppler effect with a delay-based pitch shifter

Any sound-processing model based on the simulation of wave propagation, implements an implicit simulation of the Doppler effect. In fact, these models are based on delay lines that change their length according to the relative position of source and listener, thus providing positive or negative pitch transpositions.

In general, the accuracy and naturalness of a Doppler shift reproduced by digital means depends on the accuracy of interpolation in variable-length delays. If this is not good enough, modulation products affect the transposed signal, producing remarkable artifacts.