Echo avoidance in a computational model of the precedence effect

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Abstract

The precedence effect, though a topic of continuous theoretical interest in hearing research, so far cannot be predicted explicitly by a model. Zurek (1987) reviewed the precedence effect and gave a general structure for the model of the precedence effect. However, it is still not clear how the inhibition of localization is generated. This paper proposes a computational echo-avoidance model by assuming that the precedence effect is caused by the inhibition of sound localization which depends on the estimated sound-to-echo ratio. We assume there is a neural echo-estimation mechanism in the human auditory system. It is found that a temporal pattern of aftereffect with delay and decay features, which is adopted from the previous psychological tests on the increase of the perceptual threshold of interaural time difference following a preceding impulsive sound, can be used for echo estimation. The time variance of the precedence effect is briefly discussed. The results of psychological experiments, e.g. equal-level and unequal-level paired click tests, Haas's tests and Franssen's tests, are interpreted consistently. This model can also give criteria for an available onset and an explanation of why the precedence effect occurs in transient onsets.

Introduction

When a sound is presented in a reverberant environment, listeners usually can localize the sound at the correct source position, being unaware and little influenced by the surrounding reflections. This phenomenon is referred to as the “precedence effect” (Wallach et al., 1949). The precedence effect has been a topic of continuous theoretical interest in the field of psychoacoustics for more than half a century (Gardner, 1968). The precedence effect can give important suggestions for computational sound localization in a reverberant environment (Huang et al., 1995, Huang et al., 1997b) and is also an important factor for acoustical architecture design (Haas, 1951) and stereo sound reproduction (Snow, 1953, Parkin and Humphreys, 1958). For more details, see reviews (Zurek, 1987, Grantham, 1995, Blauert, 1997).

It is well known that the binaural or spatial cues are important for the perceptual segregation of sound mixtures (Blauert, 1997, Bodden, 1993, Cherry, 1953). Therefore, the precedence effect, which influences the spatial cues in reverberant environments, also plays an important role in perceptual sound organization, or the so-called auditory scene analysis (Bregman, 1990) and its computational modeling (Cooke, 1993, Ellis, 1994, Huang et al., 1997a, Lehn, 1997). Moreover, the precedence effect also influences whether a succeeding sound is perceptible as an independent event, when two impulsive sounds are presented sequentially with a time delay (Blauert, 1997). This is the perceptual aspect of the precedence effect, which must be treated as a role in the perceptual grouping of sound events.

Computational studies on the precedence effect can give a systematic interpretation of the results of psychological tests and provide a theoretical explanation for the phenomenon. Despite the large number of psychological studies on the precedence effect, there have been few computational modeling studies. Some abstract models, e.g. funneling models (von Bekesy, 1960, Thurlow et al., 1965), inhibition models (Haas, 1951, Harris et al., 1963, Zurek, 1980, Zurek, 1987) and others (McFadden, 1973, Lindemann, 1986a, Lindemann, 1986b, Litovsky and Macmillan, 1994) have been proposed for the precedence effect. Basically, while the funneling models proposed that the localization of succeeding sounds is biased toward the direction which has been established by the first-arriving sound, the inhibition models argued that the onset of a sound may trigger a delayed reaction which inhibits the contribution of succeeding sounds to localization. In all those models, the precedence effect is considered to be triggered by an “onset”. Zurek argued that the onset should be a very “rapid” one, but no quantitative criterion was given for a rapid onset.

Furthermore, neither funneling nor inhibition models provide a consistent explanation for different types of sound sources. According to the Zurek model, the inhibition signal takes effect after a delay of about 800 μs, and lasts for a few milliseconds. The inhibition interval was determined based on the just-noticeable difference (JND) tests of interaural delay and intensity judgment which showed that the JND level increases in the interval range from about 800 μs to 5 ms. However, the psychological experiments conducted by Franssen indicated that the sound image of constant level pure tone was localized by the transient onset and could be maintained for a time interval of seconds or longer (Franssen, 1959, Hartmann and Rakerd, 1989, Blauert, 1997). Other psychological experiments, e.g. those by (Haas, 1951) using speech and filtered continuous noise, have shown that the inhibition occurs after a time delay of about 1 ms to about 50 ms according to the type of sound source used in the tests. The Zurek model cannot distinguish the different phenomena caused by different types of stimuli. One more point to be noted is that the inhibition in the Zurek model was absolute, i.e., a very small onset can inhibit any high-intensity succeeding sound. This obviously conflicts with the fact that the precedence effect can be canceled by a higher-intensity succeeding sound.

Recently, a computational implementation based on the Zurek model was reported (Martin, 1997). This algorithm used an inner hair-cell synapse (IHC) model (Meddis et al., 1990), which is basically a half-wave rectification circuit with onset enhancement by low-pass filtering, for the onset detection. According to the algorithm, the inhibition is proportional (inversely) to the output of the IHC model. Thus, the inhibition also depends on the absolute intensity of the sound in the onset. However, the fact is that the precedence effect does not depend on the absolute sound intensity.

Because humans spend much time indoors in a typical reverberant environment, the need for a human to localize sound may cause the human auditory system to adapt to the reverberant environment (Clifton et al., 1984). It is our opinion that there should be a mechanism which can estimate the level of reflected sounds and emit an inhibition signal to the sound localization mechanism, so that the neural pathway from low to high level of localization processing can be controlled to avoid the influence of reflections. Such a mechanism is possibly located in the cochlear nucleus (Oertel and Wickesberg, 1996). From this point of view, the precedence effect can be interpreted as an “echo-avoidance” effect. Here as well as later, the term “echo” is used with the wide meaning of all sounds reflected by the surroundings. In this paper we will propose a new computational model of the precedence effect, the Echo-Avoidance (EA) model (Section 2), with the echo-estimation mechanism. As the first step, we only treat the inhibition aspect in sound localization, not the perceptual aspect of the precedence effect which should be solved in the future by extending the model. We will show that the EA model of the precedence effect can be used to detect available onsets which are relatively less influenced by echoes (Section 2.1.1). The model can explain why the precedence effect occurs in transient onsets (Section 2.3) and can interpret the data obtained by several psychological experiments consistently (Section 3).

Section snippets

Echo-avoidance (EA) model

The EA model of the precedence effect is similar to the Zurek model (Zurek, 1987). It consists of two paths, one for localization cue processing and one for inhibition signal generation as shown in Fig. 1. We assume that the echo estimation and inhibition mechanism is independent for each frequency (Hafter et al., 1988). As in the Zurek model, the localization cues must contain both binaural cues and monaural cues because the precedence effect affects both binaural localization processing and

A consistent explanation of the results of some psychological tests

In this section, we will compare the schematic predictions of localization inhibition by the EA model and the related results obtained by psychological tests for some typical cases. In Fig. 8, the inhibitions predicted by the EA model, given as I=1−Ic, are indicated for the cases of (a) equal-level double clicks, (b) unequal-level double clicks and (c) a constant-level pure tone. Case (a) is the principal case where each click is short enough to be considered as impulsive sound. Many

Conclusion

We have proposed an Echo-Avoidance (EA) model of the precedence effect. By using this model, the results of psychological experiments, e.g. paired click tests, Hass's tests, and Franssen's tests, can be interpreted consistently. Criteria which can be used to judge if an onset is available for the precedence effect were given. The time variance of the precedence effect is discussed. Further systematic psychological experiments are needed to confirm the assumptions and fix the parameters of the

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