Учебники / Hearing - From Sensory Processing to Perception Kollmeier 2007

in a unified modeling framework while maintaining their predictive power. Specifically, it is investigated if the two models can help distinguishing between persistence and adaptation, the two hypothetical mechanisms underlying forward masking.

2Methods

2.1Procedure and Subjects

A three-interval, three-alternative forced-choice adaptive procedure (twodown, one-up rule) was used to determine detection thresholds in the simulations and experiments. The step size was 8 dB at the beginning and was halved after every two reversals, until it reached a minimum of 1 dB where eight reversals were obtained for threshold estimation. The starting level of the signal was 90 dB SPL. Two subjects participated as a control group. The stimuli were presented to one ear via headphones (AKG K-501) in a doublewalled, sound-attenuating booth.

2.2Stimuli

Two forward masking experiments with signal tones at 1 and 4 kHz were conducted to test the models. At 1 kHz, a 10-ms, Hanning-windowed signal was used. The masker was a 200-ms, 77-dB, 20to 5000-Hz frozen noise, no ramps were applied. The experimental design was the same as in Dau et al. (1996). At 4 kHz, a 12-ms signal, including 2-ms, raised-cosine ramps, was added to a 200-ms, 78-dB, 0- to 7000-Hz, frozen-noise masker. The masker included 2-ms, raised-cosine ramps. The design was the same as in Oxenham (2001). The offset-offset time of the signal and the masker was varied in the range from −10 to 150 ms, thus including conditions of simultaneous as well as nonsimultaneous masking.

3Models and Predictions

The processing modules of the temporal-window (TW) model according to Oxenham (2001) were implemented. The TW model uses a linear, timeinvariant integration after non-linear peripheral processing. The shape of the integration window relevant for forward masking results from two exponential functions with time constants of 4.6 ms and 16.6 ms, added with a weight of 0.17 for the longer time constant. In the nonlinear part, the model uses an instantaneous power-law compression with an exponent of 0.25 for

Fig. 4 Simplified block diagram highlighting the division stage of the temporal-window model

Fig. 5 Simplified block diagram of the AD model (upper panel). For each input stimulus condition, the adaptation loops can be replaced by a division of the input waveform with an equivalent divisor as shown in the lower panel

masker+signal is divided by the representation of the masker alone which is referred to as “divisor” in the following. The TW model divisor is shown in Fig. 6 (black line). The TW model is able to account for forward masking since the divisor only declines gradually after masker offset at 0.2 s, reflecting persisting masker energy or the effect of temporal integration. However, in addition to the

Fig. 6 Comparison of the divisors in the temporal-window model (black) and adaptation-loop model (dashed gray)

persistence of masker energy, the fact that the TW model incorporates a division of both stimulus paths is crucial for the function of the model. The division module in the current model implementation equals the ratio detection criterion, (M+S)/M, in the original TW model.

A comparable analysis of the AD model (Fig. 5) reveals that the stages of the adaptation loops can be viewed as a similar division process (upper and middle panel). The difference is that the AD model incorporates feedback while the TW model is a pure feed-forward circuit. For each input stimulus condition, however, an equivalent adaptation devisor for a feed-forward mechanism can be derived (Fig. 5, lower panel). The equivalent AD model devisor is indicated by the dashed gray line in Fig. 6. In comparison to the TW divisor, it shows a bump at the temporal position of the signal, in this case at about 250 ms. This bump reflects a “self-suppression” effect of the signal.

4.1Simplified Adaptation-loop Model

The above analysis has shown that the prominent difference between the two models could be reduced to the effect of the signal on the divisor function which reflects a “self suppression” of the signal. The AD model was further simplified (see Fig. 7) to derive the equivalent AD devisor function from the masker only, similar to the processing in the TW model. The hypothesis was that if the parameters of the temporal window in the TW model were adjusted to produce a divisor function matching the divisor of the simplified AD model, both models should predict the same forward masking curve. Figure 8 shows the matched divisors (left) and the predictions obtained with the two models (right). Both models predicted essentially the same data when their divisors were matched.

Fig. 7 Simplified adaptation-loop model where only the adaptation effect originating from the masker is considered

Fig. 8 Left: Divisor of the TW model (black) with time constants adjusted to match the devisor of the simplified AD model (dashed gray). Right: Predictions of the TW model and simplified AD model at 4 kHz with the divisors shown in the left panel

5Discussion

The key mechanism responsible for the simulation of forward masking in both models is the division of the internal representation of the signal by the representation of the persisting or temporally smoothed masker. In the temporalwindow model, this division is realized in the detection process, while it is a part of the feedback loops in the adaptation-loop model. With regard to forward masking, the temporal-window model can be viewed as a simplified adaptation model neglecting “self suppression” of the signal. In fact, both models use the identical key mechanism to describe forward masking. Thus, these model realizations can not be used to critically separate between adaptation and persistence. The concept of persistence as realized in the TW model, cannot lead to successful predictions without the ratio-based decision criterion.

The temporal-window model has proven its strength as a very flexible and well “controllable” tool to investigate, e.g., effects of peripheral compressive non-linearity on forward masking in the normal versus the impaired auditory

system (e.g., Plack and Oxenham 1998). The adaptation-loop model has proven its strength in a variety of experimental conditions in addition to forward masking, such as spectro-temporal masking and modulation detection. The model has also been used as front end in automatic speech recognition and objective speech quality assessment (whereby the detection stage was replaced by other post-processing devices). A possible modification of the adaptation stage might use a single low-pass filter in the feedback loops where the parameters of the impulse response could be adjusted in a similar way as the time constants in the temporal window model. The lack of goodness of fit in the 1-kHz case could be solved either by a variation of the parameters in the TW and AD models or by using alternative peripheral filter functions (with different ringing) at low frequencies.

6Conclusions

It was found that the TW and AD models can be considered as being essentially equivalent in predicting forward masking: the combination of integration and the signal-to-noise-ratio based detection criterion in the TW model act effectively as a simplified adaptation mechanism. However, since there is physiological evidence for adaptation along the auditory pathway, the AD model appears to be the more general approach. It shows the effect of adaptation in the internal representation of the stimuli and can be applied successfully to a broader class of masking conditions than the TW model.

Acknowledgments. This work was supported by the Danish Research Council.

References

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Oxenham AJ (2001) Forward masking: adaptation or integration? J Acoust Soc Am 109:732–741 Oxenham AJ, Moore BC (1994) Modeling the additivity of nonsimultaneous masking. Hear Res

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Comment by Kohlrausch

You provided evidence that, for one forward masking condition, the two schemes previously published to explain forward masking are conceptually equivalent and predict the same results.

My question: does this equality also apply to some of the additional properties of the adaptation loop scheme, which were considered to be important when this scheme was first proposed by Dirk Pueschel in his Ph.D. thesis? 1) The fact that forward masking curves become steeper for shorter maskers, and 2) that, in simultaneous masking, no such influence of masker duration on detection is observed, while, in contrast, signal duration has a considerable effect on detection.

In my understanding, the ability to model observation 1 lies in the different values of the time constants of the feedback loops, while observation 2 is primarily attributed to using a matched template for detection.

Reply

We would like to underline that our conclusion is that the temporal-window model can be viewed as a simplified adaptation model, not as a fully equivalent model. This implies that the temporal window model can not account for all effects that an adaptation model can cover. Particularly, changes in the forward masking curve as function of masker duration can, to our knowledge, not be accounted for by the temporal window model with a fixed set of parameters/time constants.

We do also attribute your second observation to the matched filter detection mechanism, which is conceptually different from the detector used in the temporal-window model as published in the literature. In our unified model, however, we used the matched filter detector for both the temporal-window processing scheme and the adaptation scheme. Thus, we disregarded potentially limiting effects of the original temporal-window model detector.

Comment by Plack

I agree that the TW model and the modified AD model are equivalent in most forward masking situations. However, there is considerable evidence to suggest that processes after the basilar membrane (BM) are effectively linear in the way they combine the energy of BM vibration over time, at least with respect to forward and backward masking (Plack et al. 2002, 2006). Hence, it may be advantageous to keep the non-linearity out of the adaptation loops if possible.

I’m not sure that I agree with the final statement in your paper that the AD model can be applied to a broader class of experimental masking conditions

than the TW model. The TW model has been applied successfully to forward masking, backward masking, simultaneous masking, and increment and decrement detection. Being effectively a low-pass filter, the TW can also account for gap detection, temporal integration, and some aspects of modulation detection. Although the decision device in the AD model is more sophisticated than that in the TW model, my understanding is that the AD model is successful across the full range of temporal resolution and masking tasks only when combined with an additional processing stage, such as a modulation filterbank. I like the physiological realism of the adaptation stage, but do you know of any psychophysical result that requires a simulation of adaptation to model the data?

References

Plack CJ, Oxenham AJ, Drga V (2002) Linear and nonlinear processes in temporal masking. Acustica 88:348–358

Plack CJ, Oxenham AJ, Drga V (2006) Masking by inaudible sounds and the linearity of temporal summation. J Neurosci 26:8767–8773

Reply

The temporal-window (TW) model has been powerful to demonstrate the effects of cochlear compression on forward (and backward) masking and, in particular, to account for consequences of sensorineural hearing loss on forward masking functions.

We agree that the broad applicability of the original AD model is also related to its more general detector, while the TW model uses a more simple detection mechanism. Our point in the current study is that the TW model can only function correctly if there is the assumption of the (S+N)/N-ratio criterion in the decision process, i.e., the whole concept of persistence or temporal integration after compression only holds when it is connected with this specific criterion. This, in turn, is in principle equivalent to an adaptation mechanism. Thus, we argue that the TW model represents a concept which effectively provides correct predictions in these specific conditions, however, essentially being a simplified adaptation model. As such, it does not allow simulating an internal representation of the stimulus that reflects properties of adaptation as found in physiology. We agree that it might not be necessary for a model that is used for the prediction of psychophysical detection/masking data to resemble effects of neural adaptation in the internal representation. However, in our view, the AD model remains the more general approach and therefore seems applicable to a broader class of experiments.

Regarding your first point, we would like to point out that the non-linearity in the adaptation loops is, according to our analysis, to some extent equivalent to the division process in the ratio criterion of the TW model.