Model of the Auditory System
Abstract Generated abstract
This paper describes an electronic model of the peripheral auditory system intended to study signal coding at the level of the auditory nerve. The model combines a multipath filter block, representing the basilar membrane, with sensitive threshold elements, representing the sensory field, under the hypothesis that the auditory system measures instantaneous frequency and amplitude components of an input signal. The constructed sound-frequency model uses approximately logarithmic frequency mapping, filters with quality factors near unity, and pulse-generating elements triggered at zero crossings. Although limited to about 50 sensitive elements, it produced satisfactory frequency resolution and response speed, supporting further model-based investigation of auditory stimulus coding.
Full Text
Model of the Auditory System
V. P. Bondarenko
(Presented by the scientific seminar of the Department of Computer Engineering)
The study of the mechanisms of signal processing in the human auditory system is based, on the one hand, on anatomical, electrophysiological, and psychoacoustic experiments, and, on the other, on the study of electronic models of individual elements of the organ of hearing [1, 2]. The development and investigation of such models make it possible to advance significantly in understanding the processes occurring in the human auditory system. Despite the considerable successes achieved in this direction, the mechanism of coding and processing an auditory stimulus, beginning at the level of the auditory nerve, is still not fully clear [2, 3].
The model considered by us is intended for the study of the mechanisms of signal coding at the level of the auditory nerve and includes two blocks: a block of filters (a model of the basilar membrane) and a block of sensitive elements (a model of the sensory field).
The hypothesis underlying the construction of the model was that, in the auditory system, the instantaneous frequency and amplitude of the components of the sum are measured [4, 5]
\[ f(t)=\sum_{i=1}^{n} f_i(t), \]
where \(f(t)\) is the input signal, and \(f_i(t)\) is the signal from the output of the \(i\)-th filter.
It is obvious that the model must at the same time have characteristics coinciding with the known data on the functional structure of the periphery of the human auditory system, namely: the quality factor of the model filters must be on the order of unity [6], and the dependence of the filter number, or of some coordinate \(x\), on its resonant frequency must obey the relation [3, 6]
\[ x=\ln \frac{1}{f}. \tag{1} \]
The sensitive elements, when condition (1) is fulfilled, must be uniformly distributed along the \(x\) axis and must generate a standard voltage or current pulse at the moment when the signal from the filter output crosses zero [3, 6].
The filter block was based on a multipath scheme [2]. Its block diagram is shown in Fig. 1. The model was constructed for the range of sound frequencies.
The inductance coils \(L\) are wound on Sb-3a cores. The value of \(L\) is equal to 60 mH and was selected with an accuracy of \(\pm 0.5\%\). The capacitances of the capacitors \(C_k\) were chosen from the relation [2]
\[ C_k = C_1 e^{\beta(k-1)}, \]
where \(\beta = 0.07\), \(C_1 = 6250\) pF is the capacitance of the first section and was likewise selected with an accuracy of \(\pm 0.5\%\).
Fig. 1.
The resistances of the resistors \(R_k\), in a first approximation, were chosen from the conditions
\[ R_k = R_1 e^{-\frac{\beta(k-1)}{2}}, \qquad R_1 = \frac{1}{Q}\sqrt{\frac{L}{C_1}} - r_L, \]
where \(Q\) is the required quality factor of the first section, and \(r_L\) is the active resistance of the coil \(L\).
The filters were tuned by selecting the resistances \(R_k\); for this purpose they were assembled from series-connected variable and fixed resistors. After tuning, the variable resistors were replaced by fixed ones. The final dependence \(R_k(N)\) is shown in Fig. 2 (curve 1).
Fig. 2
The total number of filters is 60. The first two and the last seven filters are not used, since they have characteristics that differ greatly from the required ones.
Matching emitter followers (EF) are placed at the filter outputs. The signal from the outputs of all EFs is normalized and is 200 mV at the resonant frequency of the filter.
The amplitude-frequency characteristics of the filters are given in Fig. 3. The quality factor of the filters is of the order of \(0.8 \div 1.2\). In Fig. 2 (curve 2) the dependence of the resonant frequency of a filter on its number is given. This dependence is approximated rather well by the expression
\[ f = \frac{33.8}{N + 3} - 0.26 \]
and with an accuracy of \(\pm 10\%\)
\[ N = 9 \ln \frac{7}{f - 0.3}, \]
where \(f\) is in kHz.
Thus, as a rough approximation \(N\) may be taken as the \(x\)-axis; a more exact study will evidently require another, nonuniform density of distribution of the sensitive elements along the \(N\)-axis.
The sensitive elements have a triggering threshold of about 2 mV, that is, they provide a dynamic range in signal processing on the order of 40 dB. The total number of sensitive elements is equal to the number of filters used. Each element consists of an amplifier, a Schmitt trigger, and a multivibrator. The duration of the output pulse is 0.1 msec and the amplitude is 15 V.
Fig. 3
This model, in combination with the summator [5], makes it possible to implement an algorithm for measuring the instantaneous frequency of a signal.
Measurement of the instantaneous amplitude of the signal is associated with making the block of sensitive elements more complicated. In this case, at the output of each filter it is necessary to install 4–10 elements with different triggering thresholds; then their total number will be 200–500 units. For comparison, it may be noted that the sensory field of the human auditory system includes about 30 thousand sensitive cells [2, 3, 6].
Despite the small number of sensitive elements (50), the model made it possible, quite simply, to obtain satisfactory frequency resolution and response speed, which to some extent confirms the proposed hypothesis concerning the mechanisms of signal transformation in the human auditory system and permits a model-based study of certain regularities of the coding of an auditory stimulus.
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