Auditory analysis of the periodicity of sound and its envelope: A mathematical model

Abstract

A mathematical model of the auditory analysis of periodicity of sound and its envelope is proposed. The model consists of a sequence of mathematical transformations that describe the signal processing stages. The following parameters and properties of the auditory system are taken into account: the crude analysis of the input acoustic signal accurate to the width of the aural critical band; the frequency dependence of the width of the aural critical band; the spectrum of the input signal analysis by a set of 3500 filters closely spaced in frequency; the absolute audibility thresholds at a given frequency; the time-domain analysis of both the output signals of each filter and the envelope profile with the help of the periodicity function; the pulsed activity of auditory neurons; the ability of the auditory system to memorize the spectral-time images of the signal and its individual parameters; the ability of the auditory system to form the perception of the loudness of sound, to memorize and compare the loudness of sound at different time moments, and to conclude which of them is higher or lower or whether they are equal accurate to a certain threshold; the dependence of the critical modulation bandwidth on the modulation frequency; and the dependence of the audibility thresholds of amplitude modulation on the modulation frequency. By an example of processing amplitude-modulated signals with various carrier-to-envelope frequency ratios, the model is shown to give a satisfactory explanation of their pitch and auditory estimate of the envelope period.