Acoustic Sensing Based on Logarithmic Differential Decomposition (I): AM-FM Feature Extraction Based on Basis Waveforms Decomposition

Abstract

It is well known that the human auditory system has acute sensitivity to AM-FM components of sounds. We are aiming to obtain an appropriate structure and algorithm underlying this, and realize it as an imbedded function of future auditory sensors. In this paper, we introduce a logarithmic differential decomposition of subband signals into basis waveforms, and show 1) AM and FM are expressed as a real part and an imaginary part of these signals, 2) the basis waveform is uniquely characterized by the corresponding zero, 3) the basis waveforms are asymptotically orthogonal each other, and hence, 4)the zeros sequence can be optimally extracted using the matched filtering of the AM-FM components by the basis waveform.