抄録
Holomorphic functions have fine mathematical properties such as the Cauchy-Rieman relation, infinite differentiability, conformality, and Laurent expandability. For treating these functions, we can apply various useful theorems such as Cauchy’s integral theorem, residue theorem, etc. In this paper, in order to introduce such a powerful mathematical foundation into the time-frequency analysis, we consider a filter bank and a complex logarithmic mapping which transform an input signal into a holomorphic function in the time-frequency domain. As an application of this framework, we show that zeros of the input signal are transformed into poles in the time-frequency domain, hence they can be used as salient and acculate features to describe the input signal. We show several experimental results of this principle.
