Fan chirp transform with nonlinear time warping

Abstract

This paper proposes an extension of a method for time-frequency analysis of nonstationary harmonic signals: the Fan Chirp Transform (FChT). In its original form, the FChT considers that each fundamental frequency (along with the higher harmonics) of the signal may vary linearly in a period of time. This model, however, may be considered poor for some types of signals, especially those whose fundamental frequencies vary rapidly with time. By allowing quadratic frequency variation, this article presents a solution to this problem, which may be considered the next step of the FChT. The proposed technique is assessed in the context of music signals.