Time-Frequency Analysis Using Local Taylor Series Expansion

Abstract

We describe an approach to time-frequency analysis based on the local approximation of the signal by a first order Taylor series. We show that the Taylor approximation provides a representation of the signal in terms of its instantaneous frequency and instantaneous bandwidth. This representation can be translated into the frequency domain in a straightforward manner. The key to this approach is the local decomposition of the signal into its components, which is similar to the problem of estimating the parameters of of complex exponentials from observation of their sum. The resulting time-frequency representation (TFR) does not have the time and frequency marginal properties shared by many of the time-frequency distributions presented in the literature, but is additive over the signal components and, by its construction, does not have cross-terms.