TIME-FREQUENCY ANALYSIS USING LOCAL TAYLOR-SERIES EXPANSION

We describe an approach to time-frequency analysis based on the local approximation of the signal by a first order Taylor series. We show th at the Taylor approximation provides a representation of the signal in terms of its instantaneous frequency and instantaneous bandwidth. Thi s representation can be translated into the frequency domain in a stra ightforward manner. The key to this approach is the local decompositio n of the signal into its components, which is similar to the problem o f estimating the parameters of of complex exponentials from observatio n 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.