The Gabor Transform and Time-Frequency Signal Analysis

Abstract

Signals are, in general, nonstationary. A complete representation of nonstationary signals requires frequency analysis that is local in time, resulting in the time-frequency analysis of signals. The Fourier transform analysis has long been recognized as the great tool for the study of stationary signals and processes where the properties are statistically invariant over time. However, it cannot be used for the frequency analysis thai is local in time. In recent years, several useful methods have been developed for the time-frequency signal analysis. They include the Gabor transform, the Zak transform, and the wavelet transform.