Short-Time Spectra and Time-Frequency Energy Distributions

Abstract

The squared magnitude of the cross-ambiguity function of two signals is shown to be given by the two-dimensional cross correlation of the individual time-frequency (t-f) energy distributions of the signals. This result is used to show that a short-time spectrum measured in the usual way is the two-dimensional convolution of the t-f energy distribution of the signal with a function which is simply related to the t-f energy distribution of the window which is used.