On the window selection and the cross terms that exist in the magnitude squared distribution of the short time Fourier transform

Abstract

The short time Fourier transform (STFT), a time-frequency representation, is linear by definition. However, the magnitude squared distribution of the STFT (the spectrogram) which signal processors often use to represent a signal is non-linear by definition. Therefore, in general, there exist cross terms in the spectrogram of a multi-component signal. The existence of these depends on (a) the nature of a multi-component signal, (b) the choice of the STFT analysis window and (c) the window length selection. This paper studies the effect of (i) the choice of the STFT analysis window, and (ii) the nature of signals to be analyzed, on the cross terms, in detail with representative examples.<>