Short-time Fourier transforms using cascade filter structures

A wide class of short-time Fourier transforms (STFT´s), or spectrograms, can be obtained by applying an infinite-length analysis window, corresponding to an impulse response of an IIR filter, at every data sample and then taking the Fourier transform. The use of the cascade form realization of the analysis window allows simple and recursive generations of a number of distinct STFT´s with different tradeoff between temporal and spectral resolutions. The temporal-spectral resolution diversity of all STFT´s (spectrograms) associated with the same window is a function of its poles and zeros as well as their order of cascade. Closed-form expressions of such diversity are derived for the case of multiple-pole and all pole analysis windows