A fast recursive STFT algorithm

The short-time Fourier transform (STFT) of a signal maps a one-dimensional signal, into a two-dimensional signal in the time-frequency plane. The combination of time-domain and frequency-domain analysis yields a more revealing picture of the signal, showing which spectral components are presented in the signal at a given time. This paper presents an efficient recursive algorithm to compute multiple-pole window STFT of a discrete-time sequence. It is shown that multiple-pole windows offer good time-frequency resolution and that the resulting STFT does not possess any sidelobes. The algorithm of multiple-pole STFT is then derived. It updates STFT only at each N-th point and enables use of the FFT algorithm for efficient computing. Numerical examples are presented.