From the STFT to the Wigner Distribution [Lecture Notes]

The analysis, processing, and parameters estimation of signals whose spectral content changes in time are of crucial interest in many applications, including radar, acoustics, biomedicine, communications, multimedia, seismic, and the car industry [1]-[11]. Various signal representations have been introduced to deal with this kind of signals within the area known as time-frequency (TF) signal analysis. The oldest analysis tool in this area is the short-time Fourier transform (STFT), as a direct extension of the classical Fourier analysis. The other key tool is the Wigner distribution (WD), introduced in signal analysis from quantum mechanics. The aim of this lecture note is to present and relate these two of the most important tools in the TF signal analysis, the STFT and the WD (introduced by two Nobel prize winners, D. Gabor and E. Wigner, respectively). This relation is a basis for the S-method (SM), an efficient and simple TF signal analysis tool providing a gradual transition between these two representations.