Quadratic and higher order time-frequency analysis based on the short-time Fourier transform

Abstract

Realization of quadratic and higher order time-frequency (TF) representations based on the short time Fourier transform (STFT) is an practically and theoretically important topic. One possible way to realize quadratic TF distributions by using spectrograms is based on the eigenvalue decomposition of the reduced interference distribution kernel. The other possible method (S-method), which is the topic of this article, is based on the direct relation between the pseudo Wigner distribution (WD) and STFT. In contrast to some other TF representations which are focused on the preservation of marginal properties and the cross terms reduction, this method is derived with the primary goal to preserve the auto-terms quality as in the WD, while avoiding (reducing) the cross-terms. The software and hardware realization of this method is very efficient, since it is completely based on the STFT. By adding one more stage to the already existing systems for the STFT realization one can significantly improve the properties of the TF representation. The S-method can be extended to the cross-terms free (reduced) realizations of the higher order TF representations, such as the polynomial Wigner-Ville distribution, and the L-Wigner distribution. It has also been used for realization of time-scale, and multidimensional space/spatial-frequency representations.