A Signal-adaptive Discrete Evolutionary Transform: Generalized Time-bandwidth Product Optimal Stft

The discrete evolutionary transform is applied to signals in a blind–way without any signal parameters. For this reason, discrete evolutionary transform is not optimal and needs an improvement by using some information about the signal. In this paper, we propose an improvement for the discrete evolutionary transform. We redefine the generalized timebandwidth product optimal short–time Fourier transform as a special case of the discrete evolutionary transform. The optimized kernel function of the short–time Fourier transform is determined according to the instantaneous frequency of LFM-type signals. Even in case of quadratic FM signals, the resulting localization of the time-frequency representations improves remarkably. The performance of this optimal discrete evolutionary transform is presented on signals whose chirp rates vary by time.