Signal-adaptive discrete evolutionary transform as a sparse time-frequency representation

Discrete evolutionary transform (DET) has usually been applied to signals in a blind-way without using any parameters to characterize the signal. For this reason, it is not optimal and needs improvement by using some information about the signal. In this paper, we propose an improvement for the discrete evolutionary transform in order to obtain a sparse representation and redefine the generalized time-bandwidth product optimal short-time Fourier transform as a special case of it. In case of linear FM-type signals, the optimized kernel function of the transform is determined according to signal parameters including the instantaneous frequency. The performance of the adaptive-DET is illustrated on three distinct cases. In case of multi-component LFM signals, when the concentration of the proposed distribution is compared to the ordinary sinusoidal-DET, the improvement is computed as 28% in terms of the ratio of norms. Furthermore we define a new and a general class of distribution functions named as the short-time generalized discrete Fourier transform (ST-GDFT) which is a larger set of signal representations including the adaptive-DET.