The discrete evolutionary transform is applied to signals in a blind-way, i.e., without using any parameters to characterize the signal. For this reason, it 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 and redefine the generalized time-bandwidth product optimal shorttime Fourier transform as a special case of the discrete evolutionary transform. The optimized kernel function of the shorttime Fourier transform is determined according to the instantaneous frequency of linear FM signals-type signals. Even in case of quadratic FM signals, the resulting localization of the time-frequency representations improves remarkably. The performance of this adaptive discrete evolutionary transform is presented on signals with time-varying instantaneous frequencies.