Application of evolutionary algorithm to signal analysis in frequency domain

In this paper, we consider the problem of creating frequency-domain representation of discrete-time signals with a very small number of samples (several or a dozen). Classical methods of frequency-domain analysis are based on using Discrete Fourier Transform (DFT). However, the DFT method often fails in case of using too small number of samples. One of reasons for that are spectral leakages resulting from convolution of signal spectrum and time window spectrum. The proposed approach to the problem is based on adaptive synthesis which makes it to be deprived of the spectral leakage drawback. To realize the adaptive synthesis idea, using an evolutionary algorithm has been proposed. Superiority of the proposed approach over the Fourier technique is shown on examples. Necessary conditions to achieve good results of our method have also been discussed.