Comparison of the Wavelet and Gabor Transforms in the Spectral Analysis of Nonstationary Signals

Two approaches to the analysis of nonstationary random processes (short-time Fourier transform and continuous wavelet transform) are compared. The comparison is based on the study of several model signals with known time-frequency characteristics. The application of the approaches is also analyzed in the study of spectral dynamics of fluorescence of cold atomic clouds excited by pulsed radiation. It is shown that the two approaches make it possible to reveal the main specific features of the signals under study. However, the continuous wavelet transform has several advantages, since the optimal conditions for the analysis using the short-time Fourier transform are reached if additional calculations aimed at determination of the optimal width of the window are performed.