Joint time-frequency resolution of signal analysis using Gabor transform

A joint time-frequency (TF) resolution of the Gabor transform-based signal analysis is investigated. First, different window functions used in the Gabor transform are compared with regard to their time duration and frequency bandwidth. Next, optimal windows with small TF support are found. Finally, a practical choice of windows maximizing signal energy concentration in the TF domain is examined. In this case, the error of signal reconstruction from the Gabor coefficients and the mean square width of the short-time signal spectrum are computed for different time-varying test signals and minimized in the optimization process. An appropriate adaptation of the window length according to the rate of frequency modulation is discussed.