Multitaper Adaptive Time-Frequency Windowed Fourier Transform Based on the Reliable Region of Window Widths

The window width of the short-time Fourier transform (STFT) has a critical effect on the resolution of the time-frequency distribution. Until now, due to the limitation of the fast Fourier transform (FFT) algorithm, traditional adaptive methods, such as the adaptive STFT and the adaptive synchrosqueezing transform (ST), either only considerer the time-domain width or only considerer the frequency-domain width. However, a more general adaptive method usually has a higher computation complexity due to the search for optimal parameters. In this paper, we propose the reliable region of the window widths for both time and frequency axes. We also simplify the searching process for optimal parameters. Moreover, based on the reliable region of the window widths, we propose a method called the multitaper adaptive time-frequency windowed Fourier transform (MATFWFT) that has time-variant and frequency-variant window size. It can simultaneously estimate the optimal window size for both the time axis and the frequency axis and achieve a time-frequency analysis result with high energy concentration.