Estimating evolutionary power spectral density using transforms

Abstract

One of the tasks of modeling a physical process by using the evolutionary process is to estimate the evolutionary power spectral density (EPSD) function. A popular method to estimate EPSD is based on the short-time Fourier transform (STFT) and temporal smoothing; another is based on the continuous wavelet transform (CWT) and non-negative matrix factorization. In the present study, we summarize the recently developed formulation for estimating the EPSD function and its residual based on STFT with different windows, S-transform, and CWT with two different wavelets. We investigate the effect of the ﾓslowﾔ variation of the modulation function on the estimated EPSD function and its residual by using numerical examples by considering these transforms, illustrating the dependency of the residual on the considered transform, and on the time and frequency.