Time-Frequency Phase Retrieval for Deconvolutive Short-Time Fourier Transform

Cohen class distributions are well-known time-frequency distributions that have been widely used to analyze different signals. However, they are impractical for signal filtering as they only provide amplitude spectra and suffer from cross-term. In this paper, deconvolutive STFT (DSTFT) is developed by estimating phase spectra and updating moduli to address residual cross-terms. We use DSTFT moduli as weights and apply a weighted least squares technique to estimate a high-resolution and almost cross-term-free Wigner-Ville distribution. Through numerical tests, we demonstrate that choosing the optimal window length can minimize cross-terms in STFT and DSTFT spectrograms, and employing thresholding or re-weighting techniques can eliminate weights associated with noise. The performance of the proposed method is demonstrated using synthetic and two real seismic wavefield separation problems, including ground roll removal in seismic shot records and polarization analysis in seismology. The results show the high performance of the proposed method in estimating phase spectra and filtering seismic data.