Harmonic wavelet transform signal decomposition and modified group delay for improved Wigner-Ville distribution

A new approach for the Wigner-Ville distribution (WVD) based on signal decomposition by harmonic wavelet transform (SDHWT) and the modified magnitude group delay function (MMGD) has been proposed. The SDHWT directly provides subband signals and the WVD of these components are concatenated to get the overall WVD without using antialias and image rejection filtering. The SDHWT and the MMGD remove the existence of crossterms (CT) and the ripple effect due to truncation of the WVD kernel without applying any window, respectively. Since there is no time and frequency smoothing, the proposed method has a better performance in terms of both time and frequency resolution and desirable properties of a time-frequency representation (TFR) than the pseudo WVD (PWVD). Further, it has a relatively better noise immunity compared to that of PWVD. In the WVD, for signal decomposition, the use of SDHWT, compared to that of a filter bank, provides almost similar results but has a significant (72%) computational advantage.