Improved Wigner–Ville distribution performance based on DCT/DFT harmonic wavelet transform and modified magnitude group delay

A new Wigner–Ville distribution (WVD) estimation is proposed. This improved and efficient WVD is based on signal decomposition (SD) by DCT or DFT harmonic wavelet transform (DCTHWT or DFTHWT) and the modified magnitude group delay (MMGD). The MMGD processing can be either in fullband or subband. The SD by DCTHWT provides better quality low leakage decimated subband components. The concatenation of WVDs of the subbands results in an overall WVD, significantly free from crossterms and Gibbs ripple. As no smoothing window is used for the instantaneous autocorrelation (IACR), MMGD removes or reduces the Gibbs ripple preserving the frequency resolution achieved by the DCT/DFT HWT. The SD by DCTHWT compared to that of DFTHWT, has improved frequency resolution and detectability. These are due to the symmetrical data extension and the consequential low leakage (bias and variance). As the zeros due to the associated white noise are removed by the MMGD effectively in subband domain than in fullband, the proposed WVD based on subband has a better noise immunity. Compared to fullband WVD, the subband WVD is computationally efficient and achieves a significantly better: frequency resolution, detectability of low-level signal in the presence of high-level one and variance. The SD-based methods, however cannot bring out the frequency transition path from band to band clearly, as there will be gap in the contour plot at the transition. For the proposed methods, the heart rate variability (HRV) real data is also considered as an example.