Time-Frequency Analysis and Noise Suppression with Shift-Invariant Wavelet Packets

Conclusion

Cross terms associated with bilinear distributions are not necessarily interpretable as interference terms. Any signal can be broken up in an infinite number of ways, each of which generates different cross terms. Therefore, it is important to choose an appropriate decomposition that separates the parts which are well delineated in the time-frequency plane. We have presented a modified Wigner distribution, where undesirable interference-terms can be eliminated while still retaining high energy concentration.

A prescribed signal is expanded into a redundant library of orthonormal wavelet-packet bases, from which the best decomposition is selected, and subsequently transformed into the Wigner domain. The discrimination between beneficial cross terms, which primarily enhance the useful properties of the time-frequency representation, and undesirable interference terms is determined according to the degree of adjacency and relative amplitudes of the interacting basis functions; Only adjacent pairs whose coefficients are large enough are related to the same component of the signal. The balance between interference terms, concentration and computational complexity is achieved by adjusting the distance and amplitude thresholds.

A translation-invariant denoising method, which uses the SIWPD and the MDL criterion has been described. The MDL principle is applied for approximating the description length of the noisy observed data and for choosing the optimal wavelet-packet basis. The proposed signal estimator, combined with the modified Wigner distribution, generates robust time-frequency representations.