Analytic wavelet packets: combining the dual-tree approach with wavelet packets for signal analysis and filtering

Authors:
Thomas Weickert;Claus Benjaminsen;Uwe Kiencke
Affiliations:
Institute of Industrial Information Technology, Universitat Karlsruhe (TH), Karlsruhe, Germany;Sennheiser Communications A/S, Denmark;Institute of Industrial Information Technology, Universitat Karlsruhe (TH), Karlsruhe, Germany
Venue:
IEEE Transactions on Signal Processing
Year:
2009

Citing 5
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Abstract

Real wavelets (or real basis fuuctions in general) suffer from two major disadvantages: shift-variance and oscillating coefficients. This paper provides a review of these problems as well as the undecimated wavelet transform which solves the problem of shift-variance. However, undecimated transforms have very high computational costs and still have oscillating coefficients. The work of Kingsbury et al. is summarized afterwards. They have presented a dual-tree complex wavelet transform (DTCWT) which is nearly shift-invariant and has smooth coefficients. Subsequently, a filter swapping scheme is developed in order to create complex wavelet packets with analytic basis functions. Finally, the effectiveness of the proposed method is demonstrated by five examples.