Overcomplete discrete wavelet transforms with rational dilation factors

Authors:
Ilker Bayram;Ivan W. Selesnick
Affiliations:
Department of Electrical and Computer Engineering, Polytechnic Institute of New York University, Brooklyn, NY;Department of Electrical and Computer Engineering, Polytechnic Institute of New York University, Brooklyn, NY
Venue:
IEEE Transactions on Signal Processing
Year:
2009

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Abstract

This paper develops an overcomplete discrete wavelet transform (DWT) based on rational dilation factors for discrete-time signals. The proposed overcomplete rational DWT is implemented using self-inverting FIR filter banks, is approximately shift-invariant, and can provide a dense sampling of the time-frequency plane. A straightforward algorithm is described for the construction of minimal-length perfect reconstruction filters with a specified number of vanishing moments; whereas, in the nonredundant rational case, no such algorithm is available. The algorithm is based on matrix spectral factorization. The analysis/synthesis functions (discrete-time wavelets) can be very smooth and can be designed to closely approximate the derivatives of the Gaussian function.