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Overcomplete Discrete Wavelet Transforms With Rational Dilation Factors

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 ti...

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Bibliographic Details
Published in:IEEE transactions on signal processing 2009-01, Vol.57 (1), p.131-145
Main Authors: Bayram, I., Selesnick, I.W.
Format: Article
Language:English
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Summary: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.
ISSN:1053-587X
1941-0476
DOI:10.1109/TSP.2008.2007097