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Overcomplete Discrete Wavelet Transforms With Rational Dilation Factors

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2 Author(s)
Bayram, I. ; Dept. of Electr. & Comput. Eng., Polytech. Inst. of New York Univ., Brooklyn, OH ; Selesnick, I.W.

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.

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Signal Processing, IEEE Transactions on  (Volume:57 ,  Issue: 1 )