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2 October 2007 Design of orthonormal and overcomplete wavelet transforms based on rational sampling factors
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Abstract
Most wavelet transforms used in practice are based on integer sampling factors. Wavelet transforms based on rational sampling factors offer in principle the potential for time-scale signal representations having a finer frequency resolution. Previous work on rational wavelet transforms and filter banks includes filter design methods and frequency domain implementations. We present several specific examples of Daubechies-type filters for a discrete orthonormal rational wavelet transform (FIR filters having a maximum number of vanishing moments) obtained using Gröbner bases. We also present the design of overcomplete rational wavelet wavelet transforms (tight frames) with FIR filters obtained using matrix spectral factorization.
© (2007) COPYRIGHT Society of Photo-Optical Instrumentation Engineers (SPIE). Downloading of the abstract is permitted for personal use only.
İlker Bayram and Ivan W. Selesnick "Design of orthonormal and overcomplete wavelet transforms based on rational sampling factors", Proc. SPIE 6763, Wavelet Applications in Industrial Processing V, 67630H (2 October 2007); https://doi.org/10.1117/12.741073
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