Design of orthonormal and overcomplete wavelet transforms based on rational sampling factors
İlker Bayram, Ivan Selesnick · Proceedings of SPIE, the International Society for Optical Engineering/Proceedings of SPIE · 2007
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.