Design of orthonormal and overcomplete wavelet transforms based on rational sampling factors

İlker Bayram, Ivan W. Selesnick, Frédéric Truchetet, Olivier Laligant
2007 Wavelet Applications in Industrial Processing V  
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
more » ... ers having a maximum number of vanishing moments) obtained using Gröbner bases. We also present the design of overcomplete rational wavelet transforms (tight frames) with FIR filters obtained using polynomial matrix spectral factorization.
doi:10.1117/12.741073 fatcat:4ts6cn7arfbg5baxiubzxfft74