Rank M Wavelets with N Vanishing Moments
- 1 April 1995
- journal article
- Published by Society for Industrial & Applied Mathematics (SIAM) in SIAM Journal on Matrix Analysis and Applications
- Vol. 16 (2) , 502-519
- https://doi.org/10.1137/s0895479893245486
Abstract
This work generalizes the rank 2 (scale factor of 2) orthogonal wavelet sequences of Daubechies to the case of a rank Mwavelet matrix. Several equivalent definitions of Nth order vanishing moments for rank M wavelets are developed. These notions are used to find an explicit formula for rank M wavelet scaling sequences with N vanishing wavelet moments (of degree N in our terminology). A full wavelet matrix (scaling sequence and $M - 1$ wavelet sequences) is constructed, with explicit examples.
Keywords
This publication has 11 references indexed in Scilit:
- Construction of compactp-waveletsConstructive Approximation, 1993
- On orthonormal wavelets and paraunitary filter banksIEEE Transactions on Signal Processing, 1993
- Wavelet Transforms and Filter BanksPublished by Elsevier ,1992
- Wavelet Matrices and the Representation of Discrete FunctionsPublished by Elsevier ,1992
- Ten Lectures on WaveletsPublished by Society for Industrial & Applied Mathematics (SIAM) ,1992
- Wavelets and Dilation Equations: A Brief IntroductionSIAM Review, 1989
- Perfect reconstruction FIR filter banks: some properties and factorizationsIEEE Transactions on Acoustics, Speech, and Signal Processing, 1989
- Orthonormal bases of compactly supported waveletsCommunications on Pure and Applied Mathematics, 1988
- Quadrature mirror filter banks, M-band extensions and perfect-reconstruction techniquesIEEE ASSP Magazine, 1987
- Problems and Theorems in Analysis IPublished by Springer Nature ,1972