Title :
Multiwavelet moments and projection prefilters
Author :
Johnson, Bruce R.
Author_Institution :
Dept. of Chem., Rice Univ., Houston, TX, USA
fDate :
11/1/2000 12:00:00 AM
Abstract :
An efficient projection procedure is derived for use of orthogonal multiwavelets in the analysis of discrete data sequences. A family of simple prefilters corresponding to numerical quadrature evaluation of the projection integrals provides exact results for locally polynomial data. The full approximation order of the multiwavelet basis can thus always be enabled. For nonpolynomial signals, the prefilters provide approximations to the coefficients of the multiwavelet series whose convergence accelerates quickly with increase in sampling rate. Comparison is also made with previous time-invariant multiwavelet prefilters
Keywords :
convergence of numerical methods; digital filters; integral equations; polynomial approximation; sequences; signal sampling; wavelet transforms; convergence; discrete data sequences; full approximation order; locally polynomial data; multiwavelet basis; multiwavelet moments; multiwavelet series; nonpolynomial signals; numerical quadrature evaluation; orthogonal multiwavelets; projection integrals; projection prefilters; projection procedure; sampling rate; time-invariant multiwavelet prefilters; Acceleration; Chemistry; Convergence; Convolution; Data analysis; Equations; Multiresolution analysis; Polynomials; Sampling methods; Signal resolution;
Journal_Title :
Signal Processing, IEEE Transactions on
