Title :
A shift-invariant discrete wavelet transform
Author :
Sari-Sarraf, Hamed ; Brzakovic, Dragana
Author_Institution :
Instrum. & Controls Div., Oak Ridge Nat. Lab., TN, USA
fDate :
10/1/1997 12:00:00 AM
Abstract :
This article presents a unifying approach to the derivation and implementation of a shift-invariant wavelet transform of one- and two-dimensional (1-D and 2-D) discrete signals. Starting with Mallat´s (1989) multiresolution wavelet representation (MRWAR), it presents an analytical process through which a shift-invariant, orthogonal, discrete wavelet transform called the multiscale wavelet representation (MSWAR) is obtained. The coefficients in the MSWAR are shown to be inclusive of those in the MRWAR with the implication that the derived representation is invertible. The computational complexity of the MSWAR is quantified in terms of the required convolutions, and its implementation is shown to be equivalent to the filter upsampling technique
Keywords :
computational complexity; convolution; signal representation; signal resolution; transforms; wavelet transforms; 1D discrete signals; 2D discrete signals; Mallat´s multiresolution wavelet representation; analytical process; computational complexity; convolutions; filter upsampling technique; multiscale wavelet representation; orthogonal wavelet transform; shift invariant discrete wavelet transform; wavelet coefficients; Computational complexity; Convolution; Discrete wavelet transforms; Filter bank; Fusion power generation; Signal generators; Signal processing; Signal resolution; Two dimensional displays; Wavelet analysis;
Journal_Title :
Signal Processing, IEEE Transactions on
