Discrete Wavelet Transforms: The Relationship of the a Trous and Mallat Algorithms

Download or read book Discrete Wavelet Transforms: The Relationship of the a Trous and Mallat Algorithms written by and published by . This book was released on 1991 with total page 6 pages. Available in PDF, EPUB and Kindle. Book excerpt: In a general sense this paper represents an effort to clarify the relationship of discrete and continuous wavelet transforms. More narrowly, it focuses on bringing together two separately motivated implementations of the wavelet transform, the algorithm a trous and Mallat's multiresolution decomposition. It is observed that these algorithms are both special cases of a single filter bank structure, the discrete wavelet transform, the behavior of which is governed by one's choice of filters. In fact, the a trous algorithm, originally devised as a computationally efficient implementation, is more properly viewed as a nonorthogonal multiresolution algorithm for which the discrete wavelet transform is exact. A systemative framework for the discrete wavelet transform is provided, and conditions are derived under which it computes the continuous wavelet transform exactly.