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Proceedings Paper

Fast algorithms for running wavelet analyses
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Paper Abstract

We present a general framework for the design and efficient implementation of various types of running (or over-sampled) wavelet transforms (RWT) using polynomial splines. Unlike previous techniques, the proposed algorithms are not necessarily restricted to scales that are powers of two; yet they all achieve the lowest possible complexity: O(N) per scale, where N is signal length. In particular, we propose a new algorithm that can handle any integer dilation factor and use wavelets with a variety of shapes (including Mexican-Hat and cosine-Gabor). A similar technique is also developed for the computation of Gabor-like complex RWTs. We also indicate how the localization of the analysis templates (real or complex B-spline wavelets) can be improved arbitrarily (up to the limit specified by the uncertainty principle) by increasing the order of the splines. These algorithms are then applied to the analysis of EEG signals and yield several orders of magnitude speed improvement over a standard implementation.

Paper Details

Date Published: 11 October 1994
PDF: 12 pages
Proc. SPIE 2303, Wavelet Applications in Signal and Image Processing II, (11 October 1994); doi: 10.1117/12.188780
Show Author Affiliations
Michael A. Unser, National Institutes of Health (United States)
Akram Aldroubi, National Institutes of Health (United States)

Published in SPIE Proceedings Vol. 2303:
Wavelet Applications in Signal and Image Processing II
Andrew F. Laine; Michael A. Unser, Editor(s)

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