Fast continuous wavelet transform

Author

Vrhel, Michael ; Lee, Chulhee ; Unser, Michael

Author_Institution

Biomed. Eng. & Instrum. Program, Nat. Inst. of Health, Bethesda, MD, USA

Volume

2

fYear

1995

fDate

9-12 May 1995

Firstpage

1165

Abstract

We introduce a general framework for the efficient computation of the continuous wavelet transform (CWT). The method allows arbitrary sampling along the scale axis, and achieves O(N) complexity per scale where N is the length of the signal. Our approach makes use of a compactly supported scaling function to approximate the analyzing wavelet. We derive error bounds on the wavelet approximation and show how to obtain any desired level of accuracy through the use of higher order representations. Finally, we present examples of implementation for different wavelets using polynomial spline approximations

Keywords

approximation theory; polynomials; signal representation; signal sampling; splines (mathematics); wavelet transforms; accuracy; compactly supported scaling function; complexity per scale; error bounds; fast algorithm; fast continuous wavelet transform; higher order representations; polynomial spline approximations; sampling; scale axis; signal analysis; signal length; wavelet approximation; Algorithm design and analysis; Biomedical computing; Biomedical engineering; Continuous wavelet transforms; Instruments; Polynomials; Sampling methods; Signal analysis; Wavelet analysis; Wavelet transforms;

fLanguage

English

Publisher

ieee

Conference_Titel

Acoustics, Speech, and Signal Processing, 1995. ICASSP-95., 1995 International Conference on

Conference_Location

Detroit, MI

ISSN

1520-6149

Print_ISBN

0-7803-2431-5

Type

conf

DOI

10.1109/ICASSP.1995.480444

Filename

480444