Fast implementation of the continuous wavelet transform with integer scales

Author

Unser, Michael ; Aldroubi, Akram ; Schiff, Steven J.

Author_Institution

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

Volume

42

Issue

12

fYear

1994

fDate

12/1/1994 12:00:00 AM

Firstpage

3519

Lastpage

3523

Abstract

We describe a fast noniterative algorithm for the evaluation of continuous spline wavelet transforms at any integer scale m. In this approach, the input signal and the analyzing wavelet are both represented by polynomial splines. The algorithm uses a combination of moving sum and zero-padded filters, and its complexity per scale is O(N), where N is the signal length. The computation is exact, and the implementation is noniterative across scales. We also present examples of spline wavelets exhibiting properties that are desirable for either singularity detection (first and second derivative operators) or Gabor-like time-frequency signal analysis

Keywords

filtering theory; signal processing; splines (mathematics); time-frequency analysis; wavelet transforms; Gabor-like analysis; complexity per scale; continuous spline wavelet transforms; fast noniterative algorithm; first derivative operators; input signal; integer scales; moving sum filters; polynomial splines; second derivative operators; signal length; singularity detection; time-frequency signal analysis; zero-padded filters; Continuous wavelet transforms; Convolution; Gabor filters; Multiresolution analysis; Polynomials; Signal analysis; Spline; Time frequency analysis; Wavelet analysis; Wavelet transforms;

fLanguage

English

Journal_Title

Signal Processing, IEEE Transactions on

Publisher

ieee

ISSN

1053-587X

Type

jour

DOI

10.1109/78.340787

Filename

340787