Fast continuous wavelet transform

Michael Vrhel, Chulhee Lee, Michael Unser

Research output: Contribution to journalConference article

9 Citations (Scopus)

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.

Original languageEnglish
Pages (from-to)1165-1168
Number of pages4
JournalICASSP, IEEE International Conference on Acoustics, Speech and Signal Processing - Proceedings
Volume2
Publication statusPublished - 1995 Jan 1
EventProceedings of the 1995 20th International Conference on Acoustics, Speech, and Signal Processing. Part 2 (of 5) - Detroit, MI, USA
Duration: 1995 May 91995 May 12

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wavelet analysis
Splines
Wavelet transforms
Polynomials
Sampling
splines
approximation
polynomials
sampling
scaling

All Science Journal Classification (ASJC) codes

  • Software
  • Signal Processing
  • Electrical and Electronic Engineering

Cite this

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Fast continuous wavelet transform. / Vrhel, Michael; Lee, Chulhee; Unser, Michael.

In: ICASSP, IEEE International Conference on Acoustics, Speech and Signal Processing - Proceedings, Vol. 2, 01.01.1995, p. 1165-1168.

Research output: Contribution to journalConference article

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AU - Unser, Michael

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AB - 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.

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JO - Proceedings - ICASSP, IEEE International Conference on Acoustics, Speech and Signal Processing

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