Fast frequency estimation by zero crossings of differential spline wavelet transform

Yu Ping Wang, Jie Chen, Qiang Wu, Kenneth R. Castleman

Research output: Contribution to journalArticle

4 Citations (Scopus)

Abstract

Zero crossings or extrema of a wavelet transform constitute important signatures for signal analysis with the advantage of great simplicity. In this paper, we introduce a fast frequency-estimation method based on zero-crossing counting in the transform domain of a family of differential spline wavelets. The resolution and order of the vanishing moments of the chosen wavelets have a close relation with the frequency components of a signal. Theoretical results on estimating the highest and the lowest frequency components are derived, which are particularly useful for frequency estimation of harmonic signals. The results are illustrated with the help of several numerical examples. Finally, we discuss the connection of this approach with other frequency estimation methods, with the high-order level-crossing analysis in statistics, and with the scaling theorem in computer vision.

Original languageEnglish (US)
Pages (from-to)1251-1260
Number of pages10
JournalEurasip Journal on Applied Signal Processing
Volume2005
Issue number8
DOIs
StatePublished - May 21 2005

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Frequency estimation
Splines
Wavelet transforms
Signal analysis
Computer vision
Statistics

Keywords

  • B-splines
  • Convergence in probability
  • Differential operators
  • Scale space
  • Simple consistent
  • Spectral analysis
  • Vanishing moments
  • Wavelets
  • Zero crossing

ASJC Scopus subject areas

  • Signal Processing
  • Hardware and Architecture
  • Electrical and Electronic Engineering

Cite this

Fast frequency estimation by zero crossings of differential spline wavelet transform. / Wang, Yu Ping; Chen, Jie; Wu, Qiang; Castleman, Kenneth R.

In: Eurasip Journal on Applied Signal Processing, Vol. 2005, No. 8, 21.05.2005, p. 1251-1260.

Research output: Contribution to journalArticle

Wang, Yu Ping ; Chen, Jie ; Wu, Qiang ; Castleman, Kenneth R. / Fast frequency estimation by zero crossings of differential spline wavelet transform. In: Eurasip Journal on Applied Signal Processing. 2005 ; Vol. 2005, No. 8. pp. 1251-1260.
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