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  • Research Article
  • Open Access

Fast Frequency Estimation by Zero Crossings of Differential Spline Wavelet Transform

EURASIP Journal on Advances in Signal Processing20052005:624376

https://doi.org/10.1155/ASP.2005.1251

  • Received: 29 April 2004
  • Published:

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.

Keywords and phrases

  • zero crossing
  • spectral analysis
  • wavelets
  • B-splines
  • scale space
  • differential operators
  • vanishing moments
  • simple consistent
  • convergence in probability

Authors’ Affiliations

(1)
Department of Computer Science and Electronic Engineering, University of Missouri-Kansas City, MO 64110, USA
(2)
Department of Mathematics and Statistics, University of Missouri-Kansas City, MO 64110, USA
(3)
Advanced Digital Imaging Research, LLC, 2450 South Shore Boulevard, Suite 305, League city, TX 77573, USA

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