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Instantaneous frequency and wave shape functions (I)

Publication ,  Journal Article
Wu, HT
Published in: Applied and Computational Harmonic Analysis
September 1, 2013

Although one can formulate an intuitive notion of instantaneous frequency, generalizing "frequency" as we understand it in e.g. the Fourier transform, a rigorous mathematical definition is lacking. In this paper, we consider a class of functions composed of waveforms that repeat nearly periodically, and for which the instantaneous frequency can be given a rigorous meaning. We show that Synchrosqueezing can be used to determine the instantaneous frequency of functions in this class, even if the waveform is not harmonic, thus generalizing earlier results for cosine wave functions. We also provide real-life examples and discuss the advantages, for these examples, of considering such non-harmonic waveforms. © 2012 Elsevier Inc.

Duke Scholars

Published In

Applied and Computational Harmonic Analysis

DOI

EISSN

1096-603X

ISSN

1063-5203

Publication Date

September 1, 2013

Volume

35

Issue

2

Start / End Page

181 / 199

Related Subject Headings

  • Numerical & Computational Mathematics
  • 4904 Pure mathematics
  • 4901 Applied mathematics
  • 0103 Numerical and Computational Mathematics
  • 0102 Applied Mathematics
  • 0101 Pure Mathematics
 

Citation

APA
Chicago
ICMJE
MLA
NLM
Wu, H. T. (2013). Instantaneous frequency and wave shape functions (I). Applied and Computational Harmonic Analysis, 35(2), 181–199. https://doi.org/10.1016/j.acha.2012.08.008
Wu, H. T. “Instantaneous frequency and wave shape functions (I).” Applied and Computational Harmonic Analysis 35, no. 2 (September 1, 2013): 181–99. https://doi.org/10.1016/j.acha.2012.08.008.
Wu HT. Instantaneous frequency and wave shape functions (I). Applied and Computational Harmonic Analysis. 2013 Sep 1;35(2):181–99.
Wu, H. T. “Instantaneous frequency and wave shape functions (I).” Applied and Computational Harmonic Analysis, vol. 35, no. 2, Sept. 2013, pp. 181–99. Scopus, doi:10.1016/j.acha.2012.08.008.
Wu HT. Instantaneous frequency and wave shape functions (I). Applied and Computational Harmonic Analysis. 2013 Sep 1;35(2):181–199.
Journal cover image

Published In

Applied and Computational Harmonic Analysis

DOI

EISSN

1096-603X

ISSN

1063-5203

Publication Date

September 1, 2013

Volume

35

Issue

2

Start / End Page

181 / 199

Related Subject Headings

  • Numerical & Computational Mathematics
  • 4904 Pure mathematics
  • 4901 Applied mathematics
  • 0103 Numerical and Computational Mathematics
  • 0102 Applied Mathematics
  • 0101 Pure Mathematics