Synchrosqueezing-based Recovery of Instantaneous Frequency from Nonuniform Samples

Details Synchrosqueezing-based Recovery of Instantaneous Frequency from Nonuniform Samples Synchrosqueezing-based Recovery of Instantaneous Frequency from Nonuniform Samples

2010-06-13

arxiv.org/abs/1006.2533v4

SIAM Journal on Mathematical Analysis 43(5):2078-2095, 2011

Mathematics

Numerical Analysis

19 pages, 9 figures

Scientific paper

10.1137/100798818

We propose a new approach for studying the notion of the instantaneous frequency of a signal. We build on ideas from the Synchrosqueezing theory of Daubechies, Lu and Wu and consider a variant of Synchrosqueezing, based on the short-time Fourier transform, to precisely define the instantaneous frequencies of a multi-component AM-FM signal. We describe an algorithm to recover these instantaneous frequencies from the uniform or nonuniform samples of the signal and show that our method is robust to noise. We also consider an alternative approach based on the conventional, Hilbert transform-based notion of instantaneous frequency to compare to our new method. We use these methods on several test cases and apply our results to a signal analysis problem in electrocardiography.

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