Synchrosqueezing-Based Recovery of Instantaneous Frequency from Nonuniform Samples

By Gaurav Singh Thakur, Hau‐Tieng Wu. SIAM Journal on Mathematical Analysis, 2010

369 citations recorded by the source corpus.

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 [Appl. Comput. Harmonic Anal., 30 (2010), pp. 243–261] and consider a variant of Synchrosqueezing, based on the short-time Fourier transform, to precisely define the instantaneous frequencies of a multicomponent 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.

Subfields: Cardiology and Cardiovascular Medicine, Computer Vision and Pattern Recognition, Signal Processing

View Paper: https://www.semanticscholar.org/paper/71975f06249823b98d459b16006ea92f7fa481f6

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In Cardiology and Cardiovascular Medicine

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Citations in the corpus

Synchroextracting Transform (2017, background): “However, considering the calculation error and that the SEO’s real part needs to be utilized in practical applications [6], [17], it is suggested that (25) be rewritten as the following equation:”
High-Order Synchrosqueezing Transform for Multicomponent Signals Analysis—With an Application to Gravitational-Wave Signal (2017, methodology): “Using the principle of wavelet-based SST (WSST), Thakur and Wu proposed an extension of SST to the TF representation given by STFT (FSST) [8], which was then proven to be robust to small bounded perturbations and noise [9].”
Theoretical analysis of the second-order synchrosqueezing transform (2016, background): “A more important difference with [19] involves the separation condition satisfied by the different modes making up the signal (Definition 3.”
Time-Frequency Reassignment and Synchrosqueezing: An Overview (2013, methodology): “The discussion above on mode retrieval is reinforced by some theoretical results mostly derived in the wavelet framework in [12] and then adapted to the STFT context in [19].”
The Synchrosqueezing algorithm for time-varying spectral analysis: Robustness properties and new paleoclimate applications (2011, neutral): “In this paper, we focus on the original, CWT-based approach studied in [15,14], although an STFT-based alternative was developed in [44] and other variants are also possible.”
Multisynchrosqueezing Transform (2019, background): “In [7] and [8], it has been proved that putting ε̃ = ε1/3 and assuming ε being sufficiently small, for |G(t, ω)| ≥ ε̃, we have the approximation”