Synchrosqueezing-based Recovery of Instantaneous Frequency from Nonuniform Samples

TL;DR

This paper introduces a robust Synchrosqueezing-based method for accurately estimating the instantaneous frequency of multi-component signals from both uniform and nonuniform samples, with applications demonstrated in electrocardiography.

Contribution

It presents a novel Synchrosqueezing approach using short-time Fourier transform for precise instantaneous frequency recovery from irregular samples.

Findings

Method is robust to noise

Effective on real electrocardiography data

Outperforms traditional Hilbert transform-based methods

Abstract

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.