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Abstract: We propose a new approach for studying the notion of the instantaneousfrequency of a signal. We build on ideas from the Synchrosqueezing theory ofDaubechies, Lu and Wu and consider a variant of Synchrosqueezing, based on theshort-time Fourier transform, to precisely define the instantaneous frequenciesof a multi-component AM-FM signal. We describe an algorithm to recover theseinstantaneous frequencies from the uniform or nonuniform samples of the signaland show that our method is robust to noise. We also consider an alternativeapproach based on the conventional, Hilbert transform-based notion ofinstantaneous frequency to compare to our new method. We use these methods onseveral test cases and apply our results to a signal analysis problem inelectrocardiography.



Author: Gaurav Thakur, Hau-Tieng Wu

Source: https://arxiv.org/







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