Extracting a shape function for a signal with intra-wave frequency modulation

TL;DR

This paper introduces a new data-driven method to extract shape functions for signals with intra-wave frequency modulation, improving analysis by leveraging low rank structures and optimization techniques.

Contribution

It generalizes time-frequency analysis with a shape function model and proposes an optimization-based approach to extract it from signals.

Findings

Effective extraction of shape functions demonstrated on synthetic signals

Robustness confirmed through tests on real signals

Low rank structure aids in shape function identification

Abstract

In this paper, we consider signals with intra-wave frequency modulation. To handle this kind of signals effectively, we generalize our data-driven time-frequency analysis by using a shape function to describe the intra-wave frequency modulation. The idea of using a shape function in time-frequency analysis was first proposed by Wu. A shape function could be any periodic function. Based on this model, we propose to solve an optimization problem to extract the shape function. By exploring the fact that s is a periodic function, we can identify certain low rank structure of the signal. This structure enables us to extract the shape function from the signal. To test the robustness of our method, we apply our method on several synthetic and real signals. The results are very encouraging.