Sparse Time-Frequency decomposition for multiple signals with same frequencies

TL;DR

This paper introduces a novel sparse time-frequency decomposition method for multiple signals sharing the same frequencies, enhancing robustness to noise and missing data through simultaneous frequency updates and efficient algorithms.

Contribution

It proposes a new data-driven approach that updates instantaneous frequencies simultaneously for multiple signals, improving robustness and efficiency in time-frequency analysis.

Findings

Effective on synthetic and real signals

Robust to noise, missing samples, and outliers

Promising performance demonstrated

Abstract

In this paper, we consider multiple signals sharing same instantaneous frequencies. This kind of data is very common in scientific and engineering problems. To take advantage of this special structure, we modify our data-driven time-frequency analysis by updating the instantaneous frequencies simultaneously. Moreover, based on the simultaneously sparsity approximation and fast Fourier transform, some efficient algorithms is developed. Since the information of multiple signals is used, this method is very robust to the perturbation of noise. And it is applicable to the general nonperiodic signals even with missing samples or outliers. Several synthetic and real signals are used to test this method. The performances of this method are very promising.