Jump Plus AM-FM Mode Decomposition
Mojtaba Nazari, Anders Rosendal Korsh{\o}j, Naveed ur Rehman

TL;DR
This paper introduces a new variational optimization method for decomposing nonstationary signals into AM-FM oscillations and jump discontinuities simultaneously, outperforming existing techniques across various real-world applications.
Contribution
The authors propose a novel joint decomposition approach that effectively extracts both oscillatory modes and jumps from complex signals using a unified optimization framework.
Findings
Superior performance on synthetic and real data
Effective extraction of jumps and oscillations simultaneously
Validated on Earth's electric field, ECG, and EEG signals
Abstract
A novel method for decomposing a nonstationary signal into amplitude- and frequency-modulated (AM-FM) oscillations and discontinuous (jump) components is proposed. Current nonstationary signal decomposition methods are designed to either obtain constituent AM-FM oscillatory modes or the discontinuous and residual components from the data, separately. Yet, many real-world signals of interest simultaneously exhibit both behaviors i.e., jumps and oscillations. Currently, no available method can extract jumps and AM-FM oscillatory components directly from the data. In our novel approach, we design and solve a variational optimization problem to accomplish this task. The optimization formulation includes a regularization term to minimize the bandwidth of all signal modes for effective oscillation modeling, and a prior for extracting the jump component. Our method addresses the limitations of…
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Taxonomy
TopicsNon-Invasive Vital Sign Monitoring · Geophysics and Sensor Technology
