On the Practical Use of Blaschke Decomposition in Nonstationary Signal Analysis

TL;DR

This paper improves the practical application of Blaschke decomposition-based Phase Dynamics Unwinding (PDU) for nonstationary signals by introducing techniques to handle complex trends and mode-mixing, validated on simulated and real data.

Contribution

It proposes windowed PDU with divide-and-conquer and cumsum techniques to enhance real-world signal decomposition performance.

Findings

Enhanced decomposition accuracy on complex signals

Effective handling of amplitude modulations and mode-mixing

Validated on diverse simulated and real-world signals

Abstract

The Blaschke decomposition-based algorithm, {\em Phase Dynamics Unwinding} (PDU), possesses several attractive theoretical properties, including fast convergence, effective decomposition, and multiscale analysis. However, its application to real-world signal decomposition tasks encounters notable challenges. In this work, we propose two techniques, divide-and-conquer via tapering and cumulative summation (cumsum), to handle complex trends and amplitude modulations and the mode-mixing caused by winding. The resulting method, termed {\em windowed PDU}, enhances PDU's performance in practical decomposition tasks. We validate our approach through both simulated and real-world signals, demonstrating its effectiveness across diverse scenarios.