On the Practical Use of Blaschke Decomposition in Nonstationary Signal Analysis

2025-08-14

AI Summary

Blaschke decomposition (PDU) suffers from modeling difficulties for complex trends and amplitude modulations in nonstationary signals, as well as mode mixing induced by phase wrapping. To address these issues, this paper proposes a divide-and-conquer strategy incorporating windowed segmentation and cumulative-sum (cumsum) preprocessing: the signal is partitioned via a sliding window, tapered windows suppress boundary effects, and cumsum integration prior to phase unwrapping provides smooth, unwrapped-phase initialization—thereby mitigating phase discontinuities and enhancing multiresolution decomposition stability. The method significantly improves adaptability to strongly nonstationary signals. Extensive validation on both synthetic and real-world data demonstrates superior decomposition accuracy and accelerated convergence compared to conventional approaches. The framework maintains theoretical rigor—grounded in Hardy space theory—while offering practical utility for engineering applications in time-frequency analysis and signal separation.

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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.

Problem

• Handling complex trends in nonstationary signals
• Addressing mode-mixing caused by winding
• Improving practical signal decomposition performance

Innovation

• Blaschke decomposition with Phase Dynamics Unwinding
• Divide-and-conquer via tapering and cumsum
• Windowed PDU for enhanced signal decomposition