On the Practical Use of Blaschke Decomposition in Nonstationary Signal Analysis
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arXiv
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| Format: | Preprint |
| Published: |
2025
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| _version_ | 1866914143212142592 |
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| author | Coifman, Ronald R. Wu, Hau-Tieng |
| author_facet | Coifman, Ronald R. Wu, Hau-Tieng |
| contents | 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. |
| format | Preprint |
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arxiv_https___arxiv_org_abs_2508_10861 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | On the Practical Use of Blaschke Decomposition in Nonstationary Signal Analysis Coifman, Ronald R. Wu, Hau-Tieng Methodology Complex Variables Data Analysis, Statistics and Probability 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. |
| title | On the Practical Use of Blaschke Decomposition in Nonstationary Signal Analysis |
| topic | Methodology Complex Variables Data Analysis, Statistics and Probability |
| url | https://arxiv.org/abs/2508.10861 |