Time-Frequency Mode Decomposition: A Morphological Segmentation Framework for Signal Analysis and Its Application

TL;DR

This paper introduces TFMD, a novel time-frequency decomposition framework that segments signals based on morphological features, automatically identifies components, and improves reconstruction accuracy and noise robustness in non-stationary signal analysis.

Contribution

The paper presents a new morphological segmentation-based approach for time-frequency mode decomposition that automatically determines the number of components and enforces mutual exclusivity, outperforming benchmark methods.

Findings

TFMD achieves superior reconstruction fidelity.

It demonstrates robustness to noise.

It offers efficient computation with competitive runtime.

Abstract

While time-frequency analysis provides rich representations of multicomponent signals, current decomposition methods often overlook the morphological structure where components manifest as distinct regions. This study introduces time-frequency mode decomposition (TFMD), a novel framework that formulates signal decomposition as a generalized morphological segmentation problem within the continuous phase space. TFMD establishes an operator-theoretic framework utilizing the short-time Fourier transform as a canonical tight frame. The methodology employs unsupervised k-means clustering to identify high-energy pixels, followed by connected component labeling to establish core regions. A novel iterative competitive dilation algorithm is then applied to expand these core regions to recover the full support of each mode and define its specific time-frequency mask for mode reconstruction. This approach automatically determines the number of components without prior specification while strictly enforcing mutual exclusivity between modes. Comprehensive numerical investigations demonstrate TFMD's superior reconstruction fidelity, noise robustness, and computational efficiency compared to benchmark methods. TFMD achieves the lowest individual mode errors across diverse non-stationary signals and secures the second-best runtime. Practical validation through wind turbine vibration analysis confirms TFMD's ability to isolate both dominant fundamental frequencies and weaker harmonic components across discrete operational states, overcoming limitations of mode splitting and mixing issues observed in benchmark methods.