STFT-based Time-Frequency Mode Decomposition: A Fast and Robust Method for Multicomponent Signal Analysis

Abstract: The decomposition of complex, multicomponent, and non-stationary signals into their constituent modes is a fundamental yet significant challenge in science and engineering. Existing methods often struggle with a trade-off among accuracy, computational cost, and the need for prior information such as the number of modes. This paper introduces time-frequency mode decomposition (TFMD), a novel framework for the fast, robust, and adaptive decomposition of such signals. TFMD operates on the principle that modes form contiguous high-energy regions in the time-frequency domain. Its non-iterative pipeline reframes signal decomposition as an image segmentation task: a signal is transformed into a spectrogram, which is then smoothed to enhance the continuity of these high-energy regions. A sequence of adaptive thresholding and connected-component labeling with size-based filtering is then employed to automatically segment the spectrogram and generate a mask for each mode. The modes are finally reconstructed via the inverse short-time Fourier transform. Validation on diverse synthetic signals demonstrates that TFMD accurately determines the number of modes and reconstructs them with high fidelity. Its performance is particularly strong in high-noise conditions. A comparative analysis confirms that TFMD provides robust, competitive performance across a wider variety of signal types, while a theoretical complexity analysis reveals its superior computational efficiency stemming from its non-iterative design. The method's practical utility is further demonstrated by successfully extracting modal responses from a real-world footbridge vibration signal. TFMD provides a computationally efficient and powerful paradigm for multicomponent signal analysis, offering a compelling balance of accuracy, versatility, and efficiency for large-scale or time-sensitive applications.