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Abstract
En 中文
A topological signal processing framework is introduced to enhance the noise robustness of synchrosqueezing-based time–frequency (TF) analysis. Designed as a postprocessing procedure applicable to any TF representation, the method produces a more energy-concentrated and sparse TF spectrum. The approach begins with the short-time Fourier transform (STFT) of a one-dimensional signal, followed by the computation of sublevel set persistence (SSP) on the noisy TF surface. By statistically filtering persistence pairs associated with noise, the instantaneous frequency is extracted with improved stability. The effectiveness of the framework is demonstrated using both simulated frequency- and amplitude-modulated signals, as well as a benchmark bat-echolocation signal, where substantial improvements are observed in TF clarity and noise robustness. Additional validation on an experimental three-story building structure further shows that the SSP-enhanced TF representation yields a distinct and continuous TF ridge, outperforming mainstream TF analysis techniques in terms of readability and energy concentration. The proposed framework provides a generalizable perspective for integrating topological methods with TF analysis, and future research will focus on extending SSP to multiscale persistence, adaptive thresholding strategies, and its coupling with advanced TF methods such as wavelet-based transforms and data-driven mode decomposition techniques.
Keywords:
robustness
sublevel set persistence
synchrosqueezing transform
time–frequency analysis
topological signal processing
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