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Analyzing and breaking down nonstationary signals into their primary components is significant in various optical applications. In this work, we design a direct, localized, and mathematically rigorous method for nonstationary signals by employing a modulated short-time Fourier transform (MSTFT) that can be implemented efficiently using fast Fourier transform, subsequently isolating energy-concentrated sets through an approximate threshold process, allowing us to directly retrieve instantaneous frequencies and signal components by determining the maximum frequency within each set. MSTFT provides a new insight into the time-frequency analysis in multicomponent signal separation and can be extended to other time-frequency transforms. Beyond the analysis of the synthetic, we also perform real dual-comb ranging signals under turbid water, and the results show an approximate 1.5 dB improvement in peak signal-to-noise ratio, further demonstrating the effectiveness of our method in challenging conditions.
Han et al. (Fri,) studied this question.