Adaptive synchrosqueezing based on a quilted short-time Fourier transform

摘要

In recent years, the synchrosqueezing transform (SST) has gained popularityas a method for the analysis of signals that can be broken down into multiplecomponents determined by instantaneous amplitudes and phases. One such versionof SST, based on the short-time Fourier transform (STFT), enables thesharpening of instantaneous frequency (IF) information derived from the STFT,as well as the separation of amplitude-phase components corresponding todistinct IF curves. However, this SST is limited by the time-frequencyresolution of the underlying window function, and may not resolve signalsexhibiting diverse time-frequency behaviors with sufficient accuracy. In thiswork, we develop a framework for an SST based on a "quilted" short-time Fouriertransform (SST-QSTFT), which allows adaptation to signal behavior in separatetime-frequency regions through the use of multiple windows. This motivates usto introduce a discrete reassignment frequency formula based on a finitedifference of the phase spectrum, ensuring computational accuracy for a widervariety of windows. We develop a theoretical framework for the SST-QSTFT inboth the continuous and the discrete settings, and describe an algorithm forthe automatic selection of optimal windows depending on the region of interest.Using synthetic data, we demonstrate the superior numerical performance ofSST-QSTFT relative to other SST methods in a noisy context. Finally, we applySST-QSTFT to audio recordings of animal calls to demonstrate the potential ofour method for the analysis of real bioacoustic signals.