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Analysis of Adaptive Synchrosqueezing Transform with a Time-varying Parameter

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Document pages: 38 pages

Abstract: The synchrosqueezing transform (SST) was developed recently to separate thecomponents of non-stationary multicomponent signals. The continuous wavelettransform-based SST (WSST) reassigns the scale variable of the continuouswavelet transform of a signal to the frequency variable and sharpens thetime-frequency representation. The WSST with a time-varying parameter, calledthe adaptive WSST, was introduced very recently in the paper "Adaptivesynchrosqueezing transform with a time-varying parameter for non-stationarysignal separation ". The well-separated conditions of non-stationarymulticomponent signals with the adaptive WSST and a method to select thetime-varying parameter were proposed in that paper. In addition, simulationexperiments in that paper show that the adaptive WSST is very promising inestimating the instantaneous frequency of a multicomponent signal, and inaccurate component recovery. However the theoretical analysis of the adaptiveWSST has not been studied. In this paper, we carry out such analysis and obtainerror bounds for component recovery with the adaptive WSST and the 2nd-orderadaptive WSST. These results provide a mathematical guarantee to non-stationarymulticomponent signal separation with the adaptive WSST.

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