Error Analysis for Sparse Time-Frequency Decomposition of Non- Integer Period Sampling Signals

Abstract

In \u00a0this \u00a0paper, \u00a0we \u00a0review \u00a0a \u00a0nonlinear \u00a0matching \u00a0pursuit \u00a0approach \u00a0(Hou \u00a0and \u00a0Shi, \u00a02013), \u00a0a \u00a0data- driven \u00a0time-frequency \u00a0analysis \u00a0method, \u00a0which \u00a0is \u00a0looking \u00a0for \u00a0the \u00a0sparsest \u00a0representation \u00a0of \u00a0multiscale \u00a0data over a dictionary consisting of all intrinsic mode functions (IMFs). In many practical problems, signals are non-integer period sampled. In other words, the time window may not contain exactly an integer number of signal periods. We consider the sparse time-frequency decomposition of non-integer period sampling signals by the nonlinear matching pursuit method and estimate the error. The estimation show that the relative error depends on the separation factor, the frequency ratio, and the number of periods of the IMF.