Linear Phase Properties Of Singular Spectrum Analysis Components And Its Application

Noise is everywhere.As a result,in the process of signal acquisition and recording,we are subject to external noise interference and other factors,so that we cannot directly extract effective information from the captured signal.Therefore,we need to carry out noise reduction and other pre-processing processes on the collected signals to eliminate all kinds of noise interference in the original signals,and then extract and utilize the effective information in the signals more effectively.At the same time,in order to restore the real information of the processed signal to the maximum extent without distortion,the pretreatment method often needs to have the property of linear phase.The properties of linear phase are originally properties of linear systems,such as FIR filters.On the one hand,we live in a world where signals tend to be nonlinear and nonstationary;On the other hand,due to the order of FIR filter design is relatively high,resulting in a huge amount of calculation.For the above reasons,we need to research the linear phase property of a nonlinear transformation to extract useful signals and complete the linea r phase theory.However,the research on the linear phase property of nonlinear transformation is rare.As an ideal nonlinear adaptive signal decomposition method for the processing of nonlinear non-stationary signals,singular spectrum analysis is a completely data-driven analysis technique without setting the basis function.With the expansion of the application of singular spectrum analysis,theoretical research becomes urgent.Different from the linear phase property of traditional filters,if the singular spectrum analysis components are symmetric or antisymmetric in the time domain,then their respective discrete Fourier transforms have the linear phase property.This thesis will focus on the linear phase property of the singular spectrum analysis components.The main contributions and innovations are as follows:(1)The linear phase properties of singular spectrum analysis components are presented and proved.As a property from linear system to nonlinear transformation,this paper proves the existence of this characteristic in theory and simulation.When the signal is linear phase,because the singular spectrum analysis components are linear phase,the noise reduction signal obtained by discarding some components is still in linear phase,which indicates that there is no group delay distortion caused by singular spectrum analysis in the process of noise reduction.(2)In order to further verify the linear phase property of the of singular spectrum analysis components,the singular spectrum analysis was applied to the preprocessing of R-peaks detection of Electrocardiograph signal.Since the Electrocardiograph signal is nearly linear phase,we replaced the nonlinear phase IIR filter with the singular spectrum analysis and then run the R-peaks detection algorithm,which significantly reduced the error rate.This application further confirms the linear phase property of the singular spectrum analysis components proposed by us,and can verify the robustness of this property,thus reducing the application limitation of the linear phase properties of singular spectrum analysis.