Research On Improvement And Application Of Threshold Function Based On Wavelet Denoising

Wavelet analysis theory is the crystallization of the common struggle of scholars in many research fields.In terms of fault diagnosis,speech signal processing,image compression,and fluid mechanics,wavelet transform has become a very important processing tool with its powerful analysis capabilities.In the modern scientific era,the interweaving characteristics of many disciplines.Fourier analysis is the basis of wavelet theory.Because Fourier transform has certain defects in signal processing,it can only deal with related stationary signals.If the signal is non-stationary,Fourier transform cannot The signal is analyzed,and wavelet analysis can perform localized analysis of the signal,reflect the important characteristics of the signal in the time and frequency domain,and perform a deeper interpretation of the signal.When analyzing related signals,it is necessary to denoise the signal first and then do the related processing.Therefore,signal denoising occupies an important position in signal processing.The traditional hard threshold and soft threshold functions have their own shortcomings,and they are powerless in the current fast-developing signal processing.Therefore,the proposal of the new wavelet threshold function is particularly important in the current signal processing.First,this article gives an overview of the relevant theories of wavelet analysis,and then introduces the relevant principles and procedures of wavelet signal denoising and common signal denoising methods in detail.Among these types of denoising methods,the wavelet threshold denoising method has the most powerful denoising effect by its maximum signal-to-noise ratio and minimum mean square error.Therefore,in-depth research and application of wavelet threshold denoising methods have become extremely important.Secondly,analyze the relevant influences of wavelet threshold denoising,including the selection of wavelet basis function,the selection of wavelet decomposition layers,the choice of the threshold rule and the choice of the threshold function..Different choices in these aspects will affect the signal.Denoising effect.This article mainly focuses on the improvement of the influencing factor of the threshold function.The hard threshold function is discontinuous,the signal is prone to large variance,and the reconstructed signal is easy to oscillate,which will eventually lead to the deterioration of the quality of the signal reconstruction effect;When the threshold function performs soft threshold processing,the wavelet coefficients of the original signal and the denoised signal have a constant deviation,which will also cause the signal reconstruction to be correspondingly affected and the reconstruction quality to deteriorate.This paper conducts research on the basis of the traditional threshold function,and constructs a new threshold function.The new threshold function has good mathematical characteristics and overcomes the related defects of the traditional threshold function.At the same time,it compares the signal-to-noise ratio and mean square error of signal denoising.Analyzing the evaluation criteria,it verifies that the new threshold function has a good denoising effect.Finally,from the perspective of the application of signal denoising,this article combines the wavelet threshold denoising method with the Elman neural network to construct a new stock price prediction model method.First,the relevant concepts of the Elman neural network method are explained,and then the Shanghai Composite Index is selected.Signal denoising processing is performed on the closing price of,and in the Elman neural network model,the denoised data signal is modeled,and relevant prediction processing is made.At the same time,the effect of neural network prediction is compared and analyzed in the two cases of data with and without denoising,and it is found that the effect of neural network prediction after threshold denoising is better.