In this paper, the shortcomings of traditional filter methods in dealing with non-stationary signals are analyzed. The principle and method of wavelet denoising are studied. The method of mixed programming with LabVIEW and Matlab is studied. The perfect graphical programming technology of LabVIEW and the powerful mathematics of Matlab are studied. The solution functions are combined to realize mathematical modeling and signal image display of wavelet denoising. The filtering process of the vibration shock signal shows the effectiveness of the wavelet denoising method in dealing with non-stationary signals.
0 Preface
Signal noise reduction is one of the classic problems in the field of signal processing. The traditional noise reduction methods mainly include a linear filtering method and a nonlinear filtering method. The filter filters the signals during operation, and only allows signals of a specific frequency band to pass. When the useful component and the noise component in the signal occupy different frequency bands, the noise component can be effectively removed. But if the spectrum of the signal and noise overlap, the classical filter will not work. These filters can be divided into high-pass, low-pass and band-pass filters according to the filtered frequency band. According to the idea of ​​designing filters, the filters can be divided into Butterworth filters, Bessel filters, elliptical filters and cut ratios. Schiff filter, etc.
In addition, the conventional filter noise reduction method is insufficient in that the entropy is increased after the signal is transformed, the non-stationaryness of the signal cannot be characterized, and the correlation of the signal cannot be obtained. In order to overcome the above shortcomings, the method of using wavelet transform to solve signal noise reduction is more and more widely used. However, due to the deep mathematical theory of wavelet transform, it is very difficult for beginners to use traditional C language programming methods. In this paper, LabVIEW and Matlab mixed programming method is used to combine LabVIEW's perfect graphic programming technology with Matlab's powerful mathematical solving function to realize mathematical modeling and signal image display of wavelet denoising.
1 Wavelet transform principle
The theory of wavelet transform mainly includes continuous wavelet transform, discrete wavelet transform and multi-resolution analysis.
1.1 Continuous wavelet transform
The family of functions {ψ a,b } generated by translation and expansion as follows is called ContIn Wavelet Transform (CWT), which is called basic wavelet.
The wavelet transform coefficients of an arbitrary function at a certain scale a and translation point b are essentially characterized by the b position, and the time period 2a Δψ is included in the frequency window of the center frequency ω* a and the bandwidth of 2 Δψ - /a The magnitude of the frequency component, as the scale a changes, the corresponding window center frequency is ω* a and the window width 2Δψ - /a also changes.
1.2 Discrete wavelet transform
In practical applications, the signals generally analyzed are discrete time series obtained after discrete sampling, and the continuous wavelet and its transformation need to be discretized for digital signal processing. The specific method is discretized by sampling its scaling factor a and translation factor b.
Where: m, n are called frequency range index and time step change index, respectively.
In the continuous wavelet transform W ψ f (a, b), since a and b are continuously changed, it is highly redundant, and as long as the mother wavelet ψ(t) satisfies the allowable condition, W ψ f (a, b) can be completely Restore the original signal f (t). For discrete wavelet transforms, since a and b are discretely sampled, in order to make Wψ f (m,n) contain enough information to recover the original signal f (t), it is necessary to impose stricter restrictions on the mother wavelet used for the transform. .
The family of functions {- }jj ∈ J in the Hilbert space H is called a frame. If A, B ∈ (0, ∞) exists, for all f ∈ H, there are:
2 Wavelet noise reduction principle
Wavelet transform has the characteristics of low entropy, multi-resolution, de-correlation and flexibility of selection. Therefore, wavelet denoising is more widely used. The threshold denoising method is a wavelet denoising method with simple implementation and good results.
The threshold denoising method is to separately process the coefficients of the layer coefficients after the wavelet decomposition are larger than and less than a certain threshold, and then inversely transform the processed wavelet coefficients to reconstruct the denoised signal. In reality, the useful signal is usually a low frequency signal, and the noise signal is usually a high frequency signal. In the process of denoising, the high frequency coefficient of the wavelet decomposition is usually thresholded to reconstruct the signal. Threshold acquisition is the key to wavelet denoising. The wavelet denoising module in this paper uses the wavelet analysis function in Matlab wavelet analysis toolbox to obtain the threshold.
The functions of signal threshold acquisition in Matlab are ddencmp, thselect, wbmpen and wdcbm. In this paper, some Matlab codes using wbmpen. wavelet denoising are as follows:
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