Matlab wavelet denoising function example

[xd,cxd,lxd]=wden(x,tptr,sorh,scal,n,'wname')

Where: the input parameter x is a signal that needs to be denoised;

1.tptr: Threshold selection criteria.

1) The principle of unbiased likelihood estimation. It is an adaptive threshold selection based on the principle of Stein's unbiased likelihood estimation (quadratic equation). For a given threshold t, its likelihood estimate is obtained, and then the likelihood t is minimized to obtain the selected threshold, which is a software threshold estimator.

2) The principle of fixed threshold (sqtwolog). The calculation formula of the fixed threshold thr2 is: thr2log(n) 2 = (6) where n is the length of the signal x(k).

3) Heuristic principle of heirsure. It is a compromise between the rigrsure principle and the sqtwolog principle. If the signal-to-noise ratio is small, the signal processed according to the rigrsure principle is relatively noisy, and the sqtwolog principle is adopted.

4) The principle of extreme value threshold (minimaxi). It uses the principle of minimax selected threshold, generating an extreme value of the minimum mean square error, it is not without errors.

2. Sorh: Threshold function selection mode, ie soft threshold (s) or hard threshold (h).

3.scal: threshold processing varies with noise level, scal=one means no change with noise level, scal=sln means adjustment based on noise level estimation of first layer wavelet decomposition, scal=mln means noise according to each layer of wavelet decomposition The level estimate is adjusted.

4.n and wname represent the n-layer decomposition of the signal using a wavelet named wname. Output denoised data xd and additional wavelet decomposition structure of xd [cxd, lxd].

Code:

% load collected signal leleccum.mat

Loadleleccum;

%==============================

% assigns the 2000th to 3450th sampling points in the signal to s

Indx=2000:3450;

s=leleccum(indx);

%============================================================

Subplot(2,2,1);

Plot(s);

TItle ('original signal');

%==============================

% db1 wavelet is used to perform 3 layers decomposition of the original signal and extract coefficients

[c,l]=wavedec(s,3,'db1');

A3=appcoef(c,l,'db1',3);

D3=detcoef(c,l,3);

D2=detcoef(c,l,2);

D1=detcoef(c,l,1);

%==============================

% Forced noise cancellation on the signal and shows the result

Dd3=zeros(1,length(d3));

Dd2=zeros(1,length(d2));

Dd1=zeros(1,length(d1));

C1=[a3dd3dd2dd1];

S1=waverec(c1,l,'db1');

Subplot(2,2,2);

Plot(s1);grid;

TItle ('signal after forced denoising');

%==============================

% Denoise the signal with the default threshold and plot the result

% Use the ddencmp function to get the default threshold of the signal

[thr,sorh,keepapp]=ddencmp('den','wv',s);

S2=wdencmp('gbl',c,l,'db1',3,thr,sorh,keepapp);

Subplot(2,2,3);

Plot(s2);grid;

TItle ('the default threshold denoised signal');

%==============================

% is denoised with a given soft threshold

Sosoftd2=wthresh(d2,'s', 1.823);

Softd3=wthresh(d3,'s', 2.768);

C2=[a3softd3softd2softd1];

S3=waverec(c2,l,'db1');

Subplot(2,2,4);

Plot(s3);grid;

TItle ('given the soft threshold denoised signal');

Ftd1=wthresh(d1,'s', 1.465);