The denoised coefficients can be obtained from the wdenoise function. Signal approximation can be done using these coefficients. Let me give an example of denoising with level 6 decomposition using ‘sym8’ wavelet.
[xden,denoisedcfs]=wdenoise( x,6, 'Wavelet', 'sym8') % xden is the denoised signal, x is the input signal
The final element of “denoisedcfs” cell array corresponds to approximation coefficients and the other elements corresponds to detail coefficients level by level. The wave decomposition vector can be found by using wavedec function. The wavelet used for denoising can be used to specify wavelet parameters for wavedec function.
[c,l] = wavedec(x,6,'sym8');
Signal approximation can be reconstructed using any level of detail coefficients and approximation coefficients. The code below reconstructs signal using 4th level detail coefficients and approximation coefficients. The detail coefficients in all other levels must be set to zero.
tmpcfs = denoisedcfs; %declare temporary cell array to use denoisedcfs for reconstruction
for ii = [1 2 3 5 6]
tmpcfs{ii} = zeros(numel(tmpcfs{ii}),1);
end
Assign the detail coefficients present in tmpcfs level by level to the wavelet decomposition vector c. Then use waverec function to reconstruct the signal approximation.
a=0;
for i=7:-1:1
c(a+1:a+numel(tmpcfs{1,i}))=tmpcfs{1,i}';
a=a+numel(tmpcfs{1,i});
end
X = waverec(c,l,'sym8'); %X is the signal approximation.
