whitening filter on signals in matlab

To apply a whitening filter on signals in MATLAB, you can follow these steps:

  1. Load or generate the signal that you want to whiten.

  2. Compute the auto-correlation matrix of the signal using the xcorr function. This will give you a symmetric matrix.

    main.m
    signal = ...; % Your signal
    autoCorrMatrix = xcorr(signal);
    
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  3. Compute the eigenvalues and eigenvectors of the auto-correlation matrix using the eig function.

    main.m
    [eigVec, eigVal] = eig(autoCorrMatrix);
    
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  4. Construct a diagonal matrix D by taking the square root of the eigenvalues.

    main.m
    D = sqrt(eigVal);
    
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  5. Compute the whitening matrix W by multiplying the eigenvectors with the inverse square root of the eigenvalues.

    main.m
    W = eigVec * inv(D);
    
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  6. Apply the whitening filter to the original signal by multiplying it with the whitening matrix.

    main.m
    whitenedSignal = W * signal;
    
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The whitenedSignal represents the signal after applying the whitening filter. Note that this process assumes that your signal is zero-mean and stationary.

Please note that this whitening filter assumes a discrete-time signal. If you have a continuous-time signal, you may need to perform additional steps such as sampling and discretization before applying the above steps.

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