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wthcoef

1-D wavelet coefficient thresholding

    Description

    wthcoef thresholds wavelet coefficients for the denoising or compression of a 1-D signal.

    example

    nc = wthcoef("a",c,l) returns coefficients obtained from the multilevel wavelet decomposition structure [c,l] by setting the approximation coefficients to zero . For information about the decomposition structure, see wavedec.

    nc = wthcoef("d",c,l,n) returns coefficients obtained from [c,l] by setting all the coefficients at detail levels specified in n to zero.

    example

    nc = wthcoef("d",c,l,n,p) returns coefficients obtained from [c,l] by rate compression defined in vectors n and p. n specifies the detail levels to be compressed and p the corresponding percentages of lower coefficients to set to zero. n and p must be of the same length.

    nc = wthcoef("t",c,l,n,t,sorh) returns coefficients obtained from [c,l] by thresholding specified in thr. n specifies the detail levels to be thresholded and t the corresponding thresholds. n and t must be of the same length.

    Examples

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    Load and plot a 1-D signal.

    load wecg
    plot(wecg)
    title("Signal")
    axis tight

    Figure contains an axes object. The axes object with title Signal contains an object of type line.

    Obtain a level 3 wavelet decomposition of the signal using the Daubechies db4 wavelet.

    wv = "db4";
    [c,l] = wavedec(wecg,3,wv);

    Use wthcoef to modify the wavelet decomposition c. Set the approximation coefficients to zero and plot the difference between the original and modified wavelet decompositions.

    nc = wthcoef("a",c,l);
    plot(c-nc)
    title("Difference")
    axis tight

    Figure contains an axes object. The axes object with title Difference contains an object of type line.

    Reconstruct a signal using the modified wavelet decomposition.

    xrec = waverec(nc,l,wv);
    plot(xrec)
    title("Reconstruction")
    axis tight

    Figure contains an axes object. The axes object with title Reconstruction contains an object of type line.

    Save the current extension mode. Change the extension mode to periodized extension.

    origmode = dwtmode("status","nodisplay");
    dwtmode("per","nodisplay")

    Load and plot a 1-D signal. The signal has 2048 samples.

    load wecg
    plot(wecg)
    title("Signal")
    axis tight

    Figure contains an axes object. The axes object with title Signal contains an object of type line.

    Obtain a level 2 wavelet decomposition of the signal using the Haar wavelet. Display the bookkeeping vector. Confirm there are 1024 detail coefficients at level 1, and 512 detail coefficients at level 2.

    wv = "haar";
    [c,l] = wavedec(wecg,2,wv);
    l
    l = 4×1
    
             512
             512
            1024
            2048
    
    

    Use wthcoef to threshold the level 1 and level 2 detail coefficients in the wavelet decomposition c. Set 75% of the level 1 detail coefficients to zero, and set 50% of the level 2 detail coefficients to zero.

    nc = wthcoef("d",c,l,[1 2],[75 50]);

    Confirm there are 256 nonzero wavelet coefficients at levels 1 and 2 in the modified wavelet decomposition nc.

    [level1,level2] = detcoef(nc,l,[1 2]);
    [nnz(level1) 1024*0.25]
    ans = 1×2
    
       256   256
    
    
    [nnz(level2) 512*0.5]
    ans = 1×2
    
       256   256
    
    

    Reconstruct a signal using the modified wavelet decomposition.

    xrec = waverec(nc,l,wv);
    plot(xrec)
    title("Reconstruction")
    axis tight

    Figure contains an axes object. The axes object with title Reconstruction contains an object of type line.

    Restore the original extension mode.

    dwtmode(origmode,"nodisplay")

    Input Arguments

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    Wavelet decomposition, specified as a vector. The vector contains the wavelet coefficients. The bookkeeping vector l contains the number of coefficients by level. c is the output of wavedec.

    Data Types: single | double
    Complex Number Support: Yes

    Bookkeeping vector, specified as a vector of positive integers. The bookkeeping vector is used to parse the coefficients in the wavelet decomposition c by level. l is the output of wavedec.

    Data Types: single | double

    Detail levels, specified as a vector of positive integers less than or equal to N, where N is the level of the wavelet decomposition used to obtain [c,l]. Specifically, N = length(l)-2.

    Data Types: double

    Percentages of coefficients to set to zero, specified as a vector of positive integers less than or equal to 100. p and n must be the same length.

    Data Types: double

    Thresholds to apply to detail coefficients, specified as a real-valued vector. t and n must be the same length.

    Data Types: double

    Type of thresholding to perform:

    • "s" — Soft thresholding

    • "h" — Hard thresholding

    Output Arguments

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    Modified wavelet decomposition, returned as a vector. nc and c have equal length.

    Extended Capabilities

    C/C++ Code Generation
    Generate C and C++ code using MATLAB® Coder™.

    Version History

    Introduced before R2006a