wthcoef

R2026b

1-D wavelet coefficient thresholding

Syntax

nc = wthcoef("a",c,l)

nc = wthcoef("d",c,l,n)

nc = wthcoef("d",c,l,n,p)

nc = wthcoef("t",c,l,n,t,sorh)

Description

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

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.

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

Modify Approximation Coefficients

Load and plot a 1-D signal.

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

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

Reconstruct a signal using the modified wavelet decomposition.

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

Threshold Wavelet Coefficients

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

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

Restore the original extension mode.

dwtmode(origmode,"nodisplay")

Input Arguments

c — Wavelet decomposition

vector

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

l — Bookkeeping vector

vector

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

n — Detail levels

vector

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

p — Percentages

vector

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

t — Thresholds

vector

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

Data Types: double

sorh — Type of thresholding

"s" | "h"

Type of thresholding to perform:

• "s" — Soft thresholding

• "h" — Hard thresholding

Output Arguments

nc — Modified wavelet decomposition

vector

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™.

GPU Code Generation
Generate CUDA® code for NVIDIA® GPUs using GPU Coder™.

Thread-Based Environment

Run code in the background using MATLAB® backgroundPool or accelerate code with Parallel Computing Toolbox™ ThreadPool.

The wthcoef function fully supports thread-based environments. For more information, see Run MATLAB Functions in Thread-Based Environment.

Version History

Introduced before R2006a

R2026b: Use thread-based environments

You can use wthcoef in thread-based environments. For more information, see Run MATLAB Functions in Thread-Based Environment.