wthresh

Soft or hard thresholding

Syntax

Y = wthresh(X,sorh,T)

Description

Y = wthresh(X,sorh,T) returns the soft or hard thresholding, indicated by sorh, of the vector or matrix X. T is the threshold value.

Examples

Hard and Soft Thresholding

Generate a signal and set a threshold.

y = linspace(-1,1,100);
thr = 0.4;

Perform hard and soft thresholding.

ythard = wthresh(y,'h',thr);
ytsoft = wthresh(y,'s',thr);

Plot the results and compare with the original signal.

subplot(1,3,1)
plot(y,y)
ylim([-1 1])
title('Original Signal')
subplot(1,3,2)
plot(y,ythard)
ylim([-1 1])
title('Hard Threshold')
subplot(1,3,3)
plot(y,ytsoft)
ylim([-1 1])
title('Soft Threshold')

Input Arguments

X — Input data

real-valued vector or matrix

Input data to threshold, specified as a real-valued vector or matrix.

Data Types: double

sorh — Type of thresholding

's' | 'h'

Type of thresholding to perform:

• 's' — Soft thresholding

• 'h' — Hard thresholding

T — Threshold value

positive real number

Threshold value, specified as a positive real number.

Output Arguments

Y — Thresholded data

real-valued vector or matrix

Thresholded data, returned as a real-valued vector or matrix. Y has the same dimensions as X.

Algorithms

If sorh is 's', Y is the soft thresholding of X: $$\text{Y}=\text{sign(X)}·{(|\text{X}|-\text{T})}_{+}$$ where

$${(x)}_{+}=\{\begin{array}{ccc}x& \text{if}& x\ge 0\\ 0& \text{otherwise}& \end{array}$$

Soft thresholding is wavelet shrinkage.

If sorh is 'h', Y is the hard thresholding of X: $$\text{Y}=\text{X}·1_{(|\text{X}|>\text{T})}$$ where

$$1_{(|\text{X}|>\text{T})}=\{\begin{array}{ccc}1& \text{if}& \left|\text{X}\right|>\text{T}\\ 0& \text{otherwise}& \end{array}$$

Hard thresholding is cruder than soft thresholding.

Extended Capabilities

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

Version History

Introduced before R2006a