wnoise

Noisy wavelet test data

Syntax

x = wnoise(fun,n)

[x,xn] = wnoise(fun,n,sqrtsnr)

[x,xn] = wnoise(___,init)

Description

x = wnoise(fun,n) returns values x of the test signal fun evaluated at 2ⁿ linearly spaced points from 0 to 1.

[x,xn] = wnoise(fun,n,sqrtsnr) returns x rescaled such that the standard deviation of x is sqrtsnr. xn is x corrupted by additive Gaussian white noise N(0,1) and has a signal-to-noise ratio (SNR) of sqrtsnr².

[x,xn] = wnoise(___,init) sets the generator seed to init before generating additive Gaussian white noise N(0,1).

Examples

Plot Wavelet Test Signals

There are six test signals. Generate and plot $2^{10}$ samples of the third test signal, heavy sine.

loc = linspace(0,1,2^10);
x = wnoise(3,10);
plot(loc,x)
title('Heavy Sine')

Generate and plot $2^{10}$ samples of the doppler test signal and a noisy version of doppler with a square root of the signal-to-noise ratio equal to 7.

[x,noisyx] = wnoise('doppler',10,7);
tiledlayout(2,1)
nexttile
plot(loc,x)
title('Clean Doppler')
ylim([-15 15])
nexttile
plot(loc,noisyx)
title('Noisy Doppler')
ylim([-15 15])

Plot all the test functions.

testFunctions = {'Blocks','Bumps','Heavy Sine', ...
    'Doppler','Quadchirp','Mishmash'};
tiledlayout(3,2)
for i=1:6
    x = wnoise(lower(testFunctions{i}),10);
    nexttile
    plot(loc,x)
    title(testFunctions{i})
end

Input Arguments

fun — Wavelet test function

positive integer | character array

Wavelet test function, specified as one of the values listed here. The six test functions are due to Donoho and Johnstone [1], [2].

• 1 or 'blocks'

• 2 or 'bumps'

• 3 or 'heavy sine'

• 4 or 'doppler'

• 5 or 'quadchirp'

• 6 or 'mishmash'

n — Exponent

positive integer

Exponent used to determine the number of linearly spaced points from 0 to 1 to evaluate the test function, specified as a positive integer. The number of linearly spaced points is 2ⁿ.

sqrtsnr — Square root of SNR

positive real number

Square root of SNR, specified by a positive real number. The test values x are rescaled such that the standard deviation of x is sqrtsnr. xn is equal to x corrupted by additive Gaussian white noise N(0,1) and has an SNR of sqrtsnr².

init — Seed

nonnegative integer

Seed used to initialize the random number generator, specified as a nonnegative integer. init is used to generate additive Gaussian white noise.

Example: [a,b] = wnoise(4,10,7,2055415866); returns a noisy version of the fourth test signal using the seed init = 2055415866.

Output Arguments

x — Test signal

real-valued vector

Test signal, returned as a real-valued vector of length 2ⁿ. x are the values of the test function specified by fun evaluated at the 2ⁿ evenly spaced points from 0 to 1. If sqrtsnr is set, the standard deviation of x is sqrtsnr.

xn — Noisy test signal

real-valued vector

Noisy test signal, returned as a real-valued vector of length 2ⁿ. xn is x corrupted by additive Gaussian white noise N(0,1) and has an SNR of sqrtsnr².

References

[1] Donoho, David L, and Iain M Johnstone. “Ideal Spatial Adaptation by Wavelet Shrinkage.” Biometrika 81, no. 3 (September 1, 1994): 425–55. https://doi.org/10.1093/biomet/81.3.425.

[2] Donoho, David L., and Iain M. Johnstone. “Adapting to Unknown Smoothness via Wavelet Shrinkage.” Journal of the American Statistical Association 90, no. 432 (December 1995): 1200–1224. https://doi.org/10.1080/01621459.1995.10476626.

Version History

Introduced before R2006a