wnoise

Noisy wavelet test data

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Syntax

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

Description

example

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

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Open Live Script

There are six test signals. Generate and plot 210 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 210 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);
subplot(2,1,1)
plot(loc,x)
title('Clean Doppler')
ylim([-15 15])
subplot(2,1,2)
plot(loc,noisyx)
title('Noisy Doppler')
ylim([-15 15])

Plot all the test functions.

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

Input Arguments

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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'

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.

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.

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

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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.

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, D. L., and I. M. Johnstone. “Ideal spatial adaptation by wavelet shrinkage.” Biometrika. Vol. 81, Issue 3, 1994, pp. 425–455.

[2] Donoho, D. L., and I. M. Johnstone. “Adapting to unknown smoothness via wavelet shrinkage.” Journal of the American Statistical Association. Vol. 90, 1995, pp. 1200–1224.

See Also

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Introduced before R2006a

Wavelet Toolbox Documentation
Support