# wnoise

Noisy wavelet test data

## 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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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);
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.

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'

• 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.