Noisy wavelet test data
X = wnoise(FUN,N)
[X,XN] = wnoise(FUN,N,SQRT_SNR)
[X,XN] = wnoise(FUN,N,SQRT_SNR,INIT)
X = wnoise(FUN,N) returns values of the test signal given by FUN, on a 2N grid of [0,1].
[X,XN] = wnoise(FUN,N,SQRT_SNR) returns a test vector X as above, rescaled such that std(X) = SQRT_SNR. The returned vector XN contains the same test vector corrupted by additive Gaussian white noise N(0,1). Then, XN has a signal-to-noise ratio of SNR = (SQRT_SNR)2.
[X,XN] = wnoise(FUN,N,SQRT_SNR,INIT) returns previous vectors X and XN, but the generator seed is set to INIT value.
The six functions below are due to Donoho and Johnstone (See "References").
|FUN = 1 or||'blocks'|
|FUN = 2 or||'bumps'|
|FUN = 3 or||'heavy sine'|
|FUN = 4 or||'doppler'|
|FUN = 5 or||'quadchirp'|
|FUN = 6 or||'mishmash'|
% Generate 2^10 samples of 'Heavy sine' (item 3). x = wnoise(3,10); % Generate 2^10 samples of 'Doppler' (item 4) and of % noisy 'Doppler' with a square root of signal-to-noise % ratio equal to 7. [x,noisyx] = wnoise(4,10,7); % To introduce your own rand seed, a fourth % argument is allowed: init = 2055415866; [x,noisyx] = wnoise(4,10,7,init); % Plot all the test functions. ind = linspace(0,1,2^10); for i = 1:6 x = wnoise(i,10); subplot(6,1,i), plot(ind,x) end % Editing some graphical properties, % the following figure is generated.
Donoho, D.L.; I.M. Johnstone (1994), "Ideal spatial adaptation by wavelet shrinkage," Biometrika, vol. 81, pp. 425–455.
Donoho, D.L.; I.M. Johnstone (1995), "Adapting to unknown smoothness via wavelet shrinkage via wavelet shrinkage," JASA, vol. 90, 432, pp. 1200–1224.