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 2^{N} 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.

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