# wnoisest

Estimate noise of 1-D wavelet coefficients

## Syntax

```STDC = wnoisest(C,L,S) STDC = wnoisest(C) STDC = wnoisest(C) ```

## Description

`STDC = wnoisest(C,L,S)` returns estimates of the detail coefficients' standard deviation for levels contained in the input vector `S`. `[C,L]` is the input wavelet decomposition structure (see `wavedec` for more information).

If `C` is a one dimensional cell array, ```STDC = wnoisest(C)``` returns a vector such that `STDC(k)` is an estimate of the standard deviation of `C{k}`.

If `C` is a numeric array, ```STDC = wnoisest(C)``` returns a vector such that `STDC(k)` is an estimate of the standard deviation of `C(k,:)`.

The estimator used is Median Absolute Deviation / 0.6745, well suited for zero mean Gaussian white noise in the de-noising one-dimensional model (see `thselect` for more information).

## Examples

collapse all

Estimate of the noise standard deviation in an N(0,1) white Gaussian noise vector with outliers.

Create an N(0,1) noise vector with 10 randomly-placed outliers.

```rng default; x = randn(1000,1); P = randperm(length(x)); indices = P(1:10); x(indices(1:5)) = 10; x(indices(6:end)) = -10;```

Obtain the discrete wavelet transform down to level 2 using the Daubechies’ extremal phase wavelet with 3 vanishing moments.

```[c,l] = wavedec(x,2,'db3'); stdc = wnoisest(c,l,1:2)```
```stdc = 1×2 0.9650 1.0279 ```

In spite of the outliers, `wnoisest` provides a robust estimate of the standard deviation.

## References

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.

## Extended Capabilities

### Apps

Introduced before R2006a

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