## Soft shrinking

Purpose

Description

Example

Macro Synopsis

Modules

Related Functions

References

### Purpose

Noise reduction by wavelet soft shrinking

### Description

"Soft shrinking" removes noise from the input signal x by the
following steps:
- compute the discrete wavelet transform of x
- replace each value d of each detail signal by

where the threshold t is ,
r is the noise level, and N the length of x.

Parameters are

- number n of octaves (decomposition depth)
- noise level
`r` (standard deviation)

### Example

"Soft shrinking" is used for the filtering of nonstationary time series,
and the smoothing of signals with unknown type of noise.

### Macro Synopsis

`y = WaveletSoftShrink(x,n,r);`

signal x,y;

int n;

float r;

### Modules

Wavelet

### Related Functions

Define wavelet, Load wavelet,
Save wavelet, Decompose,
Reconstruct, Hard shrinking,
Sure shrinking.

### References

Donoho [35]