# Documentation

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# iswt

Inverse discrete stationary wavelet transform 1-D

## Syntax

```X = iswt(SWC,'wname') X = iswt(SWA,SWD,'wname') X = iswt(SWA(end,:),SWD,'wname') X = iswt(SWC,Lo_R,Hi_R) X = iswt(SWA,SWD,Lo_R,Hi_R) X = iswt(SWA(end,:),SWD,Lo_R,Hi_R) ```

## Description

`iswt` performs a multilevel 1-D stationary wavelet reconstruction using either an orthogonal or a biorthogonal wavelet. Specify the wavelet using its name (`'wname'`, see `wfilters` for more information) or its reconstruction filters (`Lo_R` and `Hi_R`).

`X = iswt(SWC,'wname')` or ```X = iswt(SWA,SWD,'wname')``` or ```X = iswt(SWA(end,:),SWD,'wname')``` reconstructs the signal `X` based on the multilevel stationary wavelet decomposition structure `SWC` or `[SWA,SWD]` (see `swt` for more information).

`X = iswt(SWC,Lo_R,Hi_R)` or ```X = iswt(SWA,SWD,Lo_R,Hi_R)``` or `X = iswt(SWA(end,:),SWD,Lo_R,Hi_R)` reconstruct as above, using filters that you specify.

• `Lo_R` is the reconstruction low-pass filter.

• `Hi_R` is the reconstruction high-pass filter.

`Lo_R` and `Hi_R` must be the same length.

## Examples

collapse all

Demonstrate perfect reconstruction using `swt` and `iswt` with a biorthogonal wavelet.

```load noisbloc [Lo_D,Hi_D,Lo_R,Hi_R] = wfilters('bior3.5'); [swa,swd] = swt(noisbloc,3,Lo_D,Hi_D); recon = iswt(swa,swd,Lo_R,Hi_R); norm(noisbloc-recon)```
```ans = 1.1386e-13 ```

## References

Nason, G.P.; B.W. Silverman (1995), “The stationary wavelet transform and some statistical applications,” Lecture Notes in Statistics, 103, pp. 281–299.

Coifman, R.R.; Donoho D.L. (1995), “Translation invariant de-noising,” Lecture Notes in Statistics, 103, pp 125–150.

Pesquet, J.C.; H. Krim, H. Carfatan (1996), “Time-invariant orthonormal wavelet representations,” IEEE Trans. Sign. Proc., vol. 44, 8, pp. 1964–1970.