# iswt

Inverse discrete stationary wavelet transform 1-D

## Syntax

``x = iswt(swc,wname)``
``x = iswt(swa,swd,wname)``
``x = iswt(swc,LoR,HiR)``
``x = iswt(swa,swd,LoR,HiR)``

## Description

````x = iswt(swc,wname)` reconstructs the 1-D signal `x` based on the multilevel stationary wavelet decomposition `swc` using the wavelet specified by `wname`. `swc` is expected to be the output of the `swt` function. The `wname` wavelet must be the same wavelet used to obtain the `swc` structure.```
````x = iswt(swa,swd,wname)` uses the approximation coefficients `swa` and detail coefficients `swd` to reconstruct the 1-D signal. The real-valued matrices `swa` and `swd` are expected to be the outputs of the `swt` function.The syntax `iswt(swa(end,:),swd,wname)` is equivalent to `iswt(swa,swd,wname)`.```
````x = iswt(swc,LoR,HiR)` uses the scaling filter `LoR` and wavelet filter `HiR`. The filters are expected to be the reconstruction filters associated with the wavelet used to create the `swc` structure. For more information, see `wfilters`.```

example

````x = iswt(swa,swd,LoR,HiR)` uses the scaling filter `LoR` and wavelet filter `HiR`. The filters are expected to be the reconstruction filters associated with the wavelet used to create the `swc` structure. For more information, see `wfilters`.The syntax `iswt(swa(end,:),swd,LoR,HiR)` is equivalent to `iswt(swa,swd,LoR,HiR)`.```

## Examples

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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 = 1.0818e-13 ```

## Input Arguments

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Multilevel stationary wavelet decomposition, specified as a real-valued matrix. `swc` is the output of `swt`.

Data Types: `double`

Wavelet, specified as a character vector or string scalar. `iswt` supports only Type 1 (orthogonal) or Type 2 (biorthogonal) wavelets. See `wfilters` for a list of orthogonal and biorthogonal wavelets.

Approximation coefficients, specified as a real-valued matrix. `swa` is the output of `swt`.

Data Types: `double`

Detail coefficients, specified as a real-valued matrix. `swd` is the output of `swt`.

Data Types: `double`

Wavelet reconstruction filters, specified as a pair of even-length real-valued vectors. `LoR` is the scaling (lowpass) reconstruction filter, and `HiR` is the wavelet (highpass) reconstruction filter. The lengths of `LoR` and `HiR` must be equal. See `wfilters` for additional information.

Data Types: `double`

 Nason, G. P., and B. W. Silverman. “The Stationary Wavelet Transform and Some Statistical Applications.” In Wavelets and Statistics, edited by Anestis Antoniadis and Georges Oppenheim, 103:281–99. New York, NY: Springer New York, 1995. https://doi.org/10.1007/978-1-4612-2544-7_17.

 Coifman, R. R., and D. L. Donoho. “Translation-Invariant De-Noising.” In Wavelets and Statistics, edited by Anestis Antoniadis and Georges Oppenheim, 103:125–50. New York, NY: Springer New York, 1995. https://doi.org/10.1007/978-1-4612-2544-7_9.

 Pesquet, J.-C., H. Krim, and H. Carfantan. “Time-Invariant Orthonormal Wavelet Representations.” IEEE Transactions on Signal Processing 44, no. 8 (August 1996): 1964–70. https://doi.org/10.1109/78.533717.

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