# Documentation

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# lwt

1-D lifting wavelet transform

## Syntax

```[CA,CD] = lwt(X,W)X_InPlace = lwt(X,W)lwt(X,W,LEVEL)X_InPlace = lwt(X,W,LEVEL,'typeDEC',typeDEC)[CA,CD] = lwt(X,W,LEVEL,'typeDEC',typeDEC)```

## Description

`lwt` performs a 1-D lifting wavelet decomposition with respect to a particular lifted wavelet that you specify.

`[CA,CD] = lwt(X,W)` computes the approximation coefficients vector `CA` and detail coefficients vector `CD`, obtained by a lifting wavelet decomposition, of the vector `X`. `W` is a lifted wavelet name (see `liftwave`).

`X_InPlace = lwt(X,W)` computes the approximation and detail coefficients. These coefficients are stored in place:

`CA = X_InPlace(1:2:end)` and ```CD = X_InPlace(2:2:end)```

`lwt(X,W,LEVEL)` computes the lifting wavelet decomposition at level `LEVEL`.

`X_InPlace = lwt(X,W,LEVEL,'typeDEC',typeDEC)` or ```[CA,CD] = lwt(X,W,LEVEL,'typeDEC',typeDEC)``` with ```typeDEC = 'w'``` or `'wp'` computes the wavelet or the wavelet packet decomposition using lifting, at level `LEVEL`.

Instead of a lifted wavelet name, you may use the associated lifting scheme `LS`: `lwt(X,LS,...)` instead of `lwt(X,W,...)`.

For more information about lifting schemes, see `lsinfo`.

## Examples

```% Start from the Haar wavelet and get the % corresponding lifting scheme. lshaar = liftwave('haar'); % Add a primal ELS to the lifting scheme. els = {'p',[-0.125 0.125],0}; lsnew = addlift(lshaar,els); % Perform LWT at level 1 of a simple signal. x = 1:8; [cA,cD] = lwt(x,lsnew) cA = 1.9445 4.9497 7.7782 10.6066 cD = 0.7071 0.7071 0.7071 0.7071 % Perform integer LWT of the same signal. lshaarInt = liftwave('haar','int2int'); lsnewInt = addlift(lshaarInt,els); [cAint,cDint] = lwt(x,lsnewInt) cAint = 1 3 5 7 cDint = 1 1 1 1 ```

## More About

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### Algorithms

This function uses the polyphase algorithm.

`lwt` reduces to `dwt` with zero-padding extension mode and without extra-coefficients.

## References

Strang, G.; T. Nguyen (1996), Wavelets and filter banks, Wellesley-Cambridge Press.

Sweldens, W. (1998), "The Lifting Scheme: a Construction of Second Generation of Wavelets," SIAM J. Math. Anal., 29 (2), pp. 511–546.

## See Also

#### Introduced before R2006a

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