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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

expand all

### 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

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