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# lwtcoef

Extract or reconstruct 1-D LWT wavelet coefficients

## Syntax

Y = lwtcoef(TYPE,XDEC,LS,LEVEL,LEVEXT)
Y = lwtcoef(TYPE,XDEC,W,LEVEL,LEVEXT)

## Description

Y = lwtcoef(TYPE,XDEC,LS,LEVEL,LEVEXT) returns the coefficients or the reconstructed coefficients of level LEVEXT, extracted from XDEC, the LWT decomposition at level LEVEL obtained with the lifting scheme LS.

The valid values for TYPE are

TYPE Values

Description

'a'

Approximations

'd'

Details

'ca'

Coefficients of approximations

'cd'

Coefficients of details

Y = lwtcoef(TYPE,XDEC,W,LEVEL,LEVEXT) returns the same output using W, which is the name of a lifted wavelet.

## 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};

% Perform LWT at level 2 of a simple signal.
x = 1:8;
xDec = lwt(x,lsnew,2)

xDec =

4.3438    0.7071    2.1250    0.7071   13.0313    0.7071
2.0000    0.7071

% Extract approximation coefficients of level 1.
ca1 = lwtcoef('ca',xDec,lsnew,2,1)

ca1 =

1.9445    4.9497    7.7782   10.6066

% Reconstruct approximations and details.
a1 = lwtcoef('a',xDec,lsnew,2,1)

a1 =

1.3750    1.3750    3.5000    3.5000    5.5000    5.5000
7.5000    7.5000

a2 = lwtcoef('a',xDec,lsnew,2,2)

a2 =

2.1719    2.1719    2.1719    2.1719    6.5156    6.5156
6.5156    6.5156

d1 = lwtcoef('d',xDec,lsnew,2,1)

d1 =

-0.3750    0.6250   -0.5000    0.5000   -0.5000    0.5000
-0.5000    0.5000

d2 = lwtcoef('d',xDec,lsnew,2,2)

d2 =

-0.7969   -0.7969    1.3281    1.3281   -1.0156   -1.0156
0.9844    0.9844

% Check perfect reconstruction.
err = max(abs(x-a2-d2-d1))

err =

9.9920e-016
```