Extract or reconstruct 1-D LWT wavelet coefficients
Y = lwtcoef(TYPE,XDEC,LS,LEVEL,LEVEXT)
Y = lwtcoef(TYPE,XDEC,W,LEVEL,LEVEXT)
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.
% 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 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