Apply elementary lifting steps on quadruplet of filters
[LoDN,HiDN,LoRN,HiRN] = liftfilt(LoD,HiD,LoR,HiR,ELS)
liftfilt(LoD,HiD,LoR,HiR,ELS,TYPE,VALUE)
[LoDN,HiDN,LoRN,HiRN] = liftfilt(LoD,HiD,LoR,HiR,ELS) returns
the four filters LoDN, HiDN, LoRN,
and HiRN obtained by an elementary lifting step
(ELS) starting from the four filters LoD, HiD, LoR,
and HiR. The four input filters verify the perfect
reconstruction condition.
ELS is a structure such that
TYPE = ELS.type contains the type
of the elementary lifting step. The valid values for TYPE are 'p' (primal)
or 'd' (dual).
VALUE = ELS.value contains the
Laurent polynomial T associated with the elementary
lifting step (see laurpoly).
If VALUE is a vector, the associated Laurent polynomial T is
equal to laurpoly(VALUE,0).
In addition, ELS may be a scaling step. In
that case, TYPE is equal to 's' (scaling)
and VALUE is a scalar different from zero.
liftfilt(LoD,HiD,LoR,HiR,ELS,TYPE,VALUE) gives
the same outputs.
Note
If TYPE = 'p' , HiD and LoR are
unchanged.
If TYPE = 'd' , LoD and HiR are
unchanged.
If TYPE = 's' , the
four filters are changed.
If ELS is
an array of elementary lifting steps, liftfilt(...,ELS) performs
each step successively.
liftfilt(...,FLAGPLOT) plots the successive
biorthogonal pairs—scaling function and wavelet.
% Get Haar filters.
[LoD,HiD,LoR,HiR] = wfilters('haar');
% Lift the Haar filters.
twoels(1) = struct('type','p','value',...
laurpoly([0.125 -0.125],0));
twoels(2) = struct('type','p','value',...
laurpoly([0.125 -0.125],1));
[LoDN,HiDN,LoRN,HiRN] = liftfilt(LoD,HiD,LoR,HiR,twoels);
% The biorthogonal wavelet bior1.3 is obtained up to
% an unsignificant sign.
[LoDB,HiDB,LoRB,HiRB] = wfilters('bior1.3');
samewavelet = ...
isequal([LoDB,HiDB,LoRB,HiRB],[LoDN,-HiDN,LoRN,HiRN])
samewavelet =
1