function [Pc,Uc,KPc,KUc,K,U,P]=liftco(tipe,N,M) % [Pc,Uc,KPc,KUc,K,U,P]=LIFTCO(tipe,N,M) % % Like WC except also calculates Laurent polynomial matrices. % Check with LSINFO... % % Comes up with Prediction and Update coefficients % for a lifting implementation of the wavelet transform % of a certain type and with parameters N and M % where N is the vanishing moments of the primal wavelet % N-1 is the order of polynomial cancellation % M is the vanishing moments of the dual wavelet % M-1 is the order of preserved moments % These coefficients assume uniform sample spacing and perform a two-phase % "Lazy" preprocessing step. % Also returns the appropriate K,U,P which should yield % the analysis polyphase matrix upon Laurent multiplication. % % CDF is the Cohen-Daubechies-Feauveau construction % CDF(1,1) is the Orthogonal Haar bank % CDF(4,2) is the cubic B-spline % % See also MAKEWC and WC. % % Last modified by fjsimons-at-alum.mit.edu, 18.04.2006 defval('tipe','CDF') defval('N',1) defval('M',1) % Collect the operators required % They might be cell arrays themselves [h0,f0,Pc,Uc,KPc,KUc]=wc(tipe,[N M]); % Verify factorization with a Laurent polynomial % multiplication. if ~iscell(Pc) & ~iscell(Uc) K=[{KPc} {0} ; {0} {KUc}]; U=[{1} {Uc} ; {0} {1}]; P=[{0} {1} ; {1} {-Pc}]; else [K,U,P]=deal([]); end