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function [PRCond,AACond] = praacond(Hs,Gs,Ha,Ga) %PRAACOND Perfect reconstruction and anti-aliasing conditions. % If (Hs,Gs) and (Ha,Ga) are two pairs of Laurent polynomials, % [PRCond,AACond] = PRAACOND(Hs,Gs,Ha,Ga) returns the values of % PRCond(z) and AACond(z) which are the Perfect Reconstruction % and the Anti-Aliasing "values": % PRCond(z) = Hs(z) * Ha(1/z) + Gs(z) * Ga(1/z) % AACond(z) = Hs(z) * Ha(-1/z) + Gs(z) * Ga(-1/z) % % The pairs (Hs,Gs) and (Ha,Ga) are associated to perfect % reconstruction filters if and only if: % PRCond(z) = 2 and AACond(z) = 0. % % If PRCond(z) = 2 * z^d, a delay is introduced in the % reconstruction process. % M. Misiti, Y. Misiti, G. Oppenheim, J.M. Poggi 02-Jul-2003. % Last Revision: 06-Jul-2003. % Copyright 1995-2004 The MathWorks, Inc. PRCond = Hs * reflect(Ha) + Gs * reflect(Ga); AACond = Hs * modulate(reflect(Ha)) + Gs * modulate(reflect(Ga)); % In an equivalent way: % PRCond = -z*(Hs(z)*Gs(-z)-Hs(-z)*Gs(z))