bio11.m

里面囊括了基于matlab滤波器设计的各种.m文件

 %  This is the filter prototypes in the paper "A New Class of Two-Channel
% Biothogonal Filter Banks and Wavelet Bases"

E1 = sym('[0.5,0;-0.5*Belta(z),1]');
E2 = sym('[z^(-N),Belta(z);0,z^(-2*N+1)]');
E = symmul(E1,E2)
% This is polyphase matrix of analysis filter H0 and H1.
R1 = sym('[z^(-2*N+1),-Belta(z);0,z^(-N)]');
R2 = sym('[1,0;0.5*Belta(z),0.5]');
R = symmul(R1,R2)
% This is polyphase matrix of synthesis filter F0 and F1.
T = symmul(R,E);
T = simple(T);
% This is the whole transfer function
% The following is the factorization elements of E and R
A1 = sym('[1,0;-Belta(z),1]');
A2 = sym('[1,0;0,2*z^(-2*N+1)]');
A3 = sym('[1,Belta(z);0,1]');
A4 = sym('[z^(-N),0;0,1]');
symmul(A1,symmul(A2,symmul(A3,A4)))
disp('This is the same as E')
B1 = sym('[1,0;0,z^(-N)]');
B2 = sym('[1,-Belta(z);0,1]');
B3 = sym('[2*z^(-2*N+1),0;0,1]');
B4 = sym('[1,0;Belta(z),1]');
symmul(B1,symmul(B2,symmul(B3,B4)))
disp('This is the same as R')
disp('The following fact shows the relation between inverse matrix of 
E')
disp('and the matrix R, viz, inverse(E) = 2*z^(3*N-1)*R')
inv_E = simplify(inverse(E))
simplify(symmul('2*z^(3*N-1)',R))
disp('The ans is the result of 2*z^(3*N-1)*R')