Image Processing Reference
In-Depth Information
%
% Outputs:
%
q: The optimal FIR filter coefficients
%
gmin: The optimal value
%
if nargin==3
n=0
end
%% Initialization
z = tf('z');
T1 = -z^(-n);
T2=P;
[A1,B1,C1,D1]=ssdata(T1);
[A2,B2,C2,D2]=ssdata(T2);
n1 = size(A1,1);
n2 = size(A2,1);
%% FIR filter to be designed
Aq = circshift(eye(N),-1);
Aq(N,1) = 0;
Bq = [zeros(N-1,1);1];
%% Semidefinite Programming
A = [A1, zeros(n1,n2), zeros(n1,N);
zeros(n2,n1), A2, zeros(n2,N);
zeros(N,n1),Bq * C2, Aq];
B = [B1;B2;Bq * D2];
NN = size(A,1);
omega0 = (Omega(1)+Omega(2))/2;
omegab = (Omega(2)-Omega(1))/2;
P = sdpvar(NN,NN,'symmetric');
Q = sdpvar(NN,NN,'symmetric');
alpha_N1 = sdpvar(1,N);
alpha_0 = sdpvar(1,1);
g = sdpvar(1,1);
C = [C1, alpha_0 * C2, alpha_N1];
D = D1 + alpha_0 * D2;
M1r = A' * P * A+Q * A * cos(omega0)+A' * Q * cos(omega0)-P-2 * Q * cos(omegab);
M2r = A' * P * B+Q * B * cos(omega0);
M3r = B' * P * B-g;
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