Image Processing Reference
In-Depth Information
B = [B1;-Bq];
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_N1];
D = D1 - alpha_0;
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;
M1i = A' * Q * sin(omega0)-Q * A * sin(omega0);
M21i = -Q * B * sin(omega0);
M22i = B' * Q * sin(omega0);
Mr = [M1r,M2r,C';M2r',M3r,D;C,D,-1];
Mi = [M1i, M21i, zeros(NN,1);M22i, 0, 0; zeros(1,NN),0,0];
M = [Mr, Mi; -Mi, Mr];
F = set(M < 0) + set(Q > 0) + set(g > 0);
solvesdp(F,g);
%% Optimal FIR filter coefficients
q = fliplr([double(alpha_N1),double(alpha_0)]);
gmin = double(g);
7.4 Inverse FIR filtering by finite-frequency min-max
function [q,gmin] = inverseFIRff(P,Omega,N,n);
% [q,gmin]=inverseFIRff(P,Omega,N,n) computes the
% Finite-frequency optimal (delayed) inverse FIR filter Q(z) which minimizes
% J(Q) = max{|Q(exp(jw)P(exp(jw))-exp(-jwn)|, w in Omega}.
% the maximum frequency gain of QP-z^(-n) in a frequency band Omega.
% This design uses SDP via the generalized KYP lemma.
%
% Inputs:
%
P: Target stable linear system in SS object
%
Omega: Frequency band in 1x2 vector [w1,w2]
%
N: Order of the FIR filter to be designed
%
n: Delay (this can be omitted; default value=0);
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