Image Processing Reference
In-Depth Information
M1=A' * X * A-X;
M2=A' * X * B;
M3=B' * X * B-gamma;
C = [C1, alpha_0 * C2, alpha_N1];
D = D1 + alpha_0 * D2;
M = [M1, M2, C'; M2', M3, D; C, D, -gamma];
F = set(M < 0) + set(X > 0) + set(gamma > 0);
solvesdp(F,gamma);
%% Optimal FIR filter coefficients
q = fliplr([double(alpha_N1),double(alpha_0)]);
gmin = double(gamma);
7.3 FIR approximation of IIR filters by finite-frequency min-max
function [q,gmin] = approxFIRff(P,Omega,N);
% [q,gmin]=approxFIRff(P,Omega,N) computes the
% Finite-frequency optimal approximated FIR filter Q(z)
which minimizes
% J(Q) = max{|P(exp(jw))-Q(exp(jw))|, w in Omega}l.
% the maximum frequency gain of P-Q 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
%
% Outputs:
%
q: The optimal FIR filter coefficients
%
gmin: The optimal value
%
%% Initialization
[A1,B1,C1,D1]=ssdata(P);
n1 = size(A1,1);
%% FIR filter to be designed
Aq = circshift(eye(N),-1);
Aq(N,1) = 0;
Bq = [zeros(N-1,1);1];
%% Semidefinite Programming
A = blkdiag(A1,Aq);
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