What Is Optimization Toolbox?

2 TutorialStep 1: Write an M-file filtmin.m.function y = filtmin(a,w)n = length(a);y = cos(w'*(0:n-1)*2*pi)*a ;Step 2: Invoke optimization routine.% Plot with initial coefficientsa0 = ones(15,1);incr = 50;w = linspace(0,0.5,incr);y0 = filtmin(a0,w);clf, plot(w,y0,'.r');drawnow;% Set up the goal attainment problemw1 = linspace(0,0.1,incr) ;w2 = linspace(0.15,0.5,incr);w0 = [w1 w2];goal = [1.0*ones(1,length(w1)) zeros(1,length(w2))];weight = ones(size(goal));% Call fgoalattainoptions = optimset('GoalsExactAchieve',length(goal));[a,fval,attainfactor,exitflag]=fgoalattain(@(x) filtmin(x,w0)...a0,goal,weight,[],[],[],[],[],[],[],options);% Plot with the optimized (final) coefficientsy = filtmin(a,w);hold on, plot(w,y,'r')axis([0 0.5 -3 3])xlabel('Frequency (Hz)')ylabel('Magnitude Response (dB)')legend('initial', 'final')grid on2-38