MATLAB: Inserting a function in a matrix.

function matrixlinear algebraMATLAB

I am trying to solve the system above.I think I got right the first part of the quation with a for loop(code bellow)
   L   = 51;
   ws1 = 0.4*pi; 
   wp1 = 0.5*pi; 
   Ks1 = 1; 
   Kp  = 2;
   wo  = (ws1+wp1)/2;
   G   = 1000;
   w   = [0:(G)]*pi/G;
   W   = Ks1*(w<=ws1) + Kp*(w>=wp1)
   D   = (wo>=w);
   N=(L-1)/2
   m=0:N
   k=1:1001
for i = 0:N   
  
  F(i+1,:)=sum(arrayfun(@(k) (W(k).^2).*D(k).*cos(w(k).*i), 1:1000))
end
I am struggling though in the second part.My code looks like this but it does not seem to work.
for i = 0:N   
    for p = 0:N
    
        F2=@(k)(W(k).^2).*D(k).*(cos(w(k).*i).*(cos(w(k).*p))')
    end    M[i+1,p+1]=sum[arrayfun(@(k) F2(k), 1:1000)]
end
Does anyone know how I could possibly fix that.I also download the symbolic math toolbox but I was not able to find something to help me with that.

Best Answer

for  i=1:length(OM) %OM is the wk samples vector(grid size 5000 in my case)
        COS=cos( [0:N]' * OM(i) );
        Q=Q+(W(i)^2)*COS*(COS');
        P=P+(W(i)^2)*D(i)*COS;
end
A=Q\P;
A(2:end)=A(2:end)/2;
That is the code I ended up with in case someone needs something similar.
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