Sigma notation - two variables. 'for' loop or symsum?

Hello

I am trying to compute a sigma summation of a simple single column vector x, where:

N = length(x)

k = 0:N/4

i = 1:N-k

I need to solve for Axx(k):

I have tried to solve this using 'for' loops and symsum function, without success. Help is hugely appreciated, thanks.

Answer 1

[Star Strider]

This runs:

N = length(x);
for k = 0:N/4
    Axx(k+1) = 0;
    for i = 1:N-k
        Axx(k+1) = Axx(k+1) + x(i)*x(i+k);
    end
end

I’ll let you determine if it gives the answers you expect.

[Nate]

Yes - it works perfectly, thanks.

Also - this seems to work as well:

N = length(x);

for k = 0:(N/4);

     Axx(k+1) = sum((x(1:N-k,2)).*(x(1+k:N,2)));

end

[Star Strider]

My pleasure!

Answer 2

[Roger Stafford]

   Axx = x.'*hankel(x,zeros(1,N/4+1));

[Nate]

Thanks for this. I get an error when used with my 'x' vector.

Error using zeros Size inputs must be integers.

I found something that seems to work (see my comment below).

Thanks

[Roger Stafford]

That's probably because your value N is not a multiple of 4. Do this:

round(N/4)+1

instead.