Summation formula of two variables using vectorization

I am trying to implement the following formula for research purposes:

Where M = 100, so m = -100:100 and t is also a vector. and fm = f0 + m (where f0 is a defined constant)

I am able to implement this using a for loop; however, I would like to use vectorization for speed and usability. I believe there should be a way to implement this using vectors alone and no loops, but I have been having trouble doing so due to the presence of two variables in the summation. I also am not able to use the symbolic toolbox due to the application. Any advice would be appreciated.

[John D'Errico]

What is T?

[Dakota Grey]

T is the period. It is also a constant.

Answer 1

[Sebastian Castro]

You should be able to do:

sum(G(fm).*cos(2*pi*fm*t - pi*fm*T))

... assuming that G(x) is a function whose output is always the same size as its input.

- Sebastian