How to define y = f(w)*cosine(w*t) with different ranges for w & t?

Take a function: y = f(w)*cosine(w*t), with t = 0:1:1000 and f(w) is a Gaussian (or some other) distribution of w with w = 10000:10:15000; so given the range of t and w, how y can be defined? For a given value of w, cos(w*t) may be plotted (otherwise dimensions of w & t won't match) and then cos(w*t) needs to be summed over w with the proper weight provided by f(w) - but how?