How can the Fourier Transform of this function be drawn?:

f(x) = 3cos(5x) + 2sin(3y)

I suppose that the first step is to convert this into complex exponentials

f(x) = (3/2)exp(-5ix) + (3/2)exp(5ix) + iexp(-3iy) - iexp(3iy)

And then take the sum over all the allowed k values, assuming that k=(2*pi*p)/(2i) where "p" is an integer and "a" is the lattice constant? But, I'm not quite sure why I should do that; it seems like it would make the equation more confusing.

Up until this point, the periodic function has just been converted into a different form. How do I make this into a Fourier series? Is it just a matter of scooting a sigma in there, or what?

And, in the end, what will it look like? Will it look like a bunch of delta functions, or will it actually have a curve associated with it?

FYI: In our class, the ultimate point of learning to do these Fourier Transforms is so we can convert reciprocal-space crystal lattices to real-space crystal lattices (handy in x-ray diffraction) or vice-verse. Or, at least, that's my best guess.