Could you check my logic: you have a delta function in the fourier domain plus, plus you have a white noise source, put the two combined into a non-linear receiver, intermodulation between the two, intermodulation's difference tone, back to the fourier domain don't you see the output's fourier transform as a broadened spike? But what exact shape is it, this looks visually vaguely like 1/(|f - f_{0}| + c ) + b where c > 0 and height of the spike is h = 1/c. If I can add up still, that is.

Or else a similar two-sided exponential, h exp( -|f - f_{0}| ) + b