Re: laplace from frequency dependant expression
As long as your function meets Dirichlet conditions and is majorized by an exponential function, it has a Laplace transform.
However, usually we are transforming time-domain functions to s-domain (which is a generalization of frequency to a complex surface), so frankly speaking I don't understand why you would like to transform frequency-dependent function into s-domain. Especially, while supposing the time domain primary function has a right-sided complex Fourier representation, and this representation is in fact your function, the s-domain representation would be the same with s instead of f.