Calculating function from a convolution

[g.vanni]

Hi guys, here is my question.
I have two functions f(w) and c(w) and I know exactly their analytical equations.
I want a formula to calculate a third function g(w), when the only thing I know is that c=f*g (i.e. c(w) is the convolution between f and g). Are you aware of any mathematical procedure to achieve this goal?
Thank you in advance for your replies

 

[Romsek]

[MATH]c(w) = (f*g)(w) \\~\\ \text{going to the $s$ domain via the Laplace transform we obtain}\\ C(s) = F(s)G(s)\text{ where}\\ C(s) = \mathscr{L}\{c(w)\},~F(s)=\mathscr{L}\{f(w)\},~G(s) = \mathscr{L}(g(w)\}\\ G(s) = \dfrac{F(s)}{C(s)}\\ g(w) = \mathscr{L}^{-1}\left\{\dfrac{F(s)}{C(s)}\right\}[/MATH]
How amenable to getting an analytic solution for [MATH]g(w)[/MATH] this is depends on the functions involved.

I believe this procedure is called deconvolution. In this case you are deconvolving \(\displaystyle f(w)\).
In practice \(\displaystyle f(w)\) is results from imperfect sensors, or atmospheric or other disturbance of the signal \(\displaystyle g(w)\) you are trying to observe.
If you precisely know the impulse response of the "medium" as it's called, you can obtain the signal perfectly via deconvolution.
In practice you won't ever know the medium perfectly, but you might know it well enough to improve the signal you do receive.