Here is my problem:
I have a random variable $A$ that is the sum of independent random variables $B$ and $C$, i.e. $A=B+C$. All three random variables are on the real domain. $B$ is a Gaussian with known parameters and I have the form of the p.d.f. $f_A$ for $A$ with good estimate of the parameters. $A$ is symmetric around its mean, which is equal to the mean of Gaussian $B$. Assume that variances of $A$ and $B$ (and $C$) are low enough though that their p.d.f.'s are very close to zero outside the interval $[\mu-a,\mu+a]$, where $a$ is reasonable.
Unfortunately, there is no nice closed-form expression for the characteristic function of $A$. I am trying to find the p.d.f. of $C$ (though having characteristic function $\phi_C$ of $C$ would also help.)
If I had a nice form for $A$'s characteristic function $\phi_A$, I would use the fact that $f_A=f_B*f_C$, which in turn means $\phi_A=\phi_B\phi_C$, and would simply divide $\phi_A$ by characteristic function of the Gaussian (since convolution in "time" domain is multiplication in "frequency" domain) to at least get $\phi_C$ to work with.
At this point I would be happy with a numerical approximation for p.d.f. $f_C$. Poking around the web, I found that one may be able to use "deterministic deconvolution" to remove the known Gaussian p.d.f. from the p.d.f. of $A$, but I couldn't find any references on how to actually do it (there a lot of literature on the use of deconvolution in seismography though.) I tried generating a vectors $f_A(\mathbf{x})$ and $f_B(\mathbf{x})$ where $\mathbf{x}$ is a large ordered list of equally-spaced numbers from $\mu-a$ to $\mu+a$, taking FFTs of both vectors, doing element-by-element division and then taking the inverse FFT of the result, which yielded garbage. Can somebody help?