Does de-convolution have a unique solution?

Question

I'm having trouble with deconvolution (*). Let f = g * h. Where the functions f and h are given by a gamma variate of form: a(x-x0)^b exp(-[x-x0]/c). here a,b, and c are constants. How would you solve for g? Is there a unique solution for deconvolution? Why does using the discrete fourier transformation not lead to the solution?

*=convolution: f(x)=integral[g(t) h(t-x)]

Thanks for your answer. I forgot to say that I'm defining the functions f and h to be zero for x

Answer 1

Yes, there is generally a unique solution. That exponential term blows up as x approaches minus infinity. That's probably your problem. Discrete FT is spectral and assumes a periodic function. You can approximate a function that decays to zero for + and - large x as a periodic train of pulses, but not a function that blows up. Hope that helps.