Numerically computing the inverse Fourier transform

Suppose I have the Fourier transform of a function F_hat=F_hat(k), where k is the Fourier transformed variable. I have constants B,E_b,U and O. I have another Fourier transformed function p_hat(k)=exp(-0.25*k^2). The function in question is:

F_hat(k)=p_hat(k)*tanh(k)/(k*U^2+(-B+O*U+E_b*|k|-k^2)*tanh(k))

My question is, Can I get back to the variable F(x), for a given set of values of x, say -20<=x<=20?

I have written some code which numerically computes this but it is giving some odd results which I don't fully trust which is why I wonder if matlab has some inbuilt routines for this which I can quickly implement to test my code against.

Mat