Does inverse of all Fouriers transforms have a corresponding function in time domain?

18 Views Asked by At

I am trying to cancel out the following transfer function of a system:

$$\frac{( 1 - e^{(i*k*T)} ) }{ (i*k)}$$

I thought it would work if I find the inverse Fourier transform of

$$\frac{ (i*k)}{( 1 - e^{(i*k*T)} ) }$$

However I missed the fact that it is singular for some k values.

So my question is, does anything have an inverse Fourier transform? If they do not, how can I cancel out the transfer function I provided before?