The Fourier transform is invertible, so given some spectrum you can always get back to a time signal. The inverse DFT frequently arises when someone wants to take a time domain signal, convert to frequency domain, do some operation, and then convert back to time domain (e.g. approximate a Hilbert transform 5.3). Another case is when you want to simulate some signal. You may construct the spectra of the simulated signal first and then use an inverse DFT to get a time waveform instead of simulating the time waveform directly.
Again, the key thing to keep in mind when doing this is the difference between the ``mathematician's DFT'' and the ``engineer's DFT''. If you have a signal sampled at 100 Hz, and you take the DFT, an engineer usually wants to get back amplitude and phase between 0 and 50 Hz. But mathematically, the DFT really computes complex numbers between -50 Hz and 50 Hz. So depending on how your inverse DFT function works, you'll probably need to give it a complex spectra to work with or you won't get what you want.
Note: with matlab's FFT, if you have a one-sided complex (real-imaginary) spectrum and you want to take the inverse you just need zz = [ z conj(z((len-1):-1:2)) ] to create the two sided conjugate spectrum (assuming you wanted real output).
On the other hand, if you have just the amplitude portion of the spectrum, then it is impossible to reconstruct the original time-domain signal. In other words, if you have a=abs(fft(signal)), it is impossible to reconstruct signal from a.
