What kind of discrete convolution is this? Let x[n] and y[n] be defined for n=0,1, ..., N-1.

This (for example with Python's scipy fft / ifft)

a = ifft (fft(x) * fft(y))


should give the convolution 

$$a[k] = (x * y)[k] = \sum_{n=0}^{N-1} x[n] y[k-n]$$

But is it done with 


y[i] = 0 if $i&lt;0$  ?


or 


y[i] = y[N+i] if $i&lt;0$ ?  (ex : y[-3] = y[N-3] )     (in this case do we call it circular convolution?)


Note : More generally, I have good books about signal processing / Fourier transform in general, but they are not really handy handbooks for discrete finite signals (x[n] for  n=0,1, ..., N-1). Do you have a good reference of handbook for this case (discrete finite signals) ?
Fast (FFT/IFFT) convolution results in circular convolution.  

(But if sufficient zero-padding is explicitly added before the initial FFTs, circular and linear convolution would then produce identical results.)