# 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 $i<0$ ?

or

• y[i] = y[N+i] if $i<0$ ? (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) ?

• The length of both signals after zero padding has to be length(x) + length(y) - 1 – Deve Nov 26 '13 at 16:31