A time domain signal can be decomposed into sinusoids which are based on basis functions.
For a N sampled input, a cosine basis function is defined as:
$$C_k[i] = \cos\left[\dfrac{2\pi k i}{N}\right]$$
Range of Frequency $k = 0 \ldots \frac{N}{2}$, Range of $i = 0 \ldots N-1$
Why is the sinusoid angle divided by $N$?