A Dirac positioned at a point "a" in time, whether whole or not, is a cardinal sine function(The boxcar and its Fourier transform) which in turn is the discrete inverse Fourier transform (D I FT) of the exponential function (-2 π f a) limited within the Shannon bandwidth (Respected Shannon limit).
Its phase varies linearly between 0 and a.π from f =0 to the Shannon frequency limit.
When a is an integer, the Dirac thus, created appears as if it has all its samples being null except one. And the phase variation of its FT has a whole number of variations of π.