A Dirac in time is positioned on sample n, it is represented in blue in the figures on the left, over all the duration of the observation on top and over a small interval of 10 samples on the bottom. The graduations are either in samples choosing a sampling rate of 1 or in seconds.The FT of this signal is represented at right in red color by two forms, either in real and imaginary parts or in modulus and phase. The choice of graduation in time, either 1 s or 4 ms, gives graduations in reduced frequency or in Hertz.
The modulus of the FT of a Dirac is constant and equal to 1.
The phase varies linearly between 0 and n times π for frequencies of 0 to the maximum frequency. The phase, as a matter of fact, is represented between -180° and + 180°, and results from discontinuities of the curve.
The real and imaginary parts are cosine and -sine functions having a number of periods equal to n; as usualy the positive frequencies are represented, we observe n/2 periods.