periodic summation

In signal processing, any periodic function  with period P, can be represented by a summation of an infinite number of instances of an aperiodic function that are offset by integer multiples of P.  This representation is called periodic summation:

When    is alternatively represented as a complex Fourier series, the Fourier coefficients are proportional to the values (or "samples") of the continuous Fourier transform  at intervals of 1/P.  That identity is a form of the Poisson summation formula. Similarly, a Fourier series whose coefficients are samples of    at constant intervals (T) is equivalent to a periodic summation of    which is known as a discrete-time Fourier transform.