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.