Functions and mappings | Signal processing
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 . 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. The periodic summation of a Dirac delta function is the Dirac comb. Likewise, the periodic summation of an integrable function is its convolution with the Dirac comb. (Wikipedia).
