Dirac comb

In mathematics, a Dirac comb is a periodic Schwartz distribution constructed from Dirac delta functions

<math>\delta_T(t) = \sum_{n=-\infty}^{\infty} \delta(t – n T)<math>

for some given period T.

Sampling and aliasing

Multiplication of a continuous signal by a Dirac comb is sometimes called an ideal sampler with sampling rate T. When used as an ideal sampler, it can be used to understand the effects of aliasing and as a proof of the Shannon-Nyquist sampling theorem.

See Shannon-Nyquist sampling theorem for a proof using the Dirac comb.

See also

• Poisson summation formula