Dirac Comb

In mathematics, a Dirac comb is a periodic Schwartz distribution constructed from Dirac delta functions
\delta_T(t) = \sum_{n=-\infty}^{\infty} \delta(t - n T)
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

 

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