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Dirac Comb




In Mathematics , a Dirac comb is a Periodic Schwartz Distribution constructed from Dirac Delta Function s

:\delta_T(t) = \sum_{k=-\infty}^{\infty} \delta(t - k T)

for some given period ''T''. Some authors, notably Bracewell , refer to it as the Shah function (probably because its graph resembles the shape of the Cyrillic letter Sha Ш). Because the Dirac comb function is periodic, it can be represented as a Fourier Series :

:\delta_T(t) = rac{1}{T}\sum_{n=-\infty}^{\infty} e^{i 2 \pi n t/T}.


SCALING PROPERTY


The scaling property follows directly from the properties the Dirac Delta Function .




SAMPLING AND ALIASING


Multiplication of a Continuous Signal by a Dirac comb is sometimes called an ideal sampler with Sampling Interval ''T''.
When used as an ideal sampler, it can be used to understand the effects of Aliasing and as a proof of the Nyquist-Shannon Sampling Theorem .


SEE ALSO




REFERENCES