: Mathématiques: Dirac comb

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Dirac comb

In mathematics, a Dirac comb (also known as sha function, impulse train or sampling function) is a periodic function with the formula
${\\displaystyle \\operatorname {\ ext{Ш}} _{\\ T}(t)\\ :=\\sum _{k=-\\infty }^{\\infty }\\delta (t-kT)}$
for some given period ${\\displaystyle T}$ . Here t is a real variable and the sum extends over all integers k. The Dirac delta function ${\\displaystyle \\delta }$ and the Dirac comb are tempered distributions. The graph of the function resembles a comb (with the ${\\displaystyle \\delta }$ s as the comb's teeth), hence its name and the use of the comb-like Cyrillic letter sha (Ш) to denote the function.
(Wikipedia, The Free Encyclopedia, https://en.wikipedia.org/wiki/Dirac_comb)

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