Dirac comb

Common card · No. 406456

In mathematics, a Dirac comb (also known as sha function, impulse train or sampling function) is a periodic generalized function with the formula Ш T ⁡ ( t ) := ∑ k = − ∞ ∞ δ ( t − k T ) {\displaystyle \operatorname {\text{Ш}} _{T}(t):=\sum _{k=-\infty }^{\infty }\delta (t-kT)} for some given period ⁠ T {\displaystyle T} ⁠. Here ⁠ t {\displaystyle t} ⁠ is a real variable and the sum extends over all integers ⁠ k {\displaystyle k} ⁠. The Dirac delta function δ {\displaystyle \delta...

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