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Dirac comb

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} ⁠…

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Overview

Dirac-comb identity

Fourier series

Fourier transform

Sampling and aliasing

Use in directional statistics

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Map overview Semantic statistics

Dirac comb

Nodes43
Edges42
Triples29
Avg. degree1.95
Density0.046512
Components1

How this topic connects Entity context

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Dirac comb

Top relations

related to Further reading · 7
Dirac comb → BF00401584, Bibcode, Córdoba, Dirac, Letters, Mathematical Physics, S2CID
related to Fourier transform · 6
Dirac comb → Dirac, For, Fourier, Hz, The Dirac, The Fourier
related to Dirac-comb identity · 5
Dirac comb → Convolution Theorem, Dirac, Formally, In, The Dirac
related to Sampling and aliasing · 4
Dirac comb → Dirac, Due, Multiplying, This
related to Scaling · 4
Dirac comb → Dirac, Note, Since, The
related to Use in directional statistics · 3
Dirac comb → Dirac, In, Just

Important terminology Word statistics

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Important terminology

displaystyle comb dirac function text operatorname fourier delta pi infty sum transform period sampling series frac also periodic distributions frequency

Entity relationships Subject–Predicate–Object triples

SubjectPredicateObjectConfidenceSrc
Dirac combrelated to Dirac-comb identityThe Dirac0.60section
Dirac combrelated to Dirac-comb identityDirac0.60section
Dirac combrelated to Dirac-comb identityFormally0.60section
Dirac combrelated to Dirac-comb identityIn0.60section
Dirac combrelated to Dirac-comb identityConvolution Theorem0.60section
Dirac combrelated to Fourier transformThe Fourier0.60section
Dirac combrelated to Fourier transformDirac0.60section
Dirac combrelated to Fourier transformFor0.60section
Dirac combrelated to Fourier transformFourier0.60section
Dirac combrelated to Fourier transformHz0.60section
Dirac combrelated to Fourier transformThe Dirac0.60section
Dirac combrelated to Further readingCórdoba0.60section

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