Definition:Odd Impulse Pair Function
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Definition
The odd impulse pair function is the real function $\operatorname {I_I}: \R \to \R$ defined as:
- $\forall x \in \R: \map {\operatorname {I_I} } x := \dfrac 1 2 \map \delta {x + \dfrac 1 2} - \dfrac 1 2 \map \delta {x - \dfrac 1 2}$
where $\delta$ denotes the Dirac delta function.
Graph of Odd Impulse Pair Function
The graph of the odd impulse pair function is illustrated below:
It is to be understood that the blue arrows represent rays from the $x$-axis for constant $n \in \set {-\dfrac 1 2, \dfrac 1 2}$.
Sources
- 1978: Ronald N. Bracewell: The Fourier Transform and its Applications (2nd ed.) ... (previous) ... (next): Frontispiece
- 1978: Ronald N. Bracewell: The Fourier Transform and its Applications (2nd ed.) ... (previous) ... (next): Chapter $4$: Notation for some useful Functions: Summary of special symbols: Table $4.1$ Special symbols
- 1978: Ronald N. Bracewell: The Fourier Transform and its Applications (2nd ed.) ... (previous) ... (next): Inside Back Cover