- General definition
- sinc x = { sin x x , x ≠ 0 1 , x = 0 {\displaystyle \operatorname {sinc} x={\begin{cases}{\dfrac {\sin x}{x}},&x\neq 0\\1,&x=0\end{cases}}}
- Fields of application
- Signal processing, spectroscopy
- Domain
- R {\displaystyle \mathbb {R} }
- Image
- [ − 0.217234 … , 1 ] {\displaystyle [-0.217234\ldots ,1]}
- Parity
- Even
- Maxima
- 1 at x = 0 {\displaystyle x=0}
- Minima
- − 0.21723 … {\displaystyle -0.21723\ldots } at x = ± 4.49341 … {\displaystyle x=\pm 4.49341\ldots }
- Root
- π k , k ∈ Z ≠ 0 {\displaystyle \pi k,k\in \mathbb {Z} _{\neq 0}}
- Reciprocal
- { x csc x , x ≠ 0 1 , x = 0 {\displaystyle {\begin{cases}x\csc x,&x\neq 0\\1,&x=0\end{cases}}}
- Derivative
- sinc ′ x = { cos x − sinc x x , x ≠ 0 0 , x = 0 {\displaystyle \operatorname {sinc} 'x={\begin{cases}{\dfrac {\cos x-\operatorname {sinc} x}{x}},&x\neq 0\\0,&x=0\end{cases}}}