`sinc`

Normalized sinc function sin(pi*x)/(pi*x).

Category: Mathematics > Mathematical Functions

Syntax

Y = sinc(x)

Evaluates sin(pi*x)/(pi*x), with sinc(0) = 1.

Description

The normalized sinc function is the Fourier transform of a rectangular pulse. It is 1 at the origin and vanishes at every nonzero integer, with zero crossings spaced by 1. Its envelope decays like 1/(pi*abs(x)).

With symbolic input the result is the exact expression, for example sinc(sym(1)/2) is 2/pi.

Input arguments

x: Number, array or symbolic expression.

Output arguments

Y: Values of the sinc function.

Example

Exact values

sinc(sym(0))
sinc(sym(1))
sinc(sym(1)/2)
syms x
sinc(x)

Output

ans = 1
ans = 0
ans = 2/pi
ans = sin(pi*x)/(pi*x)

Notes

In MatLivre sinc returns a symbolic result even for ordinary numeric input (for example sinc(0.5) prints 2/pi). Apply double to get a number.

sinc