Sinc function definition in Wolfram Language

Questions
1

Why is the sinc function in Mathematica is different from Matlab

e.g. sinc(pi/2) in Matlab gives -0.1977
however in Mathematica it gives
Sinc[Pi/2] = -0.0544021

Also the plotting results were totally different.
In Matlab here is the code
clc
clear all
close all

t=linspace(-10,10,2000+1); t(end)=[];
y=sinc(t);
figure
hold on
plot(t,y)

/////////////////////////////////////////////////////
in Mathematica
Plot[Sinc[x],{x,-10,10}]

MathematicaSinc.jpg
MathematicaSinc.jpg360×222 6.01 KB

untitled.jpg
untitled.jpg560×420 11.3 KB

2

Because in Mathematica: Sinc[z] is equivalent to Sin[z]/z for z!=0, but is 1 for z=0.

A workaround:

  x = Pi/2; Sinc[Pi*x] // N
  (*-0.197651*)
  Sin[Pi x]/(Pi x) // N
  (*-0.197651*)

  Plot[Sinc[Pi x], {x, -10, 10}, PlotRange -> All, AxesOrigin -> {-10, -0.4}]
3

Doing some minimal research might help, e.g. Wikipedia !

4

Mathematica uses radians as the input and Matlab uses a “Normalized” sinc function. Matlab has a unitless input and multiplies it by Pi to get radians. Matlab definition is Sin(pix)/(pix).

Regards,

Neil