Difference between revisions of "Sinc"

From specialfunctionswiki
Jump to: navigation, search
 
(15 intermediate revisions by the same user not shown)
Line 1: Line 1:
The $\mathrm{sinc}$ function is defined by
+
The $\mathrm{sinc}$ function (sometimes called the "unnormalized" $\mathrm{sinc}$ function) is defined by
$$\mathrm{sinc}(x) = \left\{ \begin{array}{ll}
+
$$\mathrm{sinc}(z) = \left\{ \begin{array}{ll}
\dfrac{\sin x}{x} &; x \neq 0 \\
+
\dfrac{\sin z}{z} &; z \neq 0 \\
1 &; x=0.
+
1 &; z=0.
 
\end{array} \right.$$
 
\end{array} \right.$$
 +
It appears in the definition of the [[Sine integral]] function.
  
 
<div align="center">
 
<div align="center">
 
<gallery>
 
<gallery>
File:Sinc.png|Plot of $\mathrm{sinc}$ on $[-15,15]$.
+
File:Sincplot.png|Plot of $\mathrm{sinc}$ on $[-15,15]$.
 +
File:Complexsincplot.png|[[Domain coloring]] of $\mathrm{sinc}$.
 
</gallery>
 
</gallery>
 
</div>
 
</div>
 +
 +
=Properties=
 +
[[Sum of values of sinc]]<br />
  
 
=Videos=
 
=Videos=
[https://www.youtube.com/watch?v=xEFi0xQRCKI Infinite Product Evaluation with the Sinc Function]
+
[https://www.youtube.com/watch?v=xEFi0xQRCKI Infinite Product Evaluation with the Sinc Function]<br />
 +
[https://www.youtube.com/watch?v=sW9Sw0G8KQ4 (The Sinc Function) Inverse Fourier Transform of Sinc & Fourier Transform of Sinc]<br />
 +
[https://www.youtube.com/watch?v=ORTQTh4uh7A Fourier Transform of a Sinc Function (or Inverse Fourier Transform of a Low Pass Filter)]<br />
 +
[https://youtu.be/3Sjn3XLo5XE?t=306 Discrete-Time Signals and Systems Introduction (4/6): Special Functions]<br />
 +
[https://www.youtube.com/watch?v=xx2AQz_ZyC0 Integrating the sinc function]<br />
 +
 
 +
=See also=
 +
[[Normalized sinc]]<br />
 +
 
 +
{{:*-c functions footer}}
 +
 
 +
[[Category:SpecialFunction]]

Latest revision as of 02:19, 16 September 2016

The $\mathrm{sinc}$ function (sometimes called the "unnormalized" $\mathrm{sinc}$ function) is defined by $$\mathrm{sinc}(z) = \left\{ \begin{array}{ll} \dfrac{\sin z}{z} &; z \neq 0 \\ 1 &; z=0. \end{array} \right.$$ It appears in the definition of the Sine integral function.

Properties

Sum of values of sinc

Videos

Infinite Product Evaluation with the Sinc Function
(The Sinc Function) Inverse Fourier Transform of Sinc & Fourier Transform of Sinc
Fourier Transform of a Sinc Function (or Inverse Fourier Transform of a Low Pass Filter)
Discrete-Time Signals and Systems Introduction (4/6): Special Functions
Integrating the sinc function

See also

Normalized sinc

$*$-c functions