# Difference between revisions of "Manuals/calci/SINC"

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*In <math>SINC(X)</math>, <math>X</math> is any real number. | *In <math>SINC(X)</math>, <math>X</math> is any real number. | ||

*The full name of the function is sine cardinal,but it is commonly referred to by its abbreviation, Sinc. | *The full name of the function is sine cardinal,but it is commonly referred to by its abbreviation, Sinc. | ||

− | *The unnormalized SINC function is defined by | + | *The unnormalized SINC function is defined by : |

− | |||

− | |||

− | |||

− | |||

<math>SINC(X)=\begin{cases} | <math>SINC(X)=\begin{cases} | ||

− | 1 & for | + | 1 & for x=0 \\ |

− | + | \frac{Sin x}{x} & Otherwise\\ | |

\end{cases}</math> | \end{cases}</math> | ||

− | *The normalized SINC function is defined by <math>SINC(X)= \frac{SIN | + | *The normalized SINC function is defined by <math>SINC(X)= \frac{SIN\pi x}{\pi x}</math> . |

*The value at x = 0 is defined to be the limiting value Sinc(0) = 1. | *The value at x = 0 is defined to be the limiting value Sinc(0) = 1. | ||

*The only difference between the two definitions is in the scaling of the independent variable (the x-axis) by a factor of π. | *The only difference between the two definitions is in the scaling of the independent variable (the x-axis) by a factor of π. | ||

+ | |||

+ | ==Examples== | ||

+ | #SINC(9) = 0.04579094280463962 | ||

+ | #SINC(-34) = 0.015561255474118348 | ||

+ | #SINC(-51.7) = 0.019163025320677915 | ||

+ | |||

+ | ==Related Videos== | ||

+ | |||

+ | {{#ev:youtube|v=9sd4DWragBg|280|center|Cardinal Sin}} | ||

+ | |||

+ | ==See Also== | ||

+ | *[[Manuals/calci/SIN| SIN]] | ||

+ | *[[Manuals/calci/SINH| SINH]] | ||

+ | *[[Manuals/calci/ASINH| ASINH]] | ||

+ | |||

+ | ==References== | ||

+ | *[https://en.wikipedia.org/wiki/Sinc_function SinC] | ||

+ | |||

+ | *[[Z_API_Functions | List of Main Z Functions]] | ||

+ | *[[ Z3 | Z3 home ]] |

## Latest revision as of 15:33, 31 January 2019

**SINC(X)**

- is any real number.

## Description

- This function shows the value of the cardinal sin function.
- In , is any real number.
- The full name of the function is sine cardinal,but it is commonly referred to by its abbreviation, Sinc.
- The unnormalized SINC function is defined by :

- The normalized SINC function is defined by .
- The value at x = 0 is defined to be the limiting value Sinc(0) = 1.
- The only difference between the two definitions is in the scaling of the independent variable (the x-axis) by a factor of π.

## Examples

- SINC(9) = 0.04579094280463962
- SINC(-34) = 0.015561255474118348
- SINC(-51.7) = 0.019163025320677915