Difference between revisions of "Sinc"

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=Properties=
 
=Properties=
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[[Sum of values of sinc]]<br />
<strong>Theorem:</strong> The following formula holds:
 
$$\mathrm{sinc}(x)=\displaystyle\prod_{k=1}^{\infty} \cos \left( \dfrac{x}{2^k} \right).$$
 
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<strong>Proof:</strong> █
 
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{{:Sum of values of sinc}}
 
 
 
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<strong>Theorem:</strong> The following formula holds:
 
$$\displaystyle\sum_{k=1}^{\infty} (-1)^{k+1}\mathrm{sinc}(k)=\dfrac{1}{2}.$$
 
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<strong>Proof:</strong> █
 
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=Videos=
 
=Videos=

Revision as of 08:02, 8 June 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

<center>$*$-c functions
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