The Sinc Function

The sinc function computes the mathematical sinc function for an input vector or matrix $$x$$. Viewed as a function of time, or space, the sinc function is the inverse Fourier transform of the rectangular pulse in frequency centered at zero, with width $$2\pi$$ and unit height:

$$\mathrm{sinc}\mathit{x}=\frac{1}{2\pi }{\int }_{-\pi }^{\pi }{\mathit{e}}^{\mathit{j}\omega \mathit{x}}\mathit{d}\omega =\{\begin{array}{cc}\frac{\sin \pi \mathit{x}}{\pi \mathit{x}},& \mathit{x}\ne 0,\\ 1,& \mathit{x}=0.\end{array}$$

To plot the sinc function for a linearly spaced vector with values ranging from $$-5$$ to $$5$$, use these commands:

x = linspace(-5,5);
y = sinc(x);
plot(x,y)
grid