Energy of $\text{sinc}^2(kt)$ function multiplied by variable

1. How do you define a sinc function in Matlab?
2. What is the Fourier transform of a sinc function?
3. What is sinc function and sampling function?

How do you define a sinc function in Matlab?

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 π and unit height: sinc x = 1 2 π ∫ - π π e j ω x d ω = sin π x π x , x ≠ 0 , 1 , x = 0 .

What is the Fourier transform of a sinc function?

The Fourier transform of the sinc function is a rectangle centered on ω = 0. This gives sinc(x) a special place in the realm of signal processing, because a rectangular shape in the frequency domain is the idealized “brick-wall” filter response.

What is sinc function and sampling function?

The sinc function , also called the "sampling function," is a function that arises frequently in signal processing and the theory of Fourier transforms. The full name of the function is "sine cardinal," but it is commonly referred to by its abbreviation, "sinc." There are two definitions in common use.