Fourier transform of sinc function proof

1. What is the Fourier transform of a sinc function?
2. What is the derivative of a sinc function?
3. Is sinc function a power signal?
4. How do you find the energy of a sinc function?

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 the derivative of a sinc function?

That is, sin(ξ)/ξ = cos(ξ) for all points ξ where the derivative of sin(x)/x is zero and thus a local extremum is reached. This follows from the derivative of the sinc function: and where odd n lead to a local minimum, and even n to a local maximum.

Is sinc function a power signal?

Sinc Function

It is an energy type signal.

How do you find the energy of a sinc function?

x(t) = sin(2*pi*f*t)/(pi*t); Hi Bharat, I guess the fourier transform of the mentioned sinc function is is rectangular pulse. So instead of going for a definite integral and its convergence we can compute the energy in frequency domain.