Dft of sinc function

1. What is the magnitude of a sinc function?
2. What is the Fourier transform of a sinc function?
3. What is the derivative of a sinc function?
4. How do you find the DFT of a function?

What is the magnitude of a sinc function?

The sinc function is defined as: sinc(a) = sin(πa)/(πa), however, it is common to see the vague statement: "the sinc function is of the general form: sin(x)/x." In other words, the sinc is a sine wave that decays in amplitude as 1/x.

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.

How do you find the DFT of a function?

The DFT formula for X k X_k Xk​ is simply that X k = x ⋅ v k , X_k = x \cdot v_k, Xk​=x⋅vk​, where x x x is the vector ( x 0 , x 1 , … , x N − 1 ) .