Dtft of sinc function

1. How do you find the DTFT of a sequence?
2. What is integration of sinc function?
3. What is DTFT spectrum?

How do you find the DTFT of a sequence?

Find the DTFT of the sequence x(n)=u(n−k). ⇒F[u(n−k)]=e−jωk+e−jω(k+1)+e−jω(k+2)+... ⇒F[u(n−k)]=e−jωk(1+e−jω+e−j2ω+e−j3ω+...)

What is integration of sinc function?

The integral of a function is the value of its Fourier transform at zero, so sinc integrates to π. [ 1] By Plancherel's theorem, the integral of sinc²(x) is the integral of its Fourier transform squared, which equals π.

What is DTFT spectrum?

The spectrum of the DTFT is continuous, so either f or ω can be used. The common choice is ω, because it makes the equations shorter by eliminating the always present factor of 2π. Remember, when ω is used, the frequency spectrum extends from 0 to π, which corresponds to DC to one-half of the sampling rate.