Suppose that the bandlimited differentiator of Example 4.4 has input xc(t) = with...

Suppose that the bandlimited differentiator of Example 4.4 has input xc(t) = with

< π /T. In this problem, we wish to verify that the continuous-time signal reconstructed

from the output of the bandlimited differentiator is indeed the derivative of x_c(t).

(a) The sampled input will be x[n] = cos(ω₀n), where ω0 = < π. Determine an

expression for X(e^jω) that is valid for |ω| ≤ π.

(b) Now use Eq. (4.46) to determine the DTFT of Y(e^jω), the output of the discrete-time

system.

(c) From Eq. (4.32) determine the continuous-time Fourier transform of the output

of the D/C converter.

(d) Use the result of (c) to show that