Problem 1 Suppose that a band limited differentiator of Example 4.4 in the book has an input x(t) = \cos \left(\Omega_{0} t\right) \text { with } \Omega<\pi / T In

this problem,we wish to verify that the continuous-time signal reconstructed from the output of the band limited differentiator is indeed the derivative of xc(t). b) Use the expression below to determine the DTFT of Y (e^jw), the output of the discrete-time system. H\left(\mathrm{e}^{j \omega}\right)=\frac{j \omega}{T} a) The sampled input will be x[n] = cos(won) where wo =QoT < T. Determine an expression for X(e^jw) that is valid for |w| < T.