4.12. In the system of Figure 4.10, assume that \[ H\left(e^{j \omega}\right)=j \omega / T, \quad-\pi \leq \omega<\pi \] and $T=1 / 10 \mathrm{sec}$. (a) For each of the following inputs $x_{c}(t)$, find the corresponding output $y_{c}(t)$. (i) $x_{c}(t)=\cos (6 \pi t)$. (ii) $x_{c}(t)=\cos (14 \pi t)$. (b) Are the outputs $y_{c}(t)$ those you would expect from a differentiator?

Problem 1. A discrete time system has a unit sample response $h(n)$ as: \[ h(n)=0.5 \delta(n)+\delta(n-1)+0.5 \delta(n-2) \] 15 pts. (a) Find the system frequency response, and express it by magnitude and phase expressions. 15 pts. (b) If the input to this discrete time system is " $x(n)=5 \cos (n \pi / 4)$ " obtain it's steady state response $y(n)=$ ?

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