Question $2$

$2$ pts

Consider a discrete$-$time system whose impulse response is given by

$h(t)=\{\begin{array}{ccc}1,& n=0\text{a}\text{n}\text{d}& n=3\\ 3,& n=1\text{a}\text{n}\text{d}& n=2\\ 0,& \text{o}\text{t}\text{h}\text{e}\text{r}\text{w}\text{i}\text{s}\text{e}& \end{array}$

Determine the frequency response $H(e^{\text{j}\text{h}\text{a}\text{t}()}).$

$H(e^{\text{j}\text{h}\text{a}\text{t}()})=2e^{-\text{j}\text{h}\text{a}\text{t}\frac{}{2}}(3cos(3$hat$\frac{}{2})+cos(hat\frac{}{2}))$

$H(e^{\text{j}\text{h}\text{a}\text{t}()})=2e^{-\text{j}\text{h}\text{a}\text{t}\frac{}{2}}(cos(3$hat$\frac{}{2})+3cos(hat\frac{}{2}))$

$H(e^{\text{j}\text{h}\text{a}\text{t}()})=2e^{-\text{j}\text{h}\text{a}\text{t}\frac{}{2}}(cos(3$hat$\frac{}{2})+cos(hat\frac{}{2}))$

$H(e^{\text{j}\text{h}\text{a}\text{t}()})=2e^{-j3\text{h}\text{a}\text{t}\frac{}{2}}(cos(3$hat$\frac{}{2})+3cos(hat\frac{}{2}))$Question $2$

$2$ pts

Consider a discrete$-$time system whose impulse response is given by

$h(t)=\{\begin{array}{ccc}1,& n=0\text{a}\text{n}\text{d}& n=3\\ 3,& n=1\text{a}\text{n}\text{d}& n=2\\ 0,& \text{o}\text{t}\text{h}\text{e}\text{r}\text{w}\text{i}\text{s}\text{e}& \end{array}$

Determine the frequency response $H(e^{\text{j}\text{h}\text{a}\text{t}()}).$

$H(e^{\text{j}\text{h}\text{a}\text{t}()})=2e^{-\text{j}\text{h}\text{a}\text{t}\frac{}{2}}(3cos(3$hat$\frac{}{2})+cos(hat\frac{}{2}))$

$H(e^{\text{j}\text{h}\text{a}\text{t}()})=2e^{-\text{j}\text{h}\text{a}\text{t}\frac{}{2}}(cos(3$hat$\frac{}{2})+3cos(hat\frac{}{2}))$

$H(e^{\text{j}\text{h}\text{a}\text{t}()})=2e^{-\text{j}\text{h}\text{a}\text{t}\frac{}{2}}(cos(3$hat$\frac{}{2})+cos(hat\frac{}{2}))$

$H(e^{\text{j}\text{h}\text{a}\text{t}()})=2e^{-j3\text{h}\text{a}\text{t}\frac{}{2}}(cos(3$hat$\frac{}{2})+3cos(hat\frac{}{2}))$