Yarmusk Universib

Hijawi Faculiy of Engiseering and Techasleg

Departuent of Cannunication Keciacerief

$8.$ The impulse response of a system is given as $h(n)=(n)-(-\frac{1}{2}{)}^{n}u(n).$ For an input $x!$ and oufput $y|n|,$ the difference equation that describes the system is

a$)y[si]+2y[n-1]=2x[n]$

b$)y[n]+0\mathrm{.}5y[n-1]=0\mathrm{.}5x[n-1]$

c$)y[g]-0\mathrm{.}5y[s-1]=0\mathrm{.}5x[n-1]$

d$)y[n]+2ny[n-1]=x[n]$

e$)$ None of the above

$9.$ Consider the transfer function of a system $H(x)=\frac{2a(x-1)}{x^2+4x+4}.$ For an input $x(n)=2(n)(n+1),$ the system output is

A$)25(n+1)+6(\frac{1}{2}{)}^{n}u(n)$

B$)2(n)-6(-2{)}^{n}u(n)$

C$)28(n+1)+6(2{)}^{n}u(n)$

D$)2(n+1)-6(-2{)}^{n}u(n)$

E$)$ None of the above.

$10.$ Consider the following sequence

$x(n)=8(n)+2(n-2)+(n-3)$

The four$-$point circular convolution of $x(n)$ with itself $x(n)oxx(n)$ is

a$)48|a-1|$

b$)68[b]+5g[s-1]+48[s-2]+28[s-3]$

c$)5|n|+4[e-1]+5[s-2]+2|n-3|$

d$)28|n-1|$

e$)$ None of the above

$S$ is a discrete$-$time system whase response to any input signal $x[a]$ is $x|a{|}^{**}h|n|.$ The system frequeacy response $H$ is given by

$H(w)=\{\begin{array}{cc}1,& 1|w|\\ 0,& |w|1\end{array}$

Consider an input signal $x|g|=sin(\frac{n}{2})+cos(m\frac{a}{4}),$ for all integer $n.$ The response of system $S$ this input signal is

a$)sin(\frac{n}{2})$

c$)e^{j{}_i^2}$

b$)e^{-j{}_2^2}$

e$)$ None of the above

d$)cos(\frac{n}{4})$