EENL$210$ Signals and systems

Q:$7($B$5)$ An LTI system is defined by a differential equation: $2x^{\text{'}}(t)+10x(t)=y^{\text{'}}(t)+3y(t).$ Then $H(s)=?$

a$)2-\frac{4}{s-3}$

b$)2-3\frac{s}{s+10}$

c$)2+\frac{3}{s+10}$

d$)\frac{2s+10}{s+3}$

e$)\frac{s-9}{s+3}$

$Q$:$8($B$2)(4u(t)e^{-2t})ox(6u(t)e^{-3t})=?$

a$)24(e^{-2t}+e^{-3t}+e^{-5t})u(t)$

b$)24e^{-st}{u}^2(t)$

c$)24e^{-5t}u(t)$

d$)24(e^{-2t}-e^{-3t})u(t)$

e$)24(t-5)$

$Q$:$($D$$r$)H(a)=>$ for the oiven sustem.

a$)2-\frac{17}{s+7}$

b$)\frac{2+4s^{-1}}{1+7s^{-1}}$

c$)4+\frac{8}{1+7s^{-1}}$

d$)2s+\frac{4}{s-7}$

e$)2+4\frac{s}{s+7}$

Q:$10($B$2)$ What must be the transfer function $H(s)$ of the system if $A(s)=4s$ and $K(s)=-\frac{1}{s}$ in the given diagremo

a$)4\frac{s}{1-s^2}$

b$)4s$

c$)4\frac{s}{5}$

d$)4\frac{s}{s^2+1}$

e$)\frac{s-6}{1-\frac{s^{-1}}{4}}$

Q:$11($B$4)$ According to the Nyquist criteria, what is the minimum frequency needed for sampling a continuous time signal

$f(t)=9sin(600t+\frac{}{3})-13cos(500t+\frac{}{6})$

a$)2000Hz$

b$)500Hz$

c$)900Hz$

d$)44100Hz$

e$)600Hz$

$Q$:$12(B3)Fz$

a$)4e^{-3iz}+4e^{\frac{3}{z}}+10$

b$)4[z-3]+4[z+3]+[z]$

c$)8cos(3z)+10$

d$)8cos(3e^{-iz})+10$

e$)4(z^3+z^{-3})+10$