Q1:

The impulse response of a casual linear time-invariant system is given as h(t). Now consider the following two statements:

Statement (I)  :  principle of superposition holds.

Statement (II) :  h(t) = 0 for t< 0.

Which of the following statement is correct?

Q2:

A system with x(t) and output y(t) is defined by the input –output relation:

$Y(t)={\displaystyle \underset{-\infty }{\overset{2t}{\int }}x(t)dt}$

The system will be

Q3:

For a bounded function, is the integral of the function from -infinity to +infinity defined and finite?

Q4:

y(t) = sin(x(t-1)) : Comment on its memory aspects.

Q5:

Which of the properties does the system satisfy

y(t)=x(t)cos$\omega t$

1.Additivity

2.Homogencity

3.shift invariance

Q6:

The system is described by

y(t)=x(t)+2

The system is

Q7:

If u(t), r(t) denote the unit step and unit ramp functions respectively and u(t) * r(t) their their convolution, then the function u(t+1) * r(t-2) is given by

Q8:

The impulse response of an initially relaxed linear system is $e^{-2t}u(t)$. To produce a response of $t{e}^{-2t}u(t)$, the input must be equal to

Q9:

A Linear time invariant system with an impulse response h(t) produces output y(t) when input x(t) is applied. When the input  $x(t-\tau )$ is applied to the system with impulse response $h(t-\tau )$, the output will be

Q10:

Consider the differential equation:

$\frac{d^{2}y(t)}{d{t}^2}+2\frac{dy(t)}{dt}+y(t)=\delta (t)$with

${y(t)|}_{t=0^{-}}=-\mathrm{2 }an\mathrm{d }{\frac{dy}{dt}|}_{t=0^{-}}=0$

the numerical value of ${\frac{dy}{dt}|}_{t=0^{+}}$is

Q11:

The impulse response of a system is h(t) = tu(t).

For an input u(t-1), the output is

Q12:

s(t) is step and h(t) is impulse response of a system. Its response y(t) for any input u(t) is given by

Q13:

The impulse response of a continuous time system is given by $h(t)=\delta (t-1)+\delta (t-3).$the value of the step response at t=2 is

Q14:

The unit response impulse of a system is given as.

$c(t)=-4e^{-t}+6e^{-2t}$

The step response of the same system for$t\ge 0$is equal to.

Q15:

Given the finite length input x[n] and the corresponding finite length output y[n] of an LTI system as shown below, the impulse response h[n] of the system is

$x[n]=\{1,-1\underset{}{\}}-\begin{array}{||}\hline h[n]\\ \hline\end{array}\to y[n]=\{1,0,0,0,-1\underset{}{\}}$

           $\uparrow$                               $\uparrow$