Multiple-Choice Questions

(check all correct answers)

1.

Consider a system in which the output y(t) is generated by multiplying the input x(t) by $\cos(2\pi f_0 t)$. Which of the following is true?

$\Box$

The system is a linear system.

$\Box$

The system is not linear.

$\Box$

The system is time-invariant.

$\Box$

The system is not time-invariant.

2.

A system is given by the input-output relationship $y(t) = \int x(\tau) h(t + \tau) d\tau$. Which of the following is true?

$\Box$

The system is a linear system.

$\Box$

The system is not linear.

$\Box$

The system is time-invariant.

$\Box$

The system is not time-invariant.

3.

Let x₁(t) be a rectangular pulse of width 1, i.e.,

$$x_1(t) = \left\{ \begin{array} {cl} 1 & \mbox{for $\vert x\vert \leq \frac{1}{2}$}\\ 0 & \mbox{else} \end{array} \right.$$

Further, let x₂(t) be a triangular pulse,

$$x_2(t) = \left\{ \begin{array} {cl} a(1+x) & \mbox{for $-1... ...or $0 \leq x \leq 1$}\\ 0 & \mbox{else} \end{array} \right.$$

Which value of a makes the energy of the two signals equal?

$\Box$

a=1

$\Box$

$a= \sqrt{3}$

$\Box$

$a= 1/\sqrt{3}$

$\Box$

none of the above.

4.

Let the amplitude a of the triangular pulse be such that the energies of both signals in the previous question are the same. Then, each of the two signals is input to an ideal lowpass filter with cut-off frequency 1; the resulting output signals are denoted y₁(t) and y₂(t). Which of the following is true?

$\Box$

The energy of y₁(t) is larger than the energy of y₂(t).

$\Box$

The energy of y₁(t) is smaller than the energy of y₂(t).

$\Box$

The energy of y₁(t) is the same as the energy of y₂(t).

$\Box$

The question can not be answered with the information provided.