1. Which of the following is done to convert a continuous time signal into discrete time signal?

a) Modulating

b) Sampling

c) Differentiating

d) Integrating

Explanation: A discrete time signal can be obtained from a continuous time signal by replacing t by nT, where T is the reciprocal of the sampling rate or time interval between the adjacent values. This procedure is known as sampling.

2. The deflection voltage of an oscilloscope is a ‘deterministic’ signal.

a) True

b) False

Explanation: The behavior of the signal is known and can be represented by a saw tooth wave form. So, the signal is deterministic.

3. The even part of a signal x(t) is?

a) x(t)+x(-t)

b) x(t)-x(-t)

c) (1/2)*(x(t)+x(-t))

d) (1/2)*(x(t)-x(-t))

Explanation: Let x(t)=x

_{e}(t)+x

_{o}(t)

=>x(-t)=x

_{e}(-t)-x

_{o}(-t)

By adding the above two equations, we get

x

_{e}(t)=(1/2)*(x(t)+x(-t)).

4. Which of the following is the odd component of the signal x(t)=e^{(jt)}?

a) cost

b) j*sint

c) j*cost

d) sint

Explanation: Let x(t)=e

^{(jt)}

Now, x

_{o}(t)=(1/2)*(x(t)-x(-t))

=(1/2)*(e

^{(jt)}– e

^{(-jt)})

=(1/2)*(cost+jsint-cost+jsint)

=(1/2)*(2jsint)

=j*sint.

5. For a continuous time signal x(t) to be periodic with a period T, then x(t+mT) should be equal to ___________

a) x(-t)

b) x(mT)

c) x(mt)

d) x(t)

Explanation: If a signal x(t) is said to be periodic with period T, then x(t+mT)=x(t) for all t and any integer m.

6. Let x_{1}(t) and x_{2}(t) be periodic signals with fundamental periods T1 and T2 respectively. Which of the following must be a rational number for x(t)=x_{1}(t)+x_{2}(t) to be periodic?

a) T_{1}+T_{2}

b) T_{1}-T_{2}

c) T_{1}/T_{2}

d) T_{1}*T_{2}

Explanation: Let T be the period of the signal x(t)

=>x(t+T)=x

_{1}(t+mT

_{1})+x

_{2}(t+nT

_{2})

Thus, we must have

mT

_{1}=nT

_{2}=T

=>(T

_{1}/T

_{2})=(k/m)= a rational number.

7. Let x_{1}(t) and x_{2}(t) be periodic signals with fundamental periods T_{1} and T_{2} respectively. Then the fundamental period of x(t)=x_{1}(t)+x_{2}(t) is?

a) LCM of T_{1} and T_{2}

b) HCF of T_{1}and T_{2}

c) Product of T_{1} and T_{2}

d) Ratio of T_{1} to T_{2}

Explanation: For the sum of x

_{1}(t) and x

_{2}(t) to be periodic the ratio of their periods should be a rational number, then the fundamental period is the LCM of T

_{1}and T

_{2}.

8. All energy signals will have an average power of ___________

a) Infinite

b) Zero

c) Positive

d) Cannot be calculated

Explanation: For any energy signal, the average power should be equal to 0 i.e., P=0

9. x(t) or x(n) is defined to be an energy signal, if and only if the total energy content of the signal is a __________

a) Finite quantity

b) Infinite

c) Zero

d) None of the mentioned

Explanation: The energy signal should have a total energy value that lies between 0 and infinity.

10. What is the period of cos2t+sin3t?

a) pi

b) 2*pi

c) 3*pi

d) 4*pi

Explanation: Period of cos2t=(2*pi)/2=pi

Period of sin3t=(2*pi)/3

LCM of pi and (2*pi)/3 is 2*pi.