## Digital Signal Processing Questions and Answers Part-7

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)=xe(t)+xo(t)
=>x(-t)=xe(-t)-xo(-t)
By adding the above two equations, we get
xe(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, xo(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 x1(t) and x2(t) be periodic signals with fundamental periods T1 and T2 respectively. Which of the following must be a rational number for x(t)=x1(t)+x2(t) to be periodic?
a) T1+T2
b) T1-T2
c) T1/T2
d) T1*T2

Explanation: Let T be the period of the signal x(t)
=>x(t+T)=x1(t+mT1)+x2(t+nT2)
Thus, we must have
mT1=nT2=T
=>(T1/T2)=(k/m)= a rational number.

7. Let x1(t) and x2(t) be periodic signals with fundamental periods T1 and T2 respectively. Then the fundamental period of x(t)=x1(t)+x2(t) is?
a) LCM of T1 and T2
b) HCF of T1and T2
c) Product of T1 and T2
d) Ratio of T1 to T2

Explanation: For the sum of x1(t) and x2(t) to be periodic the ratio of their periods should be a rational number, then the fundamental period is the LCM of T1 and T2.

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