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Which of the following is done to convert a continuous time signal into discrete time signal?
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.
The deflection voltage of an oscilloscope is a ‘deterministic’ signal. True or False?
Explanation: The behavior of the signal is known and can be represented by a saw tooth wave form. So, the signal is deterministic.
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)).
Which of the following is the odd component of the signal x(t)=e(jt)?
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+jsintcost+jsint)
=(1/2)*(2jsint)
=j*sint.
For a continuous time signal x(t) to be periodic with a period T, then x(t+mT) should be equal to:
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.
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?
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.
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:
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}.
Explanation: For any energy signal, the average power should be equal to 0 i.e., P=0.
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:
Explanation: The energy signal should have total energy value that lies between 0 and infinity.
Explanation: Period of cos2t=(2*pi)/2=pi
Period of sin3t=(2*pi)/3
LCM of pi and (2*pi)/3 is 2*pi.
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