2) Which conditions justify the mutual orthogonality of two random signals X(t) & Y(t)? (Marks : 02)  Published on 19 Oct 15
a. R_{XY} , (t_{1}, t_{2} ) = 0 for every t_{1} and t_{2}
b. R_{XY} , (t_{1}, t_{2} ) = 1 for every t_{1} and t_{2}
c. R_{XY} = 0, (t_{1}, t_{2} ) = 1 for t_{1} and t_{2} instants respectively
d. R_{XY } = 1 , (t_{1}, t_{2} ) = 0 for t_{1} and t_{2} instants respectively
Answer
Explanation

ANSWER: R_{XY} , (t_{1}, t_{2} ) = 0 for every t_{1} and t_{2}
Explanation: Two random X(t) & Y(t) processes are usually said to be mutually orthogonal only and only if R_{XY}, (t_{1},t_{2}) becomes exactly equal to zero; where t_{1} & t_{2} are the two time instants at which the processes are observed.


5) Consider the statements given below:
A. All SSS (Stationary in Strict Sense) processes are also WSS (Stationary in Wide Sense)
B. All the processes that are WSS (Stationary in Wide Sense) are also absolutely SSS (Stationary in Strict Sense)
Which of them are correct? (Marks : 01)  Published on 19 Oct 15
a. A is true & B is false
b. A is false & B is true
c. Both A & B are true
d. Both A & B are false
Answer
Explanation

ANSWER: A is true & B is false
Explanation: A random process is said to be Stationary in Strict Sense (SSS) if the joint probability distribution factor remains invariant to the translation of time origin. On the contrary, it is said to be Stationary in Wide Sense if mean value m_{x} (t) is independent of time and the autocorrelation function Rx (t_{k}, t_{i}) depends only on the time difference (t_{k}  t_{i}). Hence, it is obvious that all SSS are definitely WSS but all WSS are not necessarily SSS.


6) When can a random process is said to be an ergodic process? (Marks : 01)  Published on 19 Oct 15
a. Only when time averages are less than the ensemble averages
b. Only when time averages are equal to the ensemble averages
c. Only when time averages are greater than the ensemble averages
d. none of the above
Answer
Explanation

ANSWER: Only when time averages are equal to the ensemble averages
Explanation: Random Processes can be generally and completely specified on the basis of ensemble and the time statistics since only PDFs are insufficient to describe them completely. So, any random process possessing the time averages exactly equal to averages [Probability Distribution Factor PDF (f_{x(t)} (x)] which are derived from ensemble, then it is said to be an ergodic process.

