Communication System - GATE practice papers - Electronics & Communication for Q. 538

Q.  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: A is true & B is false
 
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 mx (t) is independent of time and the autocorrelation function Rx (tk, ti) depends only on the time difference (tk - ti).
Hence, it is obvious that all SSS are definitely WSS but all WSS are not necessarily SSS.

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