EC > GATE 2025 > Random Processes
Consider a real-valued random process
f(t)=Σn=1Nanp(t-nT),
where T>0 and N is a positive integer. Here, p(t)=1 for t∈[0,0.5T] and 0 otherwise. The coefficients an are pairwise independent, zero-mean unit-variance random variables.
Read the following statements about the random process and choose the correct option.
(i) The mean of the process f(t) is independent of time t.
(ii) The autocorrelation function E[f(t)f(t+τ)] is independent of time t for all t.
(Here, E[⋅] is the expectation operation.)
f(t)=Σn=1Nanp(t-nT),
where T>0 and N is a positive integer. Here, p(t)=1 for t∈[0,0.5T] and 0 otherwise. The coefficients an are pairwise independent, zero-mean unit-variance random variables.
Read the following statements about the random process and choose the correct option.
(i) The mean of the process f(t) is independent of time t.
(ii) The autocorrelation function E[f(t)f(t+τ)] is independent of time t for all t.
(Here, E[⋅] is the expectation operation.)
Correct : a
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