12. Consider the state diagram for the two state random sequence (also .Fig. 6.1

Question

12. Consider the state diagram for the two state random sequence (also .Fig. 6.1-14 of Woods and Stark)

12. Consider the state diagram for the two state random sequence (also Fig. 6.1-14 of Woods and Stark) X-a x-b At steady state, the following equality holds true a Explain why this equality is meaningful by considering number of state transitions in each direction (i.e. from a to b, from b to a) from timen to time n+1 b)By employing this equality determine the steady state probabilities of each of the two states. c) Determine the expectation function for the random sequence. d) Let Rr [k,k-nxk -nbe the autocorrelation function. Evaluate Rx[k,k -1 and Rx [k, k 2]. Based on your results do you think that the random sequence is wide sense stationary at steady state? Explain.

Explanation / Answer

For part (a)

State diagram is symmetric w.r.t. a and b

Hence a and b can be interchanged. Hence, the equality makes sense.

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