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Unformatted text preview: (5) = p(xn−K )
k =0 p(xn−k /xn−k−1) . (6) DiscreteValued Markov Sequences (a.k.a. Markov Chains): Consider a Markov sequence Xn where at each time n the random variable Xn is discretevalued (i.e. it can only take on values from a discrete alphabet). We refer to such an Xn as a discretevalued Markov sequence, which is also referred to as a Markov chain. The idea generalizes to vector processes. Example 1  A discretevalued delayline process: Consider a stationary DT random process Im(n) which, for each time n, Im ∈ {I1 , I2 , · · · , IM }. To simplify notation, let’s refer to this random sequence as In , keeping in mind that each sample is restricted to one of the M values from its alphabet. At time n consider the vector S n = [In−1 , In−2 , · · · , In−L ]T . (7) S n is a vector Markov chain. In need not be statistically independent over time, but if it is than conditional PDF’s of S n over time will be more simply characterized. In Example 1 above, the vector S n is called the state of the Markov c...
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This document was uploaded on 10/12/2009.
 Spring '09

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