\{X_{n}\} _{n = −\infty}^{n = \infty} is an independent and identically distributed (i.i.d.) random process with X n equally likely to be + 1 or −1. \{Y_{n}\} _{n = −\infty}^{n = \infty} is another random process obtained as Y_{n} = X_{n} + 0.5X_{n−1}\:. The autocorrelation function of \{Y_{n}\} _{n = −\infty}^{n = \infty}, denoted by R_{y} [k] , is_______

GATE Electronics and Communications (EC) 2015 Shift 2 Solved Paper

Question : 60 of 65

Marks: +1, -0

\{X_{n}\} _{n = −∞}^{n = ∞}

is an independent and identically distributed (i.i.d.) random process with X_nequally likely to be

+ 1

−1

\{Y_{n}\} _{n = −∞}^{n = ∞}

is another random process obtained as

Y_{n} = X_{n} + 0.5X_{n−1}\:

. The autocorrelation function of

\{Y_{n}\} _{n = −∞}^{n = ∞}

, denoted by

R_{y} [k] ,

is_______

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