A random sequence Xn is defined by X, = A(n-K) u[n – K] where A and K are statistically independent random variables, and u[·] is a unit step sequence. Random variable A is uniformly distributed between 0 and 1. Random variable K is a discrete random variable which takes values equal to -1,0, and 1 with equal probability. (a) Determine the mean sequence µx[n] and plot its values for n = -1,0,1,2,3. (b) Determine the auto-correlation bi-sequence Rx[m,n]. (c) Comment on the stationarity of Xņ.
A random sequence Xn is defined by X, = A(n-K) u[n – K] where A and K are statistically independent random variables, and u[·] is a unit step sequence. Random variable A is uniformly distributed between 0 and 1. Random variable K is a discrete random variable which takes values equal to -1,0, and 1 with equal probability. (a) Determine the mean sequence µx[n] and plot its values for n = -1,0,1,2,3. (b) Determine the auto-correlation bi-sequence Rx[m,n]. (c) Comment on the stationarity of Xņ.
Algebra & Trigonometry with Analytic Geometry
13th Edition
ISBN:9781133382119
Author:Swokowski
Publisher:Swokowski
Chapter10: Sequences, Series, And Probability
Section10.2: Arithmetic Sequences
Problem 68E
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![A random sequence X, is defined by
X, = A"-K) u[n – K]
where A and K are statistically independent random variables, and u[·] is a unit step sequence.
Random variable A is uniformly distributed between 0 and 1. Random variable K is a discrete
random variable which takes values equal to –1, 0, and 1 with equal probability.
(a) Determine the mean sequence µx[n] and plot its values for n= –1,0,1,2,3.
(b) Determine the auto-correlation bi-sequence Rx[m, n).
(c) Comment on the stationarity of Xn.](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2F85e4b871-9d1c-4ae2-b799-fb57954f3d49%2Ffa1b493e-c67a-42b7-90e8-8b1f600a50b0%2F8af1zho_processed.png&w=3840&q=75)
Transcribed Image Text:A random sequence X, is defined by
X, = A"-K) u[n – K]
where A and K are statistically independent random variables, and u[·] is a unit step sequence.
Random variable A is uniformly distributed between 0 and 1. Random variable K is a discrete
random variable which takes values equal to –1, 0, and 1 with equal probability.
(a) Determine the mean sequence µx[n] and plot its values for n= –1,0,1,2,3.
(b) Determine the auto-correlation bi-sequence Rx[m, n).
(c) Comment on the stationarity of Xn.
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