A nonstationary respectively: random sequence X[n] has the following mean and autocovariance sequences, Ux[n]=cos(tn); Kx[n+l, n] = Kx[l] = {1,2,3,2,1} 1 Note that the up-arrow “↑” in Kx[l] above indicates the l = 0 position and that the covariance values not given are zero. This random sequence is processed through a linear system described by the difference equation y[n] =2x[n] +x[n+1]+x[n-1], -
A nonstationary respectively: random sequence X[n] has the following mean and autocovariance sequences, Ux[n]=cos(tn); Kx[n+l, n] = Kx[l] = {1,2,3,2,1} 1 Note that the up-arrow “↑” in Kx[l] above indicates the l = 0 position and that the covariance values not given are zero. This random sequence is processed through a linear system described by the difference equation y[n] =2x[n] +x[n+1]+x[n-1], -
Algebra & Trigonometry with Analytic Geometry
13th Edition
ISBN:9781133382119
Author:Swokowski
Publisher:Swokowski
Chapter10: Sequences, Series, And Probability
Section10.8: Probability
Problem 32E
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Question
![A nonstationary random sequence X[n] has the following mean and autocovariance sequences,
respectively:
Hx[n] = cos(an);
Ky[n+l,n] = Kx[@] = {1,2,3,2,1}
Note that the up-arrow "f" in Kx[l] above indicates the l = 0 position and that the covariance
values not given are zero. This random sequence is processed through a linear system described
by the difference equation
yln] = 2x[n] + x[n+1] + x[n- 1], -0<n<∞
to obtain the output random sequence Y[n].
(a) Determine the autocorrelation sequence Ry[n, n– l] of X[n].
(b) Determine the mean uy[n] of Y [n].
(c) Determine the crosscorrelation Ry y[n, n– l] between X[n] and Y[n – l].
(d) Determine the autocorrelation Ry[n,n– l] of Y[n].
(e) Is Y[n] WSS? You must justify your answer to get credit.](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2F85e4b871-9d1c-4ae2-b799-fb57954f3d49%2F123c84c7-5a52-47a7-b64f-745f169dabff%2Fumz1ee_processed.png&w=3840&q=75)
Transcribed Image Text:A nonstationary random sequence X[n] has the following mean and autocovariance sequences,
respectively:
Hx[n] = cos(an);
Ky[n+l,n] = Kx[@] = {1,2,3,2,1}
Note that the up-arrow "f" in Kx[l] above indicates the l = 0 position and that the covariance
values not given are zero. This random sequence is processed through a linear system described
by the difference equation
yln] = 2x[n] + x[n+1] + x[n- 1], -0<n<∞
to obtain the output random sequence Y[n].
(a) Determine the autocorrelation sequence Ry[n, n– l] of X[n].
(b) Determine the mean uy[n] of Y [n].
(c) Determine the crosscorrelation Ry y[n, n– l] between X[n] and Y[n – l].
(d) Determine the autocorrelation Ry[n,n– l] of Y[n].
(e) Is Y[n] WSS? You must justify your answer to get credit.
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