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Problem 4: Let X(t) be a random process as: X(t) = cos(2лft+), where is a random variable distributed uniformly over (0, 2). This means that its PDF is 1 for Є[0,2] fo()=2π 0 otherwise (a) Determine the expectation of X(t), mx(t). (b) Determine the autocorrelation function of X(t), Rx(t,t+t). (c) Is X(t) a wide sense stationary (WSS) process? Explain why. (d) Determine the power spectral density (PSD) of X(t), Sx(f).

Problem 4: Let X(t) be a random process as: X(t) = cos(2лft+), where is a random variable distributed uniformly over (0, 2). This means that its PDF is 1 for Є[0,2] fo()=2π 0 otherwise (a) Determine the expectation of X(t), mx(t). (b) Determine the autocorrelation function of X(t), Rx(t,t+t). (c) Is X(t) a wide sense stationary (WSS) process? Explain why. (d) Determine the power spectral density (PSD) of X(t), Sx(f).

Introductory Circuit Analysis (13th Edition)
Introductory Circuit Analysis (13th Edition)
13th Edition
ISBN:9780133923605
Author:Robert L. Boylestad
Publisher:Robert L. Boylestad
Chapter1: Introduction
Section: Chapter Questions
Problem 1P: Visit your local library (at school or home) and describe the extent to which it provides literature...
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Problem 4: Let X(t) be a random process as: X(t) = cos(2лft+), where is a random variable distributed uniformly over (0, 2). This means that its PDF is 1 for Є[0,2] fo()=2π 0 otherwise (a) Determine the expectation of X(t), mx(t). (b) Determine the autocorrelation function of X(t), Rx(t,t+t). (c) Is X(t) a wide sense stationary (WSS) process? Explain why. (d) Determine the power spectral density (PSD) of X(t), Sx(f).
Transcribed Image Text:Problem 4: Let X(t) be a random process as: X(t) = cos(2лft+), where is a random variable distributed uniformly over (0, 2). This means that its PDF is 1 for Є[0,2] fo()=2π 0 otherwise (a) Determine the expectation of X(t), mx(t). (b) Determine the autocorrelation function of X(t), Rx(t,t+t). (c) Is X(t) a wide sense stationary (WSS) process? Explain why. (d) Determine the power spectral density (PSD) of X(t), Sx(f).
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