Answered step by step
Verified Expert Solution
Link Copied!

Question

1 Approved Answer

I can't solve this problem. Can you explain why? Help me, please. A stationary random sequence X[n] with mean ux = 4 and auto-covariance Kxle]

I can't solve this problem. Can you explain why? Help me, please.

image text in transcribed
A stationary random sequence X[n] with mean ux = 4 and auto-covariance Kxle] = 4-lel, 10153 0, otherwise is applied as an input to a linear time-invariant (LTI) system whose impulse response h[n] is h[n] = u[n] - u[n -4] where u[n] is a unit step sequence. The output of this system is another random sequence Y [n]. (a) Determine the mean sequence My [n]. (b) Determine the crosscorrelation Rxy [m, n] between X[m] and Y [n]. (c) Determine the autocorrelation Ry [m, n] of the output Y [n]. Explanation: In this problem the system is LTI so the system operation is the convolution sum. The input random process is stationary so the output random process is also stationary hence use the simplified formulas. First compute crosscovariance Kxy [m, n] and autocovari- ance Ky [m, n] and then the respective correlations. MATLAB can be used for convolutions. Answers: (a) My = 16, (b) Rxy [(] = {..., 64, 64, 65, 67, 70, 74, 76, 76, 74, 70, 67, 65, 64, 64, ...., (c) Ky [(] = 1...,256, 256, 257, 260, 266, 276, 287, 296, 300, 296, 287, 276, 266, 260, 257, 256, 256, ...)

Step by Step Solution

There are 3 Steps involved in it

Step: 1

blur-text-image

Get Instant Access to Expert-Tailored Solutions

See step-by-step solutions with expert insights and AI powered tools for academic success

Step: 2

blur-text-image

Step: 3

blur-text-image

Ace Your Homework with AI

Get the answers you need in no time with our AI-driven, step-by-step assistance

Get Started

Recommended Textbook for

A First Course in Differential Equations with Modeling Applications

Authors: Dennis G. Zill

10th edition

978-1111827052

More Books

Students also viewed these Mathematics questions

Question

How does the quality of internal controls affect evidence?

Answered: 1 week ago

Question

4. What are the most popular traditional structures?

Answered: 1 week ago