Connexions

You are here: Home » Content » Homework 3 of Elec 430
Content Actions
Lenses

What is a lens?

Lenses

A lens is a custom view of Connexions content. You can think of it as a fancy kind of list that will let you see Connexions through the eyes of organizations and people you trust.

What is in a lens?

Lens makers point to Connexions materials (modules and collections), creating a guide that includes their own comments and descriptive tags about the content.

Who can create a lens?

Any individual Connexions member, a community, or a respected organization.

This content is ...
Affiliated with (?)
This content is either by members of the organizations listed or about topics related to the organizations listed. Click each link to see a list of all content affiliated with the organization.

  • This module is included inLens: Rice University OpenCourseWare
    By: OpenCourseWare ConsortiumAs a part of collection:"Digital Communication Systems"

    Click the "Rice University OCW" link to see all content affiliated with them.

    Rice University OCW
Tags

(?)

These tags come from the endorsement, affiliation, and other lenses that include this content.

Homework 3 of Elec 430

Module by: Behnaam Aazhang

Summary: (Blank Abstract)

Problem 1
Suppose that a white Gaussian noise X t X t is input to a linear system with transfer function given by
Hf=1if|f|≤20if|f|>2 H f 1 f 2 0 f 2 (1)
Suppose further that the input process is zero mean and has spectral height N 0 2=5 N 0 2 5 . Let Y t Y t denote the resulting output process.
  1. Find the power spectral density of Y t Y t . Find the autocorrelation of Y t Y t (i.e., R Y τ R Y τ ).
  2. Form a discrete-time process (that is a sequence of random variables) by sampling Y t Y t at time instants T T seconds apart. Find a value for T T such that these samples are uncorrelated. Are these samples also independent?
  3. What is the variance of each sample of the output process?
HW3Fig1.png
Figure 1
Problem 2
Suppose that X t X t is a zero mean white Gaussian process with spectral height N 0 2=5 N 0 2 5 . Denote Y t Y t as the output of an integrator when the input is Y t Y t .
HW3Fig2.png
Figure 2
  1. Find the mean function of Y t Y t . Find the autocorrelation function of Y t Y t , R Y t+τt R Y t τ t
  2. Let Z k Z k be a sequence of random variables that have been obtained by sampling Y t Y t at every T T seconds and dumping the samples, that is
    Z k =∫k-1TkT X τ dτ Z k τ k 1 T k T X τ (2)
    Find the autocorrelation of the discrete-time processes Z k Z k 's, that is, R Z k+mk=E Z k+m Z k R Z k m k E Z k+m Z k
  3. Is Z k Z k a wide sense stationary process?
Problem 3
Proakis and Salehi, problem 3.63, parts 1, 3, and 4
Problem 4
Proakis and Salehi, problem 3.54
Problem 5
Proakis and Salehi, problem 3.62

Comments, questions, feedback, criticisms?

Send feedback