1. Limited time only! Sign up for a free 30min personal tutor trial with Chegg Tutors
    Dismiss Notice
Dismiss Notice
Join Physics Forums Today!
The friendliest, high quality science and math community on the planet! Everyone who loves science is here!

Digital Communication Systems - Autocorrelation

  1. Nov 27, 2014 #1
    1. The problem statement, all variables and given/known data

    A white noise process W(t) with unity (N_0/2 = 1) power spectral density is input to a linear system. The output of the linear system is X(t), where

    X(t) = W(t) - W(t - 1)

    Determine the autocorrelation of X(t) and sketch it.

    2. Relevant equations

    Capture.png
    Let τ denote a time shift; that is, t = t_2 and τ = t_1 - t_2
    Capture.png

    3. The attempt at a solution

    Capture.png
    I understand that the first term on the last line is indeed equal to Capture.png . I'm however unsure what to do with the other three terms. The solution sets the other three terms to different autocorrelation functions and I'm not sure how these other three terms are autocorrelation functions as well based off of the definition.

    Here's what the solution is. I don't understand how it went from the second line to the third line.
    Capture.png
    Any help would be greatly appreciated. I also don't understand how how the solution goes from the third line to the fourth line. It seems to just simply replacing the autocorrelation functions with dirac delta functions. I'm not sure how these are equal in any way.
     
  2. jcsd
  3. Nov 29, 2014 #2
    sorry I didn't mean to post
     
Know someone interested in this topic? Share this thread via Reddit, Google+, Twitter, or Facebook

Have something to add?
Draft saved Draft deleted



Similar Discussions: Digital Communication Systems - Autocorrelation
  1. Digital systems (Replies: 1)

  2. Digital Communications (Replies: 1)

Loading...