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Unit step integration

  1. Feb 15, 2008 #1
    1. The problem statement, all variables and given/known data
    The random variable C is uniform in the interval (0,T). Find the autocorrelation
    [tex] R_x(t_1,t_2) [/tex] if X(t) = U(t-C) where U is a unit step function.

    2. Relevant equations

    3. The attempt at a solution

    [tex] R_x (t_1,t_2) = \int_{-\infty}^{\infty} U(t_1-c) U(t_2-c) f(c) dc [/tex]

    [tex] R_x (t_1,t_2) = \frac{1}{T}\int_0^T U(t_1-c) U(t_2-c) dc [/tex]

    I get stuck here. How do you integrate two shifted unit step functions?
    Last edited: Feb 15, 2008
  2. jcsd
  3. Feb 15, 2008 #2


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    Science Advisor
    Homework Helper

    By first thinking about them :smile:
    Divide the interval into three parts (assuming t1 < t2)
    1. c < t1
    2. t1 < c < t2
    3. t2 < c
    On each of these, what are the values of the step functions? What is their product? Now split the integral and do each part separately.
  4. Feb 15, 2008 #3
    Oh yeah, THANKS!
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