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Homework Help: Time Invariance of a System

  1. Sep 12, 2011 #1
    1. The problem statement, all variables and given/known data

    Determine if the following system is time invariant:

    y(t) = x(t - 2) + x(2 - t)

    2. The attempt at a solution

    I know from the solutions that the system is NOT time invariant, yet whenever I try to solve it I get the opposite result. Here's what I'm doing:

    y1(t) = x1(t - 2) + x1(2 - t)

    x2(t) = x1(t - t0)
    y2(t) = x2(t - 2) + x2(2 - t) = x1(t - t0 - 2) + x1(2 - t + t0)

    y1(t - t0) = x1(t - t0 - 2) + x1(2 - t + t0)

    Therefore y2(t) = y(t - t0)

    What am I doing wrong?

  2. jcsd
  3. Sep 12, 2011 #2


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    Staff: Mentor

    You have told us everything you know about x(t)?
  4. Sep 12, 2011 #3
    Yes; no information at all is given about x(t).
  5. Sep 12, 2011 #4
    Any takers?

    I found a case that clearly shows that the system is not time invariant, but I'd still love to know what is wrong about my proof. I can't seem to figure it out.

  6. Sep 14, 2011 #5


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    Staff: Mentor

    Please return to the specification of the problem, and quote verbatim the sentence there containing the word "odd" or "even". :smile: :smile: :smile:
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