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Time Invariance

  1. Sep 26, 2016 #1
    Okay so the question looks like this
    Determine whether the system with input x(t) and output y(t) defined by each of the following equations is time
    invariant:
    (c) y(t) =∫t+1t x(τ−α)dt where α is a constant;
    (e) y(t) = x(−t);

    There are more sub-questions but I was able to solve them. The reason I can't figure this out is the (d) has two items within the x function and the (e) question has a negative t within the x function. Help please. What do I do about the two items and negative t?
     
  2. jcsd
  3. Sep 27, 2016 #2

    Simon Bridge

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    What happens when you apply a time delay t -> t+d?
     
  4. Sep 27, 2016 #3
    The way I was thought is that for y1(t) your replace x(t) with x1(t), for y2(t) you replace x(t) with x2(t) which then equals x1(t-t0). Then if y2(t)= y1(t-t0). It's time invariant. My issue is doing that with two terms or a negative t
     
  5. Sep 27, 2016 #4

    Simon Bridge

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    How is that an issue - did you do it and see what happens?
    Note: both expressions only have "t" so where do you get "two terms" from?
     
  6. Sep 27, 2016 #5
    The first question has T and alpha, that's what I meant by two terms. It's fine, I figured it out
     
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