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Time invariance

  1. Jul 6, 2011 #1
    1. The problem statement, all variables and given/known data
    show whether the system

    y(t) = x(2t) is time variant or not


    2. Relevant equations

    a system is time invariant if a time shift in the input signals results in an identical time shift in the output signal, that is if y[n] is the output of a discrete-time, time invariant system when x[n] is the input, then y[n-n0] is the output when x[n-n0] is applied

    3. The attempt at a solution

    first of all I have the answer on my book(oppenheim) but I can't understand what he does

    what I tried to do is

    suppose we apply a signal

    x1(t) and we get an output of y1(t) = x1(2t)

    now, suppose we apply a signal x2(t) = x1(t-t0)

    we get an output of y2(t) = x2(t) = x1(2t - 2t0) = y1(t-t0)

    hence it's time invariant

    now, the book says it's time variant, and also it creates graphs to prove this point and I don't understand how he proves this..

    what am I doing wrong?
    thanks in advance
     
  2. jcsd
  3. Jul 6, 2011 #2
    actually now that I'm looking at it better

    when we have a system

    y(t) = x(2t)

    and we say let's input the x(t-2)

    will the new system be

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

    OR

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

    ?

    for the second part, and I think oppenheims graphs have something to do with the second one

    the result is correct
     
  4. Jul 7, 2011 #3
    y2(t)=x2(2t)=x1(2t-t0)=y1(t-t0/2)
    hence it is time variant :P

    This is most simply seen if you realize that y in time t is equal to x in time 2*t, which is time origin (t=0) dependent definition.
     
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