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Check to see whether it is time invariant or not?

  1. Oct 5, 2012 #1
    Hi
    the problem that I am dealing with is to check whether y[n]=T{x[n]}=x[kn] time invariant or not?

    My solution is I said z(n)=T{x[n-A]}=x[k(n-A)]

    and y[n-A]=x[k(n-A)]
    and because y[n-A]=z(n) so it is time invariant

    but solution is saying that it is time varying because z(n)=x[kn-A] meaning that A is not multiplied by n so y[n-A] is not equal to z(n).

    Can anyone explain to me why this is the case?
    Thanks
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  2. jcsd
  3. Oct 6, 2012 #2

    rude man

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    The gain is obviously a function of time. As n (which means as time) increases, so does the gain of the system - ad infinitum. Example: x[n]) = 1 for all n, then y[n] = k, 2k, 3k, ... so the system gain increases forever.
     
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