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Simple question about basic function

  1. Jul 30, 2013 #1
    1. The problem statement, all variables and given/known data
    If x2[t]= x1[t-2]
    and x3[t]=x2[2t]

    What is x3[t] in terms of x1[t]?

    a) x3[t]= x1[2(t-2)]
    b) x3[t]= x1[2t-2]




    2. Relevant equations
    which one?


    3. The attempt at a solution

    offcourse, but I am struggling with this concept of shifting. But I believe the answer should be A. since x3[t] is the compression version of x2[t], which is the shift version of x1[t].

    So the overall transformation would be x3[2(t-2)], which is not correct.
     
    Last edited: Jul 30, 2013
  2. jcsd
  3. Jul 30, 2013 #2

    HallsofIvy

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    I don't see any "attempt at a solution". Have you not tried?
     
  4. Jul 30, 2013 #3


    offcourse, but I am struggling with this concept of shifting. But I believe the answer should be A. since x3[t] is the compression version of x2[t], which is the shift version of x1[t].

    So the overall transformation would be x3[2(t-2)], which does not correct.
     
  5. Jul 30, 2013 #4

    HallsofIvy

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    This problem is not so much about "shifting" as it is about understanding functional notation. You are given that x2[t]= x1[t- 2]. That is exactly the same thing as saying that x2[y]= x1[y- 2] or x2[a]= x1[a- 2]. Whatever is in the braces of x2, in the x1 function, you subtract 2 from it. In x3[t]= x2[2t], what is "in the braces of x2" is "2t" so x3[t]= x2[2t]. What do you get when you replace "t" with "2t" in x1?
     
  6. Jul 30, 2013 #5

    CompuChip

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    I think this one is easiest to see algebraically. Let's rename some variables to avoid confusion. So let
    x2(u) = x1(u - 2)
    x3(v) = x2(2v)

    Now set v = t. What will u be?
     
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