How to determine whether periodic or not

Discussion in 'Homework Help' started by glorimda, Mar 29, 2012.

  1. glorimda

    Thread Starter New Member

    Oct 12, 2011
    17
    0
    I've got stuck in here while solving exercise problem.

    How can I determine whether this is periodic or not.

    1.

    eq.jpg

    I can't find way to do of this due to summation.


    2.
    y1(t)=x(2t) and y2(t)=x(t/2)

    I need to determine whether followings are true and find the fundamental period.

    <1> if x(t) is periodic, then y1(t) is periodic.
    <2> if y1(t) is periodic, then x(t) is periodic.

    Could anybody help me plz?
     
  2. panic mode

    Senior Member

    Oct 10, 2011
    1,318
    304
    first of all what is 'periodic'?

    as i recall it is a signal with value that eventually repeats itself (and not just once but over and over).

    due to exponential term and n changing, magnitude will never be the same.
    that is quite strong argument against 'periodic'.

    alternatively - plot it.
     
  3. Georacer

    Moderator

    Nov 25, 2009
    5,142
    1,266
    Is the "star" the convolution operator or just an ordinary multiplication?
     
  4. glorimda

    Thread Starter New Member

    Oct 12, 2011
    17
    0
    panic mode// As you mentioned, that seems obvious, but is that all I can answer? I mean I think I need to show it in some mathematical way.
    Georacer// That is just an multiplication.
     
  5. Georacer

    Moderator

    Nov 25, 2009
    5,142
    1,266
    In general, a signal is periodic if x(t)=x(t+T), where T is the period.

    However, right now my math fails to prove if it is indeed periodic. My gut says it's not.
     
  6. glorimda

    Thread Starter New Member

    Oct 12, 2011
    17
    0
    It turned out to be aperiodic. you're right. But I want to prove it in mathematical way. Not just by intuition.
     
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