Signal Correct?

Discussion in 'Homework Help' started by Anthony Quah, Mar 30, 2008.

  1. Anthony Quah

    Thread Starter Active Member

    Dec 1, 2007
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    Determine whether it is periodic or aperiodic ?
    x(n) = u(n) – u(n – 10)

    my solution :

    u(n) = 1 , n > 0
    u(n-10) = 1 , n > 10


    pls view the attachment...i have plot the graph when the time(n) is more than 0...it will goes "1" and continue goes "1" when the n which is time at 10..so it is continuous signal...my answer is periodic

    Help needed from you all to help with this..thanks
     
  2. Mark44

    Well-Known Member

    Nov 26, 2007
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    Your graph looks OK, but how do you get that it's periodic? For a function to be periodic with period p, it must be true that f(x) = f(x + p) for any x in the domain of f.
     
  3. Anthony Quah

    Thread Starter Active Member

    Dec 1, 2007
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    by theory periodic signal repeat it self every T second..since my one are using unit step which mean when t > 0 it will go "1" and futher to go t > 10 it will go "1" since the signal keep repeating at constant time it satify the theory of x(t) = (t + T ) ...

    i am not sure if i am right but this is what i have in mind...any help would be appreciated...thanks
     
  4. Mark44

    Well-Known Member

    Nov 26, 2007
    626
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    Anthony,
    By definition a periodic function with period T repeats every T seconds. From your graph,
    Code ( (Unknown Language)):
    1.  
    2.          / 0, if n < 0
    3. x(n) =  | 1 , if 0 <= n < 10
    4.          \ 0, if n >= 10
    5.  
    Since you claim that this function is periodic, what's the period T? I'm looking for a number.

    Now if you can find the period T, can you convince me that x(n) = x(n + T) for any choice of n?
    Mark
     
  5. Anthony Quah

    Thread Starter Active Member

    Dec 1, 2007
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    just got news from my lecturer..my answer is wrong...any ideal to solve this equation?
     
  6. studiot

    AAC Fanatic!

    Nov 9, 2007
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    Your original definition is a (linear) recurrence relation. Look in your notes for solutions to this type of equation.
     
  7. Mark44

    Well-Known Member

    Nov 26, 2007
    626
    1
    No, I disagree. If it were a recurrence relation, it would define x(n) in terms of preceding values of x, and would give some starting value.

    Anthony,
    Your first post says that you are supposed to determine whether this function is periodic or aperiodic. You have told us that you think it's periodic. I have been attempting to point out to you that it is not.

    Is there anything you need to do other than say whether it is periodic?
    Mark
     
  8. Anthony Quah

    Thread Starter Active Member

    Dec 1, 2007
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    i just ask my lecturer and Mark..u are right...it is aperiodic signal...but i just cant find any solution to it...any tactic to solve it?
     
  9. studiot

    AAC Fanatic!

    Nov 9, 2007
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    Yes, Mark, I should have guessed from Tony's previous post that he is studying transforms and has a Z transform here, not a recurrence relation.

    Since I did the other one it's your turn.
     
  10. Mark44

    Well-Known Member

    Nov 26, 2007
    626
    1
    Anthony,
    You've said a couple of times that you need to "solve" this problem. Based on the information you have given us, I don't see that there is a solution necessary. Unless I am missing something, all that you need to do is state that the function is either periodic or not periodic (i.e., aperiodic). The graph you provided should be strong evidence that this function is aperiodic. (BTW, the graph should not have any vertical lines in it, just a discrete set of points at (1,1), (2,1), ..., (10,1).)

    What you show as your solution is not a solution. All you are doing is providing the definitions of u(n) and u(n - 10).

    For a function that is periodic, there has to be a cycle that repeats a fixed pattern. Considering the function you're working with, the 10 points above the horizontal axis would have to be followed by 10 more points one unit below the axis, and then 10 more above the axis, and 10 more below the axis, and so on. Think of how the graph of y = sin(x) looks.

    If your instructor isn't satisfied when you show him/her the graph of this function and you use that as evidence that the function is aperiodic, ask him/her to give you a hint as to what you need to provide.

    Studiot,
    If Anthony is working with Z transforms, he has a ways to go, since he didn't recognize an integration symbol in another post.

    Mark
     
  11. studiot

    AAC Fanatic!

    Nov 9, 2007
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    Mark is certainly correct give us more information to receive better answers.

    Your last two posts were labelled 'signal...'

    The first one looked like part of a heaviside function calculation.

    http://forum.allaboutcircuits.com/showthread.php?t=10508

    This thread contains a question in the format used by several electronic Institutions for their question papers for Z transform calculations, in sampling theory.

    Where

    U(n) is the Heaviside function and x(n) is the output.

    What are we actually dealing with here?
     
  12. Anthony Quah

    Thread Starter Active Member

    Dec 1, 2007
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    ok..i already post the question in detail...view the attachment...thank you for trying to help me understand..it is the toughest subject i trying to learn..:(
     
  13. Mark44

    Well-Known Member

    Nov 26, 2007
    626
    1
    Anthony,
    You're making this problem more difficult than it really is.
    1) State whether the function is periodic or aperiodic.
    2. If it's periodic, state the period. [By implication, if it's not periodic, don't do anything.]

    In this case, your answer requires only one word.
     
  14. Anthony Quah

    Thread Starter Active Member

    Dec 1, 2007
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    Mark,

    thank for the quick reply ...i do need to prove it is aperiodic...i dont know how to prove it...
     
  15. Mark44

    Well-Known Member

    Nov 26, 2007
    626
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    The problem that you sent doesn't say anything about proving anything. Why do you think you need to prove this? It should be sufficient to show your instructor the graph of this function.
     
  16. Anthony Quah

    Thread Starter Active Member

    Dec 1, 2007
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    i was thinking that showing my instructor the graph and state that it didnt have period of T ..so it couldnt be periodic signal..^^

    Mark and studiot,
    really thank for the help..
     
  17. Mark44

    Well-Known Member

    Nov 26, 2007
    626
    1
    Just tell him/her that it isn't periodic.
     
  18. Anthony Quah

    Thread Starter Active Member

    Dec 1, 2007
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    yes sir..^^
     
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