Periodic or Aperiodic signal

Discussion in 'Homework Help' started by Anthony Quah, Mar 26, 2008.

  1. Anthony Quah

    Thread Starter Active Member

    Dec 1, 2007
    80
    0
    Guy,

    I am doing Signal and System home work..i need some help to confirm if my step were the correct method of doing it... here goes

    *Determine whether the signals is periodic? and state its period.

    Question 1 :
    x(n) = u(n) - u(n-10)

    Solution :
    x(n) = u(n - T) - u(n - T - 10)
    x(n) = u(n - kT) - u(n - lT - 10 )

    since l/k cannot be express therefore the signal is not periodic.



    Question 2 :
    x(n) = sin (n)

    Solution :
    x(n + T) = sin (n + T)
    T = 2 pie
    = 2 x 3.142
    = 6.238
    T is not integer, therefore x(n) = sin (n) is not periodic signal
     
  2. surbhi

    New Member

    Mar 26, 2008
    5
    0
    periodic signal is that which satisfy the following equation, i.e.

    x(n) = x( n+t)
    t is any part of periodic signal or it may be 2 pie

    Question 1 :
    x(n) = u(n) - u(n-10)

    Solution :
    this problem can be solved by using diagram method
    as u(n) = 1, n>0

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

    when these terms are subtracted, we get x(n) = 1, 0<n<10
    so we can't say that x(n) is periodic
    u can show its diagram also.


    Question 2 :
    x(n) = sin (n)

    Solution :
    x(n + T) = sin (n + T)
    T = 2 pie

    sin(n) = sin ( n + 2 pie)

    so x(n) is a periodic signal.
     
  3. Anthony Quah

    Thread Starter Active Member

    Dec 1, 2007
    80
    0
    anyone can confirm if this was right?
     
  4. veritas

    Active Member

    Feb 7, 2008
    167
    0
    yes, surbhi is correct
     
  5. Anthony Quah

    Thread Starter Active Member

    Dec 1, 2007
    80
    0
    in Question 2 base on my own calculation it show that it is not a periodic signal when 2 pie is not an integer BUT Surbhi say is periodic signal?
     
  6. veritas

    Active Member

    Feb 7, 2008
    167
    0
    If you are referring to a discrete signal, then an irrational period will create an aperiodic signal. The fact that it is not an integer is irrelevant.

    For continuous signals, then any period will create a periodic signal.


    *edit*
    to clarify for you:

    I think you mean to say "single L/K cannot be expressed as the ratio of two integers, the signal is therefore not periodic"
     
  7. Anthony Quah

    Thread Starter Active Member

    Dec 1, 2007
    80
    0
    ok..thank guy..i will need time to digest it.. ^^
     
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