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Prove the sum of 2 signals is periodic?

  1. Aug 17, 2006 #1
    hey guys - just a question regarding a systems and signals course:

    if i've got two disctrete signals: x1[n] and x2[n]

    if i know both signals are periodic (individually) how do i prove the sum of these signals is periodic?

    requirement for periodicty (one signal): x[n+N] = x[n]

    where n and N are integers - remeber - discrete signals!!

    thanks!!

    John
     
  2. jcsd
  3. Aug 17, 2006 #2
    Lcm (n1,n2)
     
    Last edited: Aug 17, 2006
  4. Aug 17, 2006 #3
    EvLer >> Please elaborate...lowest common multiple of n1 and n2??? not entirely sure what you mean ..thanks...
     
  5. Aug 17, 2006 #4
    let k = lcm(n1, n2) which is the lowest common multiplier

    x(n+k) = x1(n+k) + x2(n+k)

    Since k is the lowest common multiplier, that means that it will satisfy the requirement for both signals (for example: x1(n+2) = x1(n+4) = x1(n+6) = ... ). So you have

    x(n+k) = x1(n) + x2(n)
     
  6. Aug 18, 2006 #5
    Thanks Mohammad!

    John
     
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