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Difficult discrete-time periodicity problem

  1. Jan 31, 2012 #1
    1. The problem statement, all variables and given/known data

    Determine whether x[n] is periodic, if so find the fundamental period.

    ps forgive my notation, i'm new to physics forums and haven't had a chance to figure out the exact notation syntax yet.

    x[n]=cos(π/6 * n^2)

    3. The attempt at a solution

    x(n) is periodic when x(n) = x(n +N)

    x(n+N) = cos(π/6 * (n+N)^2)

    π/6(2*n*N + N^2) = k*2*π

    this is kinda where i got stuck

    (2*n*N + N^2) = 12 * k
  2. jcsd
  3. Feb 1, 2012 #2


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    welcome to pf!

    hi jti5017! welcome to pf! :smile:

    try using the X2 button just above the Reply box :wink:

    is it true for the same N, for all n ? :wink:
  4. Feb 1, 2012 #3
    thanks for the reply!

    it has to be true for all n to be periodic by definition i believe.
    i mean, i've personally never heard of a sinusoidal period being a function of time (in this case discrete time)

    And there are an infinite number of 'N's (provided it is periodic) but I am specifically looking for the lowest N, the fundamental period
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