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Sampling from a stochastic process

  1. Oct 11, 2013 #1
    1. The problem statement, all variables and given/known data

    Given X(t) = cos(2[itex]\pi[/itex]50t + ω),

    where the stochastic variable ω is uniformly distributed between 0 and 2[itex]\pi[/itex].

    Suppose the sampling frequency fs is 30 Hz. What frequency interval is covered after the sampling?

    2. Relevant equations

    Normalized frequency when sampling can be made by changing the time units to t = k*d, where k is an integer and d is the sampling distance, so fs = 1/d, which means d = 1/30 s.


    3. The attempt at a solution

    Performing the sampling we get

    x(t) = cos(2[itex]\pi[/itex](50/30)*k + ω) = cos(2[itex]\pi[/itex](5/3)*k + ω) = cos(2[itex]\pi[/itex](2/3)*k + ω)

    The normalized frequency is thus 2/3. Since the normalized frequency can be written as
    v = f/fs, this gives us a frequency interval as a point at 20 Hz ((2/3)*30 = 20)

    1. The problem statement, all variables and given/known data

    I think I should put here what my actual problem is. The problem is that the book give the answer as 10 Hz and I have no idea how they arrived at that. Could it be that it's wrong in the answers section of the book?

    I would very much appreciate any feedback/pointers on what could be wrong here.

    Thank in advance!
     
    Last edited: Oct 12, 2013
  2. jcsd
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