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The average of a random process

  1. May 4, 2013 #1
    Hello all,

    I have the following continuous-time random process:

    [tex]v(t)=\sum_{k=0}^{K-1}\alpha_k(t)d_k+w(t)[/tex]

    where d_k are i.i.d. random variables with zero mean and variance 1, alpha_k(t) is given, and w(t) is additive white Gaussian process of zero-mean and variance N_0.

    Can we say that the average power of v(t) is E{|v(t)|^2}?

    Thanks
     
  2. jcsd
  3. May 4, 2013 #2

    Office_Shredder

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    That probably depends on what v is physically. Velocity?
     
  4. May 4, 2013 #3
    Thanks for replying.

    v(t) is the received signal in a communication system.
     
  5. May 5, 2013 #4

    Office_Shredder

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    The word average can be used to refer to two things here. Expectation of a random variable is often referred to as average - what you have written down is the expected value of the instantaneous power of the signal. The average power of a (deterministic) signal is often defined as
    [tex] \lim_{T \to \infty} \frac{1}{T} \int_{-T/2}^{T/2} |f(t)|^2 dt [/tex]

    This doesn't depend on t at all - if you want the expected value of this, then you need to do more work
     
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