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Average Power of a Signal

Discussion in 'Miscellaneous [BG]' started by Bassline_Delux, May 1, 2006.

  1. A sinusoidal signal s(t) = A sin(ωt + θ) can be expressed as a sum of two components:
    s(t) = A sinωt cosθ + A cosωt sinθ

    Show that the average power of this signal is equal to the sum of the average powers of its two components.

    For the love of god. Could someone help me out on this one. My brain is imploding.
  2. Mike Money

    Mike Money In Memoriam

    Mar 18, 2003
    Bakersfield California
    Avatar Speakers Endorsing Hooligan
  3. J_C_L


    Apr 25, 2006
    Some of this is pretty foggy in what's left of my mind.

    Take the integral of the square (I think) of the first representation of the signal to find the average power (it's really v^2/R, but the Rs are constant and will cancel out).

    Then take the integral of the squre of each of the pieces of the signal for the second representation. Then add this together. Show this equals the integral of the first representation and you are done.:)

    But you may really be asking how to integrate these things. On that I have no recollection, my calculus is decades gone from my mind. :(

    Doubt that helps much, but there you go.

    It also occurs to me that this might be easy to do in the frequency domain. If that is the case, then convert these to a frequency domain representations and do the power calculations on the spectrum, rather than on the time domain representation.

    [Edited about 10 times]

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