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Math Help - Integration involving the minimization of signal transmission error

  1. #1
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    Integration involving the minimization of signal transmission error

    I'm studying the transmission of signals and have come across an integration that I don't understand. I understand the mechanics of the integration,
    but not the purpose for solving it the way my textbook does.
    Background: It is used to solve for a constant c which is a multiplier of signal error
    function. The integration gives c, such that the signal error will be minimized.

    The integral is: c = [1/pi] Definite integral (limits 0 to 2pi) f(t) sin(t) dt, where f(t)
    represents the signal and sin t, an approximation of the signal.
    My text evaluates as follows:
    [1/pi] (Integral (limits 0 to pi) sint t dt + Integral (limits pi to 2pi) -sin t dt) = 4/pi

    Again, I understand the integration, but not why it is broken into the sum of the 2 integrals. What is the reasoning behind this process? Thanks for the help.
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  2. #2
    Grand Panjandrum
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    Quote Originally Posted by kaiser0792 View Post
    I'm studying the transmission of signals and have come across an integration that I don't understand. I understand the mechanics of the integration,but not the purpose for solving it the way my textbook does.

    Background: It is used to solve for a constant c which is a multiplier of signal error
    function. The integration gives c, such that the signal error will be minimized.

    The integral is:

    c = [1/pi] Definite integral (limits 0 to 2pi) f(t) sin(t) dt,

    where f(t) represents the signal and sin t, an approximation of the signal.

    My text evaluates as follows:

    [1/pi] (Integral (limits 0 to pi) sint t dt + Integral (limits pi to 2pi) -sin t dt) = 4/pi

    Again, I understand the integration, but not why it is broken into the sum of the 2 integrals. What is the reasoning behind this process? Thanks for the help.
    What happened to f(t)? You are not telling us the whole story are you?

    CB
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