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Magnitude of filter response

  1. May 13, 2013 #1
    1. The problem statement, all variables and given/known data

    F(w) = a / [1 - be^(-jwT)]

    where a and b are constants

    Find the magnitude of this filter response

    2. Relevant equations

    e^(-jX) = cos(X) - isin(X)


    3. The attempt at a solution

    the answer is a/ √[1-2bcos(wT) + b^2*cos^2(2wT)]

    but I cant seem to get rid of sines.



    F(w) = a / [1 - be^(-jwT)]
    = a / [ 1 - b(cos(wT) - isin(wT) ]
    = a / [1 - bcos(wT) + ibsin(wT)]
    |F(w| = √{ a^2/ [1 - bcos(wT) + ibsin(wT)]^2}
    = a /√[1-2bcos(wT) + b^2*cos^2(wT) + i 2bsin(wT) - i 2b^2*sin(wT)cos(wT) -b^2*sin^2(wT)]

    Can anyone point me at the right direction??
     
  2. jcsd
  3. May 13, 2013 #2

    NascentOxygen

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    Staff: Mentor

    I think you'll find that when determining the magnitude, you take ( Real^2 + Imag^2 ). The i operator itself does not appear in the magnitude term.
     
  4. May 13, 2013 #3
    Where did you get this from? It's not correct.
     
  5. May 14, 2013 #4

    rude man

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    Homework Helper
    Gold Member

    Where did this come from? Makes no sense, and you can't have an imaginary component in a magnitude.

    In general, given (a + jb)/(c + jd), a thru d real, magnitude = √(a2 + b2)/√(c2 + d2).

    Plus, miles is right, the given answer is incorrect.
     
    Last edited: May 14, 2013
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