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Magnitude of Complex Exponential Polynomial Inequality

  1. Feb 16, 2012 #1
    1. The problem statement, all variables and given/known data

    Digital filter analysis - this is just one part of a multi-part question I can't move forward with. It's supposed to be an auxilliary question and isn't the "meat" of the problem.

    Find b, such that maximum of the magnitude of the frequency response function b/(1-0.8e\^{-jw}+0.81e^{-j2w}) is 1

    2. Relevant equations

    3. The attempt at a solution

    I've tried decomposing real and imaginary sinusoids but I'm unsure how to use them in the absolute value function. I never had an intuitive understanding of this in undergrad, and now at the graduate level it's simply expected to be second nature.
  2. jcsd
  3. Feb 17, 2012 #2


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    Homework Helper

    first find the w that maximises the expression, then take the magnitude and b will b equal to 1 divded by that result
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