Determining Filter type from |H(jw)|^2

Discussion in 'Homework Help' started by jegues, Mar 18, 2012.

  1. jegues

    Thread Starter Well-Known Member

    Sep 13, 2010
    735
    43
    See figure attached for problem statement, as well as my attempt at the problem.

    How do we go about determining what type of filter it is?

    I am fairly certain I did part b) correctly.
     
  2. mlog

    Member

    Feb 11, 2012
    276
    36
    Check your math for ω≈0. Also, make a quick plot of the gain with some other ω values, say, 0, 1, 2, 3, 4, 5, 10, 20. What do you see?
     
  3. jegues

    Thread Starter Well-Known Member

    Sep 13, 2010
    735
    43
    I can see that the conclusion I drew is incorrect, but what is the formal method to finding what type of filter it is?

    In the exam I can't quickly plot these things without a calculator.
     
  4. mlog

    Member

    Feb 11, 2012
    276
    36
    Maybe someone else has a better idea, but there are a few things you can do. You already did one of them. Check the values (limits) where ω approaches 0 and infinity. The next is inspection. You can see the numerator in this case is zero at ω=2. So think about that. You know the gain is unity at ω at 0 and infinity, and the gain is 0 at ω=2. Sounds like it could be a notch filter (band-reject). The other thing you could do is to take the first and second derivatives to look for minima and maxima, but that could get messy on an exam. Unless the polynomial is a well recognized form or unless you have a table of filters, I would test the limits and use inspection for the obvious.
     
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