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Finding whether a filter is low/high/band pass

  1. Apr 25, 2017 #1
    1. The problem statement, all variables and given/known data
    Consider the IIR filter yn = xn - yn-2

    State whether the filter is low, high, or band pass.

    2. Relevant equations
    The Z-transform: $$H(z) = \frac {1} {1+z^2},$$

    Subbing ##z = e^{2πiw}## : $$H(w) = \frac {1} {1+e^{4πiw}},$$

    Amplitude response: $$|H(w)| = \sqrt{{(\frac {1} {1 + cos{(4πw)}})}^2 + {(\frac {1} {sin{(4πw)}})}^2},$$

    3. The attempt at a solution
    I set up the domain ##w = [0,1]##

    ##w = 0##

    Amplitude response would equal ##\frac {1} {2}##

    ##w = \frac {1} {2}##

    Amplitude response would equal ##\frac {1} {2}##

    ##w = 1##

    Amplitude response would equal ##\frac {1} {2}##

    Doesn't this not prove anything? I know the answer is band pass, but I would expect zeroes on both ends and a number greater than zero in the middle.
     
  2. jcsd
  3. Apr 26, 2017 #2

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