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Homework Help: Create High-pass filter

  1. May 21, 2012 #1
    With bilinear transform (s=z-1/z+1) determine the differential equation for a 1st order discrete HP filter fith samplingfrequency f_s=150 Hz and lower cutoff frequency f_c=50 Hz. Also set the passpandgain to 1.

    This is how i did:

    Discrete variable: Ω=2π/3

    Equivalent cuttof frequency for analog filter: ω_a=sqrt(3)

    Analog HP-filter transfer function: H(s)=(s/s+ω_a)

    Then use the bilinear transform om H(s).

    how do i get passbandgain = 1?

    If they mean H(z)=H(1)=1 by that, then H(z)=0, so that cant be right.

    Because my answer didnt seem correct. Help please. :D
  2. jcsd
  3. May 23, 2012 #2
    How did you get corner frequency ω_a=sqrt(3)? Should be ω_a=2πf = 2π(50) right?
    How did you get discrete variable Ω=2π/3?, your independent variables are z and s right?

    You are missing your sampling frequency in your bilinear transform. It should be: s=150(z-1)/(z+1).

    By the way with such a low sample freq compared to corner frequency (150Hz and 50Hz respectively) this will be a very bad discrete time realization of your first order filter (see attached image, red is ideal first order, blue is your discrete time realization, vertical is dB).
    Does this help?

    Attached Files:

    Last edited: May 23, 2012
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