Creating a 1st Order High-Pass Filter Using Bilinear Transform

[beyondlight]

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 can't be right.

Because my answer didnt seem correct. Help please. :D

 

[the_emi_guy]

beyondlight,
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?