MATLAB Program for butterworth filter using bilinear transformation method

MATLAB PROGRAM:

clc ;

close all;

clear all; 

b=input('enter numerator coefficient of analog filter:')

a=input('enter denominator coefficient of analog filter:')

f=input('enter sampling frequency:')

Ts=1/f

[bz,az]=bilinear(b,a,f)

disp('equavilent digital transfer function H(Z)is =')

systf=tf(bz,az,Ts)

 

figure(1)

freqz(bz,az)

figure(2)

zplane(bz,az)

 

disp('the residues, pole locations and the direct terms are:') ;

[R,p,c]=residuez(bz,az)

OUTPUT:

enter numerator coefficient of analog filter:2

b =

     2

enter denominator coefficient of analog filter:[1 3 2]

a =

     1     3     2

enter sampling frequency:1

f =

     1

Ts =

     1

bz =

    0.1667    0.3333    0.1667

az =

    1.0000   -0.3333    0.0000

equavilent digital transfer function H(Z)is =

systf =

  0.1667 z^2 + 0.3333 z + 0.1667
  ------------------------------
    z^2 - 0.3333 z + 7.401e-17

Sample time: 1 seconds
Discrete-time transfer function.

the residues, pole locations and the direct terms are:

R =

   1.0e+15 *

    0.0000
   -2.2518

p =

    0.3333
    0.0000

c =

   2.2518e+15

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