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Butterworth, Chebyshev I/II and Elliptic filters in MATLAB

by Forrest Sheng Bao http://fsbao.net

% Copyleft (C) Forrest Sheng Bao 1984-2009 http://fsbao.net
% with Dept. of Electrical and Computer Engineering and Dept. of Computer Science, Texas Tech University, Lubbock, Texas, USA
%
% This program shows the orders and frequency/phase properties of four different kinds of filters, Butterworth, Chebyshev Type I, Chebyshev Type II and Elliptic.
% The filter is expected to have a cutoff frequency at 200 Hz with attenuation 40 db/octave. The sampling frequency is 2000 Hz.
%
% This program licensed in GNU GENERAL PUBLIC LICENSE (GPL) v3 or later.
% If you do not know what GNU GPL is, please visit http://www.gnu.org/copyleft/gpl.html


close all
clear all

cutoff =  200;
Fs = 2000;
wp = cutoff/(Fs/2);
ws = 400/(Fs/2);
rp = 3;
rs = 43;
for i=1:4
    if i == 1
        [order, wn] = buttord(wp, ws, rp, rs);
        sprintf('the min. order of Butterworth filter is %d', order)
        [b,a] = butter(order,wn);
        figure()
        freqz(b,a,512,Fs)
        title('Butterworth filter, attenuation = 40 db/octave, cutoff=200')
    elseif i==2
        [order, wn] = cheb1ord(wp, ws, rp, rs);
        sprintf('the min. order of Chebyshev Type 1 filter is %d', order)
        [b,a] = cheby1(order,rp,wn);
        figure()
        freqz(b,a,512,Fs)
        title('Chebyshev Type I filter, attenuation = 40 db/octave, cutoff=200')
    elseif i==3
        [order, wn] = cheb2ord(wp, ws, rp, rs);
        sprintf('the min. order of Chebyshev Type II filter is %d', order)
        [b,a] = cheby2(order,rp,wn);
        figure()
        freqz(b,a,512,Fs)
        title('Chebyshev Type II filter, attenuation = 40 db/octave, cutoff=200')
    elseif i==4
        [order, wn] = ellipord(wp, ws, rp, rs);
        sprintf('the min. order of elliptic filter is %d', order)
        [b,a] = ellip(order,rp,rs,wn);
        figure()
        freqz(b,a,512,Fs)
        title('Elliptic filter, attenuation = 40 db/octave, cutoff=200')
    else
        disp('error')
    end
end

ans =

the min. order of Butterworth filter is 7

ans =

the min. order of Chebyshev Type 1 filter is 4

ans =

the min. order of Chebyshev Type II filter is 4

ans =

the min. order of elliptic filter is 3

Plot images are omitted here. Please run the code to get them.