% ************IIR Analog Butterworth Filter Design ******************%
%************* Author : Arun Prakash A ******************************%

clc;
clear all;
close all;
% Specifications
Wp=2*pi*100; % Passband cutoff in rad/s
Ws=2*pi*200; % stopband cutoff in rad/s
Fs=8000;  % Sampling Frequency
Ts=1/Fs;
wp=Wp*Ts; % Digital passband cutoff freq in rad/sample
ws=Ws*Ts; % Digital stopband cutoff freq in rad/sample
ap=3; % passband attenuation in dB
as=30; % stopband Attenuation in dB

% Design Starts from here
[N,wc]=buttord(wp,ws,ap,as,'s'); % returns order and Wc
[zeros,poles,kf]=buttap(N); % returns Pole locations and gain
[ztn,ptn]=zp2tf(zeros,poles,kf);  % cooefficients of denominator polynomial
[normalized_zeros,normalized_poles]=lp2lp(ztn,ptn,wc);  % Denormalize 
[mag,freq]=freqs(normalized_zeros,normalized_poles,500); % plot magnitude response

%plot the magnitude response
plot((freq/(2*pi))*Fs,20*log10(abs(mag))); % ./ 2*pi to see an integer of freq in Hz
axis([0 400 -50 0 ])
title('Analog Butterworth Filter');
xlabel('Frequency  in Hz'); 
ylabel('Magnitude in dB'); 
grid on