EXPERIMENT - 8

AIM

To design a $2^{nd}$ order Band Pass Butterworth Filter with band edges at 0.4 and 0.7. Plot it's Magnitude and Phase response.

THEORY

The Butterworth filter is a type of signal processing filter designed to have as flat a frequency response as possible in the passband. It is also referred to as a maximally flat magnitude filter.

A band-pass filter is a device that passes frequencies within a certain range and rejects (attenuates) frequencies outside that range.

MATLAB COMMANDS USED

* [b a]=butter(order,[W1 W2],'filter type');
* [H,w]=freqz(b,a);

MATLAB CODE

[b a]=butter(2,[0.4 0.7],'bandpass');
[H,w]=freqz(b,a);
figure(1);
plot(w/pi,abs(H),'r','linewidth',2,
'linesmoothing','on');
axis([0 1 0 1.1]);
grid on;
title(['Amplitude Response of a butterworth
bandpass filter with band edges at ',
num2str(.4),' and ',num2str(.7)]);
xlabel('Frequency (rad/sample)');
ylabel('Gain')

figure(2);

plot(w,angle(H),'black','linewidth',2,
'linesmoothing','on');
title(['Amplitude Response of a butterworth 
bandpass filter with band edges at '
,num2str(.4),' and ',num2str(.7)]);
xlabel('Frequency (rad/sample)');
ylabel('Phase (rad)');
grid on;

RESULT

The phase and magnitude response of $2^{nd}$ order Band pass butterworth filter has been designed and plotted.