EXPERIMENT - 7
AIM
To design a 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(8,[0.4 0.7],'bandpass');
[H,w]=freqz(b,a);
figure(1);
plot(w/pi,abs(H),'black','linewidth',2,
'linesmoothing','on');
axis([0 1 0 1.1]);
grid on;
title(['Amplitude Response of a 8th order
butterworth bandpass filter with band edges
at ',num2str(.4),' and ',num2str(.7)]);
xlabel('Frequency (rad/sample)');
ylabel('Gain');
display(['Denominator coefficients are
:',num2str(round(b*100)/100)])
display(['Numerator coefficients are
:',num2str(round(a*100)/100)])
figure(2);
plot(w,angle(H),'black','linewidth',2,
'linesmoothing','on');
title(['Amplitude Response of a 8th order
butterworth bandpass filter with band
edges at ',num2str(.4),' and ',num2str(.7)]);
xlabel('Frequency (rad/sample)');
ylabel('Phase (rad)');
grid on;
figure(3);
zplane(b,a,'black')
title('8th-Order Butterworth band
pass Digital Filter');
legend('zeros','poles')
RESULT
The phase and magnitude response of order Band pass butterworth filter has been designed and plotted of given specification. Also plotted it's zero-pole plot.