Butterworth Digital Low Pass Filter

Matlab program to design Butter-worth Digital Low Pass Filter.

clc; clear all; close all;

rp=input('Enter the Passband ripple (In db) = ');

rs=input('Enter the Stopband attenuation (In db) = ');

fpc=input('Enter the Passband corner frequency (In Hz) = ');

fsc=input('Enter the Stopband corner frequency (In Hz) = ');

fs=input('Enter the Sampling frequency (In Hz) = ');

fn=fs/2; % Unit frequency is the Nyquist frequency, defined as half the sampling frequency

Wp=fpc/fn; % Normalized passband corner frequency

Ws=fsc/fn; % Normalized stopband corner frequency

[n,Wn]=buttord(Wp,Ws,rp,rs); % n = Minimum order & Wn = cut-off frequency for Butterworth filter.

[b,a]=butter(n,Wn);

L=1024; %L define length of vectors h and w [Default value of L is 512 samples when not define]

[h,w] = freqz(b,a,L); % It returns frequency response vector h & angular frequency vector w

wi=w/pi; % Normalized angular frequency vector

mag = 20*log10(abs(h)); %Magnitude of h

ang = angle(h); %Angle of h

subplot(2,1,1);

plot(wi,mag);

title('Magnitude Response [Butterworth Digital Low Pass Filter]');

ylabel('Gain in dB -->');

xlabel('Normalised Frequency ( x pi rad/sample)-->');

grid on;

subplot(2,1,2);

plot(wi,ang);

title('Phase Response');

xlabel('Normalised Frequency ( x pi rad/sample)-->');

ylabel('Phase in radians -->');

grid on;

Enter the Passband ripple (In db) = 2

Enter the Stopband attenuation (In db) = 40

Enter the Passband corner frequency (In Hz) = 400

Enter the Stopband corner frequency (In Hz) = 800

Enter the Sampling frequency (In Hz) = 2000

Scigyan