Question

Please use MATLAB to answer. for a 4th order lowpass butterworth digital filter. fc:0.35 sampling freq: 10Hz find passband and stopband of both analogue and discrete butterworth filter.

Answer 1

MATLAB code is given below in bold letters.

clc;
close all;
clear all;

% define N
N = 4;

% define fs
fs = 10;

% define fc
fc = 0.35;

% obtain the butterworth filter coefficients
[B,A] = butter(N,fc,'low');

% define the discrete transfer function
H = tf(B,A,1/fs)

% Now plot the pole-zero diagram of the filter
figure;
zplane(B,A);grid on;

result:

Transfer function:
0.03049 z^4 + 0.1219 z^3 + 0.1829 z^2 + 0.1219 z + 0.03049
----------------------------------------------------------
z^4 - 1.175 z^3 + 0.9256 z^2 - 0.3104 z + 0.04766

Pole zero plot is given below: