Question

Using matlab

a) Find the transfer function of a fourth order Butterworth filter and plot the magnitude response.

b) Find the poles.

Answer 1

Matlab code:

%%
clear all;
close all;
clc;
%%

% since the type of filter is not give
% Let us consider a low pass filter with cut-off frquency fc
% the that data is sampled at fs
% then 2*pi*fc/fs is the cut-off point in rad/sample
% butter is a commond used to design a butter-worth filter with n, Wn as
% paramenter
% n is the order of filter
% Wn is the cut-off frequency
% the command butter give an output [z,p]
% z is the zeros and p is the poles

fc = 300;                   % cut-off frequency
fs = 1000;                  % sample frequency
n = 4;                      % order of filter
[z,p] = butter(n,fc/(fs/2)); % filter design of 4th order and 0.6*pi rad/sample cut-off frequency
freqz(z,p)                     % magnitude and phase response of the system

transfer_function=tf(z,p)           % transfer function of the system
poles=roots(p)                     % is the poles of the system
figure;
pzmap(transfer_function)            % x represent poles and o respresent zeros
grid on;

Magnitude Response:

Pole zero graph: