Question

Create a MATLAB script with the following specifications:

An IIR high-pass filter that has the magnitude response below 0.2 for frequencies 0-60 Hz, and the magnitude response between 0.8 and 1.2 for frequencies between ?144 − XY? Hz and 200 Hz.

Sampling frequency is 400Hz.

Answer 1

MATLAB code is given below in bold letters.

clc;
close all;
clear all;

% define sampling frequency
fs = 400; % 400 Hz

% define fc
fc = 100; % 100 Hz

% define the filter characteristics
Wp = 144/fs/2;
Ws = 60/fs/2;
Rp = -20*log10(1-0.2);% passband ripple
Rs = -20*log10(0.2);% stopband attenuation

% obtain the required order of the butterworth filter for the given requirements.
N = buttord(Wp, Ws, Rp, Rs);

% obtain the filter coefficients
[b,a] = butter(N,0.5,'high')

% plot the frequency response
figure;
freqz(b,a);

RESULT:

The filter coefficients are given below

b =

0.1667 -0.5000 0.5000 -0.1667

a =

1.0000 -0.0000 0.3333 -0.0000

The frequency reponse is plotted below.