Question

1. Using Matlab, Design a High-Pass Filter (HPF) using with a cutoff frequency of 500Hz when used with a sampling frequency of 1500Hz.

• Compare designs using an order-8 IIR elliptic filter to an order-32 FIR filter by plotting the magnitude of the two designs on the same plot.

Answer 1

MATLAB script:

clc;close all;clear all;
%specifications for HPF
Fs=1500;%sampling frequency
%cut offf frequency
wp=2*500/Fs;
%Elliptic Filter design for order 8
Rp=1;Rs=60;%Assumption
%elliptic returns 2n order transfer function.
% Hence enter order =4 for 8th order filter
[b,a] = ellip(4,Rp,Rs,wp,'high');
w=0:pi/1000:pi
H1=freqz(b,a,w);
%Elliptic Filter design for order 32
[b,a] = ellip(16,Rp,Rs,wp,'high');
H2=freqz(b,a,w);
figure;
subplot(211)
plot(w/pi,(abs(H1)),'r','LineWidth',3);hold on;grid on;
plot(w/pi,(abs(H2)),'g','LineWidth',3);hold off;
legend('Elliptic for order 8','Elliptic for order 32')
xlabel('w X pi')
ylabel('|H(w)|')
title('Magnitude plot')

subplot(212)
plot(w/pi,20*log10(abs(H1)),'r','LineWidth',3);hold on;grid on;
plot(w/pi,20*log10(abs(H2)),'g','LineWidth',3);hold off;
legend('Elliptic for order 8','Elliptic for order 32')
xlabel('w X pi')
ylabel('|H(w)| in db')
title('Log Magnitude plot')