Question

1. Using Matlab, Design a Band-Stop Filter (BSF) that removes frequencies from 500Hz to 1000Hz in a signal that is sampled at 10kHz.

• Compare an elliptic filter of order 12 and 6 to an order-12 Yule-Walker filter design
• Plot the magnitude of the two designs on the same plot.

Answer 1

MATLAB code:

%specifications for BSF

Fs=10000;%sampling frequency

%band edge frequencies

wp1=2*500/Fs;wp2=2*1000/Fs;

%Yule walker design

f = [0 wp1 wp2 1];

m = [1 0 0 1];N=12;

[b,a] = yulewalk(N,f,m);

w=0:pi/1000:pi;

H = freqz(b,a,w);

plot(w/pi,20*log10(abs(H)),'b');hold on;

xlabel('w X pi');ylabel('|H(w)| in db')

%Elliptic Filter design for order 12

Rp=2;Rs=40;%Assumption

wp=[wp1 wp2];

[b,a] = ellip(6,Rp,Rs,wp,'stop');%elliptic returns 2n order transfer function. Hence enter order =6 for 12th order filter

H=freqz(b,a,w);

plot(w/pi,20*log10(abs(H)),'r');hold on;grid on;

%Elliptic Filter design for order 6

[b,a] = ellip(3,Rp,Rs,wp,'stop');%elliptic returns 2n order transfer function. Hence enter order =3 for 6th order filter

H=freqz(b,a,w);

plot(w/pi,20*log10(abs(H)),'m');hold off;

legend('Yule walker for order 12','Elliptic for order 12','Elliptic for order 6')

ylim([-100,20])