Question

DSP Lab Exercise 9 Given below are the Impulse Response h(n), of the four main types of FIR Digital filters. Use appropriate MATLAB expressions to find: a) System Response (H(z) b) Pole-zero diagram c) Amplitude Response d) Phase Response 1. FIR Low-Pass Digital Filter ,n= 0.1 |[d(n) + δ(n-I))-1 h(n) 0, otherwise 2. FIR High-Pass Digital Filter 0, otherwise 3. FIR Band-Pass Digital Filter 0, otherwise 4. FIR Band-Stop Digital Filter , n = 0,2 0, otherwise Note: Your final answer to each section (low-pass, High-pass. .etc.) should be the same you have in Lecture notes (Presentation on Filter Concepts-1)

Answer 1

1)matlab code and result

9amm an response in matlab frad fistH usig z- fronofoom (a) FIR LPF (b) FIR HPF 2 (C) FIR 8PF 3-22 (르의 1-2' H(Z) = 2 (a) FIR BSF 2 and se t, Pz pdat, andzon in matab

clear;clc;
%for part (a) FIR LPF digital filter
b1=[1 1];
a1=[2 0];
H1=tf(b1,a1,-1);
[h1,w1]=freqz(b1,a1);
%for part (b) FIR HPF digital filter
b2=[1 -1];
a2=[2 0];
H2=tf(b2,a2,-1);
[h2,w2]=freqz(b2,a2);
%for part (c) FIR BPF digital filter
b3=[1 0 -1];
a3=[2 0 0];
H3=tf(b3,a3,-1);
[h3,w3]=freqz(b3,a3);
%for part (d) FIR BSF digital filter
b4=[1 0 1];
a4=[2 0 0];
H4=tf(b4,a4,-1);
[h4,w4]=freqz(b4,a4);
figure(1);
subplot(221);pzplot(H1);
title('pole zero plot of FIR LPF digital filter');
subplot(222);pzplot(H2);
title('pole zero plot of FIR HPF digital filter');
subplot(223);pzplot(H3);
title('pole zero plot of FIR BPF digital filter');
subplot(224);pzplot(H4);
title('pole zero plot of FIR BSF digital filter');
figure(2);
subplot(221);plot(w1,abs(h1));
title('magnitude response plot of FIR LPF digital filter');
xlabel('\omega');ylabel('|H(\omega)|');
xlim([0 pi]);xticks(0:pi/4:pi);
xticklabels({'0','\pi/4','\pi/2','3\pi/4','\pi'});
subplot(222);plot(w1,abs(h2));
title('magnitude response plot of FIR HPF digital filter');
xlabel('\omega');ylabel('|H(\omega)|');
xlim([0 pi]);xticks(0:pi/4:pi);
xticklabels({'0','\pi/4','\pi/2','3\pi/4','\pi'});
subplot(223);plot(w1,abs(h3));
title('magnitude response plot of FIR BPF digital filter');
xlabel('\omega');ylabel('|H(\omega)|');
xlim([0 pi]);xticks(0:pi/4:pi);
xticklabels({'0','\pi/4','\pi/2','3\pi/4','\pi'});
subplot(224);plot(w1,abs(h4));
title('magnitude response plot of FIR BSF digital filter');
xlabel('\omega');ylabel('|H(\omega)|');
xlim([0 pi]);xticks(0:pi/4:pi);
xticklabels({'0','\pi/4','\pi/2','3\pi/4','\pi'});
figure(3);
subplot(221);plot(w1,angle(h1));
title('phase response plot of FIR LPF digital filter');
xlabel('\omega');ylabel('\angle(H(\omega))');
xlim([0 pi]);xticks(0:pi/4:pi);
xticklabels({'0','\pi/4','\pi/2','3\pi/4','\pi'});
subplot(222);plot(w1,angle(h2));
title('phase response plot of FIR HPF digital filter');
xlabel('\omega');ylabel('\angle(H(\omega))');
xlim([0 pi]);xticks(0:pi/4:pi);
xticklabels({'0','\pi/4','\pi/2','3\pi/4','\pi'});
subplot(223);plot(w1,angle(h3));
title('phase response plot of FIR BPF digital filter');
xlabel('\omega');ylabel('\angle(H(\omega))');
xlim([0 pi]);xticks(0:pi/4:pi);
xticklabels({'0','\pi/4','\pi/2','3\pi/4','\pi'});
subplot(224);plot(w1,angle(h4));
title('phase response plot of FIR BSF digital filter');
xlabel('\omega');ylabel('\angle(H(\omega))');
xlim([0 pi]);xticks(0:pi/4:pi);
xticklabels({'0','\pi/4','\pi/2','3\pi/4','\pi'});

pole zero p t of FIR LPF digital filter pole zero plot of FIR HPF digital filter 0.5 0.5 -0.5 0.5 1 0.8 0.6 0.4 0.2 00.20.40.6 0.8 1 Real Axis 1 0.8 0.6 0.4 0.2 00.2 0.4 0.6 0.8 Real Axis pole zero plot of FIR BPF digital filter pole zero plot of FIR BSF digital filter 0.5 0.5 -0.5 0.5 1 0.8 0.6 -D.4 -0.2 0 0.2 0.4 0.6 0.8 1 0.8 -D.6 -0.4 -0.2 0 0.2 0.4 0.6 0.8 Real Axis Real Axis

magnitude response plot of FIR LPF digital filter magnitude response plot of FIR HPF digital filter 0.8 0.8 0.6 0.6 0.4 0.4 0.2 0.2 π/4 3a14 3114 magnitude response plot of FIR BPF digital filter magnitude response plot of FIR BSF digital filter 0.8 0.8 0.6 0.6 0.4 0.4 0.2 0.2 π/4 T12 3 /4 3T14

phase response plot of FIR LPF digital filter phase response plot of FIR HPF digital filter -0.2 -0.4 0.6 -0.8 0.8 0.6 0.4 0.2 1.2 1.4 1.6 3xI4 T/2 3T 4 phase response plot of FIR BPF digital filter phase response plot of FIR BSF digital filter 1.5 0.5 0.5 -0.5 0.5 1.5 -2 3π/4 3πί4