-
Notifications
You must be signed in to change notification settings - Fork 0
/
Bandstop.m
215 lines (161 loc) · 5.43 KB
/
Bandstop.m
1
2
3
4
5
6
7
8
9
10
11
12
13
14
15
16
17
18
19
20
21
22
23
24
25
26
27
28
29
30
31
32
33
34
35
36
37
38
39
40
41
42
43
44
45
46
47
48
49
50
51
52
53
54
55
56
57
58
59
60
61
62
63
64
65
66
67
68
69
70
71
72
73
74
75
76
77
78
79
80
81
82
83
84
85
86
87
88
89
90
91
92
93
94
95
96
97
98
99
100
101
102
103
104
105
106
107
108
109
110
111
112
113
114
115
116
117
118
119
120
121
122
123
124
125
126
127
128
129
130
131
132
133
134
135
136
137
138
139
140
141
142
143
144
145
146
147
148
149
150
151
152
153
154
155
156
157
158
159
160
161
162
163
164
165
166
167
168
169
170
171
172
173
174
175
176
177
178
179
180
181
182
183
184
185
186
187
188
189
190
191
192
193
194
195
196
197
198
199
200
201
202
203
204
205
206
207
208
209
210
211
212
213
214
%Part 2 - pole-zero plot
r=0.8;
w0 = 0.25*pi;
num = [1 -exp(-1i*w0)-exp(1i*w0) 1];
den = [1 -r*exp(-1i*w0)-r*exp(1i*w0) r^2];
z= roots(num);
p = roots(den);
figure
zplane(z,p)
title('Pole Zero Plot of H(z) for r = 0.8, Wo=0.25*pi')
%Part 3 - freqz for trial values of varying r
%-----r = 0.2, keep wo = 0.25*pi -----------
r=0.2; w0 = 0.25*pi;
num = [1 -exp(-1i*w0)-exp(1i*w0) 1]; %b vector
den = [1 -r*exp(-1i*w0)-r*exp(1i*w0) r^2]; % a vector
[H,W] = freqz(num,den);
figure
plot(W, abs(H));
title(['Magnitude Response with r=' , num2str(r), ', w0=', num2str(w0)]);grid
xlabel('w (rad/sample)');ylabel('|H(z)|');
figure
plot(W, angle(H));
title(['Phase Response with r=' , num2str(r), ', w0=', num2str(w0)]);grid
xlabel('w (rad/sample)');ylabel('Phase');
%-----r = 0.6, keep wo = 0.25*pi -----------
r=0.6; w0 = 0.25*pi;
num = [1 -exp(-1i*w0)-exp(1i*w0) 1]; %b vector
den = [1 -r*exp(-1i*w0)-r*exp(1i*w0) r^2]; % a vector
[H,W] = freqz(num,den);
figure
plot(W, abs(H));
title(['Magnitude Response with r=' , num2str(r), ', w0=', num2str(w0)]);grid
xlabel('w (rad/sample)');ylabel('|H(z)|');
figure
plot(W, angle(H));
title(['Phase Response with r=' , num2str(r), ', w0=', num2str(w0)]);grid
xlabel('w (rad/sample)');ylabel('Phase');
%-----r = 0.8, keep wo = 0.25*pi -----------
r=0.8; w0 = 0.25*pi;
num = [1 -exp(-1i*w0)-exp(1i*w0) 1]; %b vector
den = [1 -r*exp(-1i*w0)-r*exp(1i*w0) r^2]; % a vector
[H,W] = freqz(num,den);
figure
plot(W, abs(H));
title(['Magnitude Response with r=' , num2str(r), ', w0=', num2str(w0)]);grid
xlabel('w (rad/sample)');ylabel('|H(z)|');
figure
plot(W, angle(H));
title(['Phase Response with r=' , num2str(r), ', w0=', num2str(w0)]);grid
xlabel('w (rad/sample)');ylabel('Phase');
%Part 3 - freqz for trial values of varying Wo
%-----r = 0.8, keep wo = 0.25*pi -----------
r=0.8; w0 = 0.25*pi;
num = [1 -exp(-1i*w0)-exp(1i*w0) 1]; %b vector
den = [1 -r*exp(-1i*w0)-r*exp(1i*w0) r^2]; % a vector
[H,W] = freqz(num,den);
figure
plot(W, abs(H));
title(['Magnitude Response with r=' , num2str(r), ', w0=', num2str(w0)]);grid
xlabel('w (rad/sample)');ylabel('|H(z)|');
figure
plot(W, angle(H));
title(['Phase Response with r=' , num2str(r), ', w0=', num2str(w0)]);grid
xlabel('w (rad/sample)');ylabel('Phase');
%-----r = 0.8, keep wo = 0.5*pi -----------
r=0.8; w0 = 0.5*pi;
num = [1 -exp(-1i*w0)-exp(1i*w0) 1]; %b vector
den = [1 -r*exp(-1i*w0)-r*exp(1i*w0) r^2]; % a vector
[H,W] = freqz(num,den);
figure
plot(W, abs(H));
title(['Magnitude Response with r=' , num2str(r), ', w0=', num2str(w0)]);grid
xlabel('w (rad/sample)');ylabel('|H(z)|');
figure
plot(W, angle(H));
title(['Phase Response with r=' , num2str(r), ', w0=', num2str(w0)]);grid
xlabel('w (rad/sample)');ylabel('Phase');
%-----r = 0.8, keep wo = 1*pi -----------
r=0.8; w0 = 1*pi;
num = [1 -exp(-1i*w0)-exp(1i*w0) 1]; %b vector
den = [1 -r*exp(-1i*w0)-r*exp(1i*w0) r^2]; % a vector
[H,W] = freqz(num,den);
figure
plot(W, abs(H));
title(['Magnitude Response with r=' , num2str(r), ', w0=', num2str(w0)]);grid
xlabel('w (rad/sample)');ylabel('|H(z)|');
figure
plot(W, angle(H));
title(['Phase Response with r=' , num2str(r), ', w0=', num2str(w0)]);grid
xlabel('w (rad/sample)');ylabel('Phase');
%-----r = 0.8, keep wo = 0.75*pi -----------
r=0.8; w0 = 2*pi;
num = [1 -exp(-1i*w0)-exp(1i*w0) 1]; %b vector
den = [1 -r*exp(-1i*w0)-r*exp(1i*w0) r^2]; % a vector
[H,W] = freqz(num,den);
figure
plot(W, abs(H));
title(['Magnitude Response with r=' , num2str(r), ', w0=', num2str(w0)]);grid
xlabel('w (rad/sample)');ylabel('|H(z)|');
figure
plot(W, angle(H));
title(['Phase Response with r=' , num2str(r), ', w0=', num2str(w0)]);grid
xlabel('w (rad/sample)');ylabel('Phase');
%Part 4(a-e),5(a-c) - generate 400 samples of 300Hz sine wave
fsamp = 8192;
n = 0:(1/fsamp):0.0488;
x = 0.8*cos(2*pi*(300)*n);
figure
plot(n,x)
title('300Hz sine wave sampled at rate 8192Hz vs. time');grid
xlabel('n (samples)');ylabel('x[n]');
%Part 4(d) eliminate the 300Hz component
r=0.4; w0 = (2*pi*300)/8192;
b = [1 -exp(-1i*w0)-exp(1i*w0) 1];
a = [1 -(r*exp(-1i*w0)+r*exp(1i*w0)) r^2];
Y = filter(b,a,x);
figure
plot(n,Y)
title(['Notch filter output with r=' , num2str(r), ', w0=', num2str(w0)]);grid
xlabel('n (samples)');ylabel('y[n],x[n]');grid on
hold on
plot(n,x)
hold off
legend('Filtered output y[n]','300Hz signal input x[n]')
%Part 4(e) transient of filter output
r=0.5; w0 = (2*pi*300)/8192;
b = [1 -exp(-1i*w0)-exp(1i*w0) 1];
a = [1 -(r*exp(-1i*w0)+r*exp(1i*w0)) r^2];
Y2 = filter(b,a,x);
figure
plot(n,Y2)
title(['Notch filter output with r=' , num2str(r), ', w0=', num2str(w0)]);grid
xlabel('n (samples)');ylabel('y[n],x[n]');grid on
r=0.7; w0 = (2*pi*300)/8192;
b = [1 -exp(-1i*w0)-exp(1i*w0) 1];
a = [1 -(r*exp(-1i*w0)+r*exp(1i*w0)) r^2];
Y3 = filter(b,a,x);
figure
plot(n,Y3)
title(['Notch filter output with r=' , num2str(r), ', w0=', num2str(w0)]);grid
xlabel('n (samples)');ylabel('y[n],x[n]');grid on
%Part 5
load Project2Data(1).mat
%soundsc(sig, fs)
% The sound segment is in sig vector and fs is the sampling frequency.
r=0.1; w0 = (2*pi*300)/8192;
b = [1 -exp(-1i*w0)-exp(1i*w0) 1];
a = [1 -(r*exp(-1i*w0)+r*exp(1i*w0)) r^2];
Y = filter(b,a,sig);
soundsc(Y, fs)
%% Section II
[b,a] = butter(2,[.07 .10],'stop');
[H,W] = freqz(b,a);
figure
plot(W, abs(H));
title('Unquantized Magn. response of 4th order Butterworth filter');grid
xlabel('w (rad/sample)');ylabel('|H(z)|');
figure
plot(W, angle(H));
title('Unquantized Phase response of 4th order Butterworth filter');grid
xlabel('w (rad/sample)');ylabel('Phase');