1 ## Copyright (C) 2000 Paul Kienzle <pkienzle@users.sf.net>
3 ## This program is free software; you can redistribute it and/or modify it under
4 ## the terms of the GNU General Public License as published by the Free Software
5 ## Foundation; either version 3 of the License, or (at your option) any later
8 ## This program is distributed in the hope that it will be useful, but WITHOUT
9 ## ANY WARRANTY; without even the implied warranty of MERCHANTABILITY or
10 ## FITNESS FOR A PARTICULAR PURPOSE. See the GNU General Public License for more
13 ## You should have received a copy of the GNU General Public License along with
14 ## this program; if not, see <http://www.gnu.org/licenses/>.
16 ## Compute chebyshev type II filter order and cutoff for the desired response
17 ## characteristics. Rp is the allowable decibels of ripple in the pass
18 ## band. Rs is the minimum attenuation in the stop band.
20 ## [n, Wc] = cheb2ord(Wp, Ws, Rp, Rs)
21 ## Low pass (Wp<Ws) or high pass (Wp>Ws) filter design. Wp is the
22 ## pass band edge and Ws is the stop band edge. Frequencies are
23 ## normalized to [0,1], corresponding to the range [0,Fs/2].
25 ## [n, Wc] = cheb2ord([Wp1, Wp2], [Ws1, Ws2], Rp, Rs)
26 ## Band pass (Ws1<Wp1<Wp2<Ws2) or band reject (Wp1<Ws1<Ws2<Wp2)
27 ## filter design. Wp gives the edges of the pass band, and Ws gives
28 ## the edges of the stop band.
34 function [n, Wc] = cheb2ord(Wp, Ws, Rp, Rs)
38 elseif length(Wp) != length(Ws)
39 error("cheb2ord: Wp and Ws must have the same length");
40 elseif length(Wp) != 1 && length(Wp) != 2
41 error("cheb2ord: Wp,Ws must have length 1 or 2");
42 elseif length(Wp) == 2 && ...
43 (all(Wp>Ws) || all(Ws>Wp) || diff(Wp)<=0 || diff(Ws)<=0)
44 error("cheb2ord: Wp(1)<Ws(1)<Ws(2)<Wp(2) or Ws(1)<Wp(1)<Wp(2)<Ws(2)");
49 ## returned frequency is the same as the input frequency
52 ## warp the target frequencies according to the bilinear transform
53 Ws = (2/T)*tan(pi*Ws./T);
54 Wp = (2/T)*tan(pi*Wp./T);
62 error ("band reject is not implement yet.");
65 ## if high pass, reverse the sense of the test
70 Wa=(Wp.^2 - Ws(1)*Ws(2))./(Wp*(Ws(1)-Ws(2)));
75 ## compute minimum n which satisfies all band edge conditions
76 stop_atten = 10^(abs(Rs)/10);
77 pass_atten = 10^(abs(Rp)/10);
78 n = ceil(acosh(sqrt((stop_atten-1)/(pass_atten-1)))/acosh(1/Wa));
84 %! [n, Wc] = cheb2ord (1000/(Fs/2), 1200/(Fs/2), 0.5, 29);
87 %! plot ([0, 1000, 1000, 0, 0], [0, 0, -0.5, -0.5, 0], ";;");
90 %! title("Pass band Wp=1000 Rp=0.0");
91 %! xlabel("Frequency (Hz)");
92 %! ylabel("Attenuation (dB)");
93 %! [b, a] = cheby2 (n, 29, Wc);
94 %! [h, w] = freqz (b, a, [], Fs);
95 %! plot (w, 20*log10(abs(h)), ";;");
96 %! axis ([ 0, 1500, -1, 0]);
100 %! plot ([1200, Fs/2, Fs/2, 1200, 1200], [-29, -29, -500, -500, -29], ";;");
102 %! axis ([ 0, Fs/2, -250, 0]);
103 %! title("Stop band Ws=1200 Rs=29");
104 %! xlabel("Frequency (Hz)");
105 %! ylabel("Attenuation (dB)");
107 %! [b, a] = cheby2 (n, 29, Wc);
108 %! [h, w] = freqz (b, a, [], Fs);
109 %! plot (w, 20*log10(abs(h)), ";;");
113 %! plot ([0, 1000, 1000, 0, 0], [0, 0, -0.5, -0.5, 0], ";;");
115 %! axis ([ 800, 1010, -0.6, -0.0]);
116 %! title("Pass band detail Wp=1000 Rp=0.5");
117 %! xlabel("Frequency (Hz)");
118 %! ylabel("Attenuation (dB)");
120 %! [b, a] = cheby2 (n, 29, Wc);
121 %! [h, w] = freqz (b, a, [800:1010], Fs);
122 %! plot (w, 20*log10(abs(h)), "r;filter n;");
123 %! [b, a] = cheby2 (n-1, 29, Wc);
124 %! [h, w] = freqz (b, a, [800:1010], Fs);
125 %! plot (w, 20*log10(abs(h)), "b;filter n-1;");
126 %! [b, a] = cheby2 (n+1, 29, Wc);
127 %! [h, w] = freqz (b, a, [800:1010], Fs);
128 %! plot (w, 20*log10(abs(h)), "g;filter n+1;");
132 %! plot ([1200, Fs/2, Fs/2, 1200, 1200], [-29, -29, -500, -500, -29], ";;");
134 %! axis ([ 1190, 1210, -40, -20]);
135 %! title("Stop band detail Wp=1200 Rp=29");
136 %! xlabel("Frequency (Hz)");
137 %! ylabel("Attenuation (dB)");
139 %! [b, a] = cheby2 (n, 29, Wc);
140 %! [h, w] = freqz (b, a, [1190:1210], Fs);
141 %! plot (w, 20*log10(abs(h)), "r;filter n;");
142 %! [b, a] = cheby2 (n-1, 29, Wc);
143 %! [h, w] = freqz (b, a, [1190:1210], Fs);
144 %! plot (w, 20*log10(abs(h)), "b;filter n-1;");
145 %! [b, a] = cheby2 (n+1, 29, Wc);
146 %! [h, w] = freqz (b, a, [1190:1210], Fs);
147 %! plot (w, 20*log10(abs(h)), "g;filter n+1;");