1 ## Copyright (C) 2000 Paul Kienzle <pkienzle@users.sf.net>
2 ## Copyright (C) 2000 Laurent S. Mazet
4 ## This program is free software; you can redistribute it and/or modify it under
5 ## the terms of the GNU General Public License as published by the Free Software
6 ## Foundation; either version 3 of the License, or (at your option) any later
9 ## This program is distributed in the hope that it will be useful, but WITHOUT
10 ## ANY WARRANTY; without even the implied warranty of MERCHANTABILITY or
11 ## FITNESS FOR A PARTICULAR PURPOSE. See the GNU General Public License for more
14 ## You should have received a copy of the GNU General Public License along with
15 ## this program; if not, see <http://www.gnu.org/licenses/>.
17 ## Compute chebyshev type I filter order and cutoff for the desired response
18 ## characteristics. Rp is the allowable decibels of ripple in the pass
19 ## band. Rs is the minimum attenuation in the stop band.
21 ## [n, Wc] = cheb1ord(Wp, Ws, Rp, Rs)
22 ## Low pass (Wp<Ws) or high pass (Wp>Ws) filter design. Wp is the
23 ## pass band edge and Ws is the stop band edge. Frequencies are
24 ## normalized to [0,1], corresponding to the range [0,Fs/2].
26 ## [n, Wc] = cheb1ord([Wp1, Wp2], [Ws1, Ws2], Rp, Rs)
27 ## Band pass (Ws1<Wp1<Wp2<Ws2) or band reject (Wp1<Ws1<Ws2<Wp2)
28 ## filter design. Wp gives the edges of the pass band, and Ws gives
29 ## the edges of the stop band.
33 function [n, Wc] = cheb1ord(Wp, Ws, Rp, Rs)
37 elseif length(Wp) != length(Ws)
38 error("cheb1ord: Wp and Ws must have the same length");
39 elseif length(Wp) != 1 && length(Wp) != 2
40 error("cheb1ord: Wp,Ws must have length 1 or 2");
41 elseif length(Wp) == 2 && ...
42 (all(Wp>Ws) || all(Ws>Wp) || diff(Wp)<=0 || diff(Ws)<=0)
43 error("cheb1ord: Wp(1)<Ws(1)<Ws(2)<Wp(2) or Ws(1)<Wp(1)<Wp(2)<Ws(2)");
48 ## returned frequency is the same as the input frequency
51 ## warp the target frequencies according to the bilinear transform
52 Ws = (2/T)*tan(pi*Ws./T);
53 Wp = (2/T)*tan(pi*Wp./T);
61 error ("band reject is not implement yet.");
64 ## if high pass, reverse the sense of the test
69 Wa=(Ws.^2 - Wp(1)*Wp(2))./(Ws*(Wp(1)-Wp(2)));
74 ## compute minimum n which satisfies all band edge conditions
75 stop_atten = 10^(abs(Rs)/10);
76 pass_atten = 10^(abs(Rp)/10);
77 n = ceil(acosh(sqrt((stop_atten-1)/(pass_atten-1)))/acosh(Wa));
83 %! [n, Wc] = cheb1ord (1000/(Fs/2), 1200/(Fs/2), 0.5, 29);
86 %! axis ([ 0, 1500, -1, 0]);
87 %! title("Pass band Wp=1000 Rp=0.5");
88 %! xlabel("Frequency (Hz)");
89 %! ylabel("Attenuation (dB)");
91 %! plot ([0, 1000, 1000, 0, 0], [0, 0, -0.5, -0.5, 0], ";;");
93 %! [b, a] = cheby1 (n, 0.5, Wc);
94 %! [h, w] = freqz (b, a, [], Fs);
95 %! plot (w, 20*log10(abs(h)), ";;");
99 %! axis ([ 0, Fs/2, -250, 0]);
100 %! title("Stop band Ws=1200 Rs=29");
101 %! xlabel("Frequency (Hz)");
102 %! ylabel("Attenuation (dB)");
104 %! plot ([1200, Fs/2, Fs/2, 1200, 1200], [-29, -29, -500, -500, -29], ";;");
106 %! [b, a] = cheby1 (n, 0.5, Wc);
107 %! [h, w] = freqz (b, a, [], Fs);
108 %! plot (w, 20*log10(abs(h)), ";;");
112 %! axis ([ 990, 1010, -0.6, -0.4]);
113 %! title("Pass band detail Wp=1000 Rp=0.5");
114 %! xlabel("Frequency (Hz)");
115 %! ylabel("Attenuation (dB)");
117 %! plot ([0, 1000, 1000, 0, 0], [0, 0, -0.5, -0.5, 0], ";;");
119 %! [b, a] = cheby1 (n, 0.5, Wc);
120 %! [h, w] = freqz (b, a, [990:1010], Fs);
121 %! plot (w, 20*log10(abs(h)), ";filter n;");
122 %! [b, a] = cheby1 (n-1, 0.5, Wc);
123 %! [h, w] = freqz (b, a, [990:1010], Fs);
124 %! plot (w, 20*log10(abs(h)), ";filter n-1;");
125 %! [b, a] = cheby1 (n+1, 0.5, Wc);
126 %! [h, w] = freqz (b, a, [990:1010], Fs);
127 %! plot (w, 20*log10(abs(h)), ";filter n+1;");
131 %! axis ([ 1190, 1210, -40, -20]);
132 %! title("Stop band detail Wp=1200 Rp=29");
133 %! xlabel("Frequency (Hz)");
134 %! ylabel("Attenuation (dB)");
136 %! plot ([1200, Fs/2, Fs/2, 1200, 1200], [-29, -29, -500, -500, -29], ";;");
138 %! [b, a] = cheby1 (n, 0.5, Wc);
139 %! [h, w] = freqz (b, a, [1190:1210], Fs);
140 %! plot (w, 20*log10(abs(h)), ";filter n;");
141 %! [b, a] = cheby1 (n-1, 0.5, Wc);
142 %! [h, w] = freqz (b, a, [1190:1210], Fs);
143 %! plot (w, 20*log10(abs(h)), ";filter n-1;");
144 %! [b, a] = cheby1 (n+1, 0.5, Wc);
145 %! [h, w] = freqz (b, a, [1190:1210], Fs);
146 %! plot (w, 20*log10(abs(h)), ";filter n+1;");