1 ## Copyright (C) 1999 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 butterworth 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] = buttord(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] = buttord([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.
30 ## Theory: |H(W)|^2 = 1/[1+(W/Wc)^(2N)] = 10^(-R/10)
31 ## With some algebra, you can solve simultaneously for Wc and N given
32 ## Ws,Rs and Wp,Rp. For high pass filters, subtracting the band edges
33 ## from Fs/2, performing the test, and swapping the resulting Wc back
34 ## works beautifully. For bandpass and bandstop filters this process
35 ## significantly overdesigns. Artificially dividing N by 2 in this case
36 ## helps a lot, but it still overdesigns.
40 function [n, Wc] = buttord(Wp, Ws, Rp, Rs)
43 elseif length(Wp) != length(Ws)
44 error("buttord: Wp and Ws must have the same length");
45 elseif length(Wp) != 1 && length(Wp) != 2
46 error("buttord: Wp,Ws must have length 1 or 2");
47 elseif length(Wp) == 2 && (all(Wp>Ws) || all(Ws>Wp) || diff(Wp)<=0 || diff(Ws)<=0)
48 error("buttord: Wp(1)<Ws(1)<Ws(2)<Wp(2) or Ws(1)<Wp(1)<Wp(2)<Ws(2)");
52 warning("buttord: seems to overdesign bandpass and bandreject filters");
57 ## if high pass, reverse the sense of the test
59 Wp(stop) = 1-Wp(stop); # stop will be at most length 1, so no need to
60 Ws(stop) = 1-Ws(stop); # subtract from ones(1,length(stop))
62 ## warp the target frequencies according to the bilinear transform
63 Ws = (2/T)*tan(pi*Ws./T);
64 Wp = (2/T)*tan(pi*Wp./T);
66 ## compute minimum n which satisfies all band edge conditions
67 ## the factor 1/length(Wp) is an artificial correction for the
68 ## band pass/stop case, which otherwise significantly overdesigns.
69 qs = log(10^(Rs/10) - 1);
70 qp = log(10^(Rp/10) - 1);
71 n = ceil(max(0.5*(qs - qp)./log(Ws./Wp))/length(Wp));
73 ## compute -3dB cutoff given Wp, Rp and n
74 Wc = exp(log(Wp) - qp/2/n);
76 ## unwarp the returned frequency
77 Wc = atan(T/2*Wc)*T/pi;
79 ## if high pass, reverse the sense of the test
80 Wc(stop) = 1-Wc(stop);