/usr/share/octave/packages/signal-1.3.0/ncauer.m is in octave-signal 1.3.0-1.
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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 | ## Copyright (C) 2001 Paulo Neis <p_neis@yahoo.com.br>
##
## This program is free software; you can redistribute it and/or modify it under
## the terms of the GNU General Public License as published by the Free Software
## Foundation; either version 3 of the License, or (at your option) any later
## version.
##
## This program is distributed in the hope that it will be useful, but WITHOUT
## ANY WARRANTY; without even the implied warranty of MERCHANTABILITY or
## FITNESS FOR A PARTICULAR PURPOSE. See the GNU General Public License for more
## details.
##
## You should have received a copy of the GNU General Public License along with
## this program; if not, see <http://www.gnu.org/licenses/>.
## usage: [Zz, Zp, Zg] = ncauer(Rp, Rs, n)
##
## Analog prototype for Cauer filter.
## [z, p, g]=ncauer(Rp, Rs, ws)
## Rp = Passband ripple
## Rs = Stopband ripple
## Ws = Desired order
##
## References:
##
## - Serra, Celso Penteado, Teoria e Projeto de Filtros, Campinas: CARTGRAF,
## 1983.
## - Lamar, Marcus Vinicius, Notas de aula da disciplina TE 456 - Circuitos
## Analogicos II, UFPR, 2001/2002.
function [zer, pol, T0]=ncauer(Rp, Rs, n)
## Cutoff frequency = 1:
wp=1;
## Stop band edge ws:
ws=__ellip_ws(n, Rp, Rs);
k=wp/ws;
k1=sqrt(1-k^2);
q0=(1/2)*((1-sqrt(k1))/(1+sqrt(k1)));
q= q0 + 2*q0^5 + 15*q0^9 + 150*q0^13; #(....)
D=(10^(0.1*Rs)-1)/(10^(0.1*Rp)-1);
## Filter order maybe this, but not used now:
## n=ceil(log10(16*D)/log10(1/q))
l=(1/(2*n))*log((10^(0.05*Rp)+1)/(10^(0.05*Rp)-1));
sig01=0; sig02=0;
for m=0 : 30
sig01=sig01+(-1)^m * q^(m*(m+1)) * sinh((2*m+1)*l);
endfor
for m=1 : 30
sig02=sig02+(-1)^m * q^(m^2) * cosh(2*m*l);
endfor
sig0=abs((2*q^(1/4)*sig01)/(1+2*sig02));
w=sqrt((1+k*sig0^2)*(1+sig0^2/k));
##
if rem(n,2)
r=(n-1)/2;
else
r=n/2;
endif
##
wi=zeros(1,r);
for ii=1 : r
if rem(n,2)
mu=ii;
else
mu=ii-1/2;
endif
soma1=0;
for m=0 : 30
soma1 = soma1 + 2*q^(1/4) * ((-1)^m * q^(m*(m+1)) * sin(((2*m+1)*pi*mu)/n));
endfor
soma2=0;
for m=1 : 30
soma2 = soma2 + 2*((-1)^m * q^(m^2) * cos((2*m*pi*mu)/n));
endfor
wi(ii)=(soma1/(1+soma2));
endfor
##
Vi=sqrt((1-(k.*(wi.^2))).*(1-(wi.^2)/k));
A0i=1./(wi.^2);
sqrA0i=1./(wi);
B0i=((sig0.*Vi).^2 + (w.*wi).^2)./((1+sig0^2.*wi.^2).^2);
B1i=(2 * sig0.*Vi)./(1 + sig0^2 * wi.^2);
## Gain T0:
if rem(n,2)
T0=sig0*prod(B0i./A0i)*sqrt(ws);
else
T0=10^(-0.05*Rp)*prod(B0i./A0i);
endif
## zeros:
zer=[i*sqrA0i, -i*sqrA0i];
## poles:
pol=[(-2*sig0*Vi+2*i*wi.*w)./(2*(1+sig0^2*wi.^2)), (-2*sig0*Vi-2*i*wi.*w)./(2*(1+sig0^2*wi.^2))];
## If n odd, there is a real pole -sig0:
if rem(n,2)
pol=[pol, -sig0];
endif
##
pol=(sqrt(ws)).*pol;
zer=(sqrt(ws)).*zer;
endfunction
## usage: ws = __ellip_ws(n, rp, rs)
## Calculate the stop band edge for the Cauer filter.
function ws=__ellip_ws(n, rp, rs)
kl0 = ((10^(0.1*rp)-1)/(10^(0.1*rs)-1));
k0 = (1-kl0);
int = ellipke([kl0 ; k0]);
ql0 = int(1);
q0 = int(2);
x = n*ql0/q0;
kl = fminbnd(@(y) __ellip_ws_min(y,x) ,eps, 1-eps);
ws = sqrt(1/kl);
endfunction
## usage: err = __ellip_ws_min(kl, x)
function err=__ellip_ws_min(kl, x)
int=ellipke([kl; 1-kl]);
ql=int(1);
q=int(2);
err=abs((ql/q)-x);
endfunction
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