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ellipord.m

## Copyright (C) 2001 Paulo Neis
##
## 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 2 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: [n,wp] = ellipord(wp,ws, rp,rs)
##
## Calculate the order for the elliptic filter (discrete)
## wp: Cutoff frequency
## ws: Stopband edge
## rp: decibels of ripple in the passband.
## rs: decibels of ripple in the stopband.
##
## References: 
##
## - Lamar, Marcus Vinicius, Notas de aula da disciplina TE 456 - Circuitos 
##   Analogicos II, UFPR, 2001/2002.

## Author: Paulo Neis <p_neis@yahoo.com.br>


function [n, Wp] = ellipord(Wp, Ws, Rp, Rs)
##

[rp, cp]=size(Wp);
[rs, cs]=size(Ws);
if ( !(length(Wp)<=2 && (rp==1 || cp==1) && length(Ws)<=2 && (rs==1 || cs==1)) )
      error ("ellipord: frequency must be given as w0 or [w0, w1]");
elseif (!all(Wp >= 0 & Wp <= 1 & Ws >= 0 & Ws <= 1)) #####
      error ("ellipord: critical frequencies must be in (0 1)");
elseif (!(length(Wp)==1 || length(Wp) == 2 & length(Ws)==1 || length(Ws) == 2))
      error ("ellipord: only one filter band allowed");
elseif (length(Wp)==2 && !(Wp(1) < Wp(2)))
      error ("ellipord: first band edge must be smaller than second");
elseif (length(Ws)==2 && !(length(Wp)==2))
      error ("ellipord: you must specify band pass borders.");
elseif (length(Wp)==2 && length(Ws)==2 && !(Ws(1) < Wp(1) && Ws(2) > Wp(2)) )
      error ("ellipord: ( Wp(1), Wp(2) ) must be inside of interval ( Ws(1), Ws(2) )");
elseif (length(Wp)==2 && length(Ws)==1 && !(Ws < Wp(1) || Ws > Wp(2)) )
      error ("ellipord: Ws must be out of interval ( Wp(1), Wp(2) )");
endif




# sampling frequency of 2 Hz
T = 2;

Wpw = tan(pi.*Wp./T); # prewarp
Wsw = tan(pi.*Ws./T); # prewarp

##pass/stop band to low pass filter transform:
if (length(Wpw)==2 && length(Wsw)==2)
      wp=1;
      w02 = Wpw(1) * Wpw(2);  # Central frequency of stop/pass band (square)
      w3 = w02/Wsw(2);
      w4 = w02/Wsw(1);
      if (w3 > Wsw(1))
            ws = (Wsw(2)-w3)/(Wpw(2)-Wpw(1));
      elseif (w4 < Wsw(2))
            ws = (w4-Wsw(1))/(Wpw(2)-Wpw(1));
      else
            ws = (Wsw(2)-Wsw(1))/(Wpw(2)-Wpw(1));
      endif
elseif (length(Wpw)==2 && length(Wsw)==1)
      wp=1;
      w02 = Wpw(1) * Wpw(2);
      if (Wsw > Wpw(2))
            w3 = w02/Wsw;
            ws = (Wsw - w3)/(Wpw(2) - Wpw(1));
      else
            w4 = w02/Wsw;
            ws = (w4 - Wsw)/(Wpw(2) - Wpw(1));
      endif
else
      wp = Wpw;
      ws = Wsw;
endif

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);

n=ceil(log10(16*D)/log10(1/q));

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