dfdhb.m

AFD - Advanced Filter Design using MATLABMiroslav D. Lutovac, Dejan V. Tosicversion 1.00 released 15

function [numH,denH] = dfdhb(n,a,e,fp,k,gama,b)

% dfdhb.m  dfd normalized transfer function
%
%   Authors: Dejan V. Tosic, Miroslav D. Lutovac, 1999.03.07
%                 [e-mail]
%                 [e-mail]
%
%   Copyright (c) 1999 by Tosic & Lutovac
%   $Revision: 1.0 $  $Date: 1999/03/07 03:07:42 $
%
%   References:
%        Miroslav D. Lutovac, Dejan V. Tosic, Brian L. Evans
%           Advanced Filter Design for Signal Processing
%                   Using MATLAB and Mathematica

%  calls:
%% dfdxna.m, dfdsnaei.m, dfdzbl.m

X = dfdxna(n,a);
nX = length(X);
for ind = 1:nX
 S(ind) = dfdsnaei(n,a,e,ind);
end

if abs(n-2*fix(n/2)) ~= 0
 X((n+1)/2) = 1/10^6;
end

zz = dfdzbl(j*a*ones(size(X))./X,fp);
zp = dfdzbl(S,fp);

if abs(n-2*fix(n/2)) ~= 0
 zz((n+1)/2) = -1;
end

ZZ=zeros(n,1);   ZP=zeros(n,1);
if abs(n-2*fix(n/2)) == 0
  for i=1:n/2
    ZZ(i) = (-b*(1+zz(i)) + sqrt((b*(1+zz(i)))^2-4*(1+gama*zz(i))*(gama+zz(i)))) /...
                       (2*(1+gama*zz(i)));
    ZZ(n-i+1)=(-b*(1+zz(i))-sqrt((b*(1+zz(i)))^2-4*(1+gama*zz(i))*(gama+zz(i))))/...
                       (2*(1+gama*zz(i)));
    ZP(i) = (-b*(1+zp(i)) + sqrt((b*(1+zp(i)))^2-4*(1+gama*zp(i))*(gama+zp(i)))) /...
                       (2*(1+gama*zp(i)));
    ZP(n-i+1)=(-b*(1+zp(i))-sqrt((b*(1+zp(i)))^2-4*(1+gama*zp(i))*(gama+zp(i))))/...
                       (2*(1+gama*zp(i)));
  end
else
  for i=1:(n-1)/2
    ZZ(i) = (-b*(1+zz(i)) + sqrt((b*(1+zz(i)))^2-4*(1+gama*zz(i))*(gama+zz(i)))) /...
                       (2*(1+gama*zz(i)));
    ZZ(n-i)=(-b*(1+zz(i))-sqrt((b*(1+zz(i)))^2-4*(1+gama*zz(i))*(gama+zz(i))))/...
                       (2*(1+gama*zz(i)));
    ZP(i) = (-b*(1+zp(i)) + sqrt((b*(1+zp(i)))^2-4*(1+gama*zp(i))*(gama+zp(i)))) /...
                       (2*(1+gama*zp(i)));
    ZP(n-i)=(-b*(1+zp(i))-sqrt((b*(1+zp(i)))^2-4*(1+gama*zp(i))*(gama+zp(i))))/...
                       (2*(1+gama*zp(i)));
  end
    ZP(n) = (-b*(1+zp((n+1)/2)) ...
         + sqrt((b*(1+zp((n+1)/2)))^2-4*(1+gama*zp((n+1)/2))*(gama+zp((n+1)/2)))) /...
                       (2*(1+gama*zp((n+1)/2)));
    ZP(n+1) = (-b*(1+zp((n+1)/2)) ...
         - sqrt((b*(1+zp((n+1)/2)))^2-4*(1+gama*zp((n+1)/2))*(gama+zp((n+1)/2)))) /...
                       (2*(1+gama*zp((n+1)/2)));
end

g = 1;
numH = 1;

denH = 1;
if abs(n-2*fix(n/2)) == 0
  for i=1:n/2
    g = g * (2 -2*real(zz(i))) / (1 -2*real(zp(i)) + abs(zp(i))^2);
    g = g* (1+2*gama*real(zp(i))+gama^2*abs(zp(i))^2)/(1+gama^2+2*gama*real(zz(i))) ;
    numH = conv(numH, [1 -2*real(ZZ(i))               1]);
    denH = conv(denH, [1 -2*real(ZP(i))    abs(ZP(i))^2]);
    numH = conv(numH, [1 -2*real(ZZ(n-i+1))           1]);
    denH = conv(denH, [1 -2*real(ZP(n-i+1)) abs(ZP(n-i+1))^2]);
  end
    g = g * sqrt(1+e^2);
else
  for i=1:(n-1)/2
    g = g * (2 -2*real(zz(i))) / (1 -2*real(zp(i)) + abs(zp(i))^2);
    g = g/(1+gama^2+2*gama*real(zz(i))) *(1+2*gama*real(zp(i))+gama^2*abs(zp(i))^2);
    numH = conv(numH, [1 -2*real(ZZ(i))               1]);
    denH = conv(denH, [1 -2*real(ZP(i))    abs(ZP(i))^2]);
    numH = conv(numH, [1 -2*real(ZZ(n-i))               1]);
    denH = conv(denH, [1 -2*real(ZP(n-i))  abs(ZP(n-i))^2]);
  end
    g = 2*g/(1 -zp((n+1)/2));
    numH = conv(numH, [1 0 -1]);
    denH = conv(denH, [1 -(ZP(n)+ZP(n+1)) ZP(n)*ZP(n+1)]);
    g = g* (1+gama*zp((n+1)/2))/(1-gama) ;
end
numH = numH/g;