non dissipative ladder filters

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calculate the inductances and capacitances of a non-dissipative analog ladder filter

unitarh(G,F,lim)
function H = unitarh(G,F,lim)

%	 H = unitarh(G,F,lim)
%	 Unitarity relation ; calculation of the numerator H of the reflexion 
%   coefficient of the s parameter matrix of an analog filter
%   from the polynome G, the denominator of all s parameters,
%	 and the polynome F, the numerator of the transmission coefficient, 
%   using   H*hurwitz(H) = G*hurwitz(G) - F*hurwitz(F) ;
%	 the roots with least (normally negative) real parts, in H*hurwitz(H),
%	 are retained for building H.
%	 The coefficients of H which are either less than sqrt(eps) or less 
% 	 than  lim  if 3 arguments are introduced, are set to zero.
%   P. MURET 26-nov-2002

if prod(size(G)) ~= length(G) | prod(size(F)) ~= length(F)
   error('the arguments must be vectors.');
end

if length(G) < length(F)
   error('the degree of G must not be less than that of F');
end

%	calculation of the square hurwitzian moduli:
Godd = hurwitz(G);
Fodd = hurwitz(F);
G2 = conv(G,Godd);
F2 = conv(F,Fodd);

%	the length of the second polynome is fitted to that of the first one
%	by adding zeros at the beginning, and the unitary relation is done
ng2=length(G2);
nf2=length(F2);
Z=zeros(1,ng2-nf2);
DH2=G2 - [Z F2];

%	roots of the resulting polynome are extracted and sorted out, 
%	beginning with that with the most positive real part, 
%	in decreasing order. Then the first half is suppressed,
%	leaving only the roots with negative real parts.
RH2=roots(DH2);
degh=length(RH2)/2;
RnH2=esort(RH2);
RnH2(1:degh)=[];
H=poly(RnH2);

%	setting the too small coefficients of H to zero
for k = 1:degh
	if (abs(H(k))-sqrt(eps)) < 0, H(k)=0; end
	if nargin == 3
   	if (abs(H(k))- lim) <0, H(k)=0; end
	end
end

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