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+function Hd=iodelay(H,d)
+// Author: Serge Steer, Copyright INRIA
+ if or(size(H.num)<>size(d)) then error('Dimension mismatch'),end
+ Hd=mlist(['rd','H','iodelay'],H,d)
+endfunction
+
+//element wise product overloading functions
+function H=%rd_x_rd(H1,H2)
+// Author: Serge Steer, Copyright INRIA
+ H=mlist(['rd','H','iodelay'],H1.H.*H2.H,H1.iodelay+ H2.iodelay)
+endfunction
+function H=%rd_x_r(H1,H2)
+// Author: Serge Steer, Copyright INRIA
+ H=mlist(['rd','H','iodelay'],H1.H.*H2,H1.iodelay)
+endfunction
+function H=%r_x_rd(H1,H2)
+// Author: Serge Steer, Copyright INRIA
+ H=mlist(['rd','H','iodelay'],H1.*H2.H,H2.iodelay)
+endfunction
+function H=%rd_x_s(H1,H2)
+// Author: Serge Steer, Copyright INRIA
+ H=mlist(['rd','H','iodelay'],H1.H.*H2,H1.iodelay)
+endfunction
+function H=%s_x_rd(H1,H2)
+// Author: Serge Steer, Copyright INRIA
+ H=mlist(['rd','H','iodelay'],H1.*H2.H,H2.iodelay)
+endfunction
+
+//column concatenation overloading functions
+function H=%rd_c_rd(H1,H2)
+// Author: Serge Steer, Copyright INRIA
+ H=mlist(['rd','H','iodelay'],[H1.H H2.H],[H1.iodelay,H2.iodelay])
+endfunction
+function H=%rd_c_r(H1,H2)
+// Author: Serge Steer, Copyright INRIA
+ H=mlist(['rd','H','iodelay'],[H1.H H2],[H1.iodelay,zeros(H2.num)])
+endfunction
+function H=%r_c_rd(H1,H2)
+// Author: Serge Steer, Copyright INRIA
+ H=mlist(['rd','H','iodelay'],[H1 H2.H],[zeros(H1.num),H2.iodelay])
+endfunction
+function H=%rd_c_s(H1,H2)
+// Author: Serge Steer, Copyright INRIA
+ H=mlist(['rd','H','iodelay'],[H1.H H2],[H1.iodelay,zeros(H2.num)])
+endfunction
+function H=%s_c_rd(H1,H2)
+// Author: Serge Steer, Copyright INRIA
+ H=mlist(['rd','H','iodelay'],[H1 H2.H],[zeros(H1.num),H2.iodelay])
+endfunction
+
+//row concatenation overloading functions
+function H=%rd_f_rd(H1,H2)
+// Author: Serge Steer, Copyright INRIA
+ H=mlist(['rd','H','iodelay'],[H1.H;H2.H],[H1.iodelay;H2.iodelay])
+endfunction
+function H=%rd_f_r(H1,H2)
+// Author: Serge Steer, Copyright INRIA
+ H=mlist(['rd','H','iodelay'],[H1.H;H2],[H1.iodelay;zeros(H2.num)])
+endfunction
+function H=%r_f_rd(H1,H2)
+// Author: Serge Steer, Copyright INRIA
+ H=mlist(['rd','H','iodelay'],[H1;H2.H],[zeros(H1.num);H2.iodelay])
+endfunction
+function H=%rd_f_s(H1,H2)
+// Author: Serge Steer, Copyright INRIA
+ H=mlist(['rd','H','iodelay'],[H1.H;H2],[H1.iodelay;zeros(H2.num)])
+endfunction
+function H=%s_f_rd(H1,H2)
+// Author: Serge Steer, Copyright INRIA
+ H=mlist(['rd','H','iodelay'],[H1;H2.H],[zeros(H1.num);H2.iodelay])
+endfunction
+
+//matrix product overloading functions
+function H=%rd_m_rd(H1,H2)
+// Author: Serge Steer, Copyright INRIA
+ D1=H1.iodelay
+ D2=H2.iodelay
+ D=D1*D2;
+ for k=1;size(D2,2)
+ for l=1:size(D1,1)
+ d=D1(l,:)+(D2(:,k)')
+ if or(d(1)<>d) then error('Delays mismatched'),end
+ D(l,k)=d
+ end
+ end
+ H=mlist(['rd','H','iodelay'],H1.H*H2.H,D)
+endfunction
+function H=%rd_m_r(H1,H2)
+// Author: Serge Steer, Copyright INRIA
+ D1=H1.iodelay
+ for l=1:size(D1,1)
+ if or(D1(l,1)<>D1(l,:)) then error('Delays mismatched'),end
+ end
+ H=mlist(['rd','','iodelay'],H1.H*H2,D1)
+endfunction
+function H=%rd_m_s(H1,H2)
+// Author: Serge Steer, Copyright INRIA
+ D1=H1.iodelay
+ for l=1:size(D1,1)
+ if or(D1(l,1)<>D1(l,:)) then error('Delays mismatched'),end
+ end
+ H=mlist(['rd','H','iodelay'],H1.H*H2,D1)
+endfunction
+function H=%r_m_rd(H1,H2)
+// Author: Serge Steer, Copyright INRIA
+ D2=H2.iodelay
+ for l=1:size(D2,2)
+ if or(D2(1,l)<>D2(:,l)) then error('Delays mismatched'),end
+ end
+ H=mlist(['rd','H','iodelay'],H1*H2.H,D2)
+endfunction
+function H=%s_m_rd(H1,H2)
+// Author: Serge Steer, Copyright INRIA
+ D2=H2.iodelay
+ for l=1:size(D2,2)
+ if or(D2(1,l)<>D2(:,l)) then error('Delays mismatched'),end
+ end
+ H=mlist(['rd','H','iodelay'],H1*H2.H,D2)
+endfunction
+
+//Addition overloading functions
+function H=%rd_a_rd(H1,H2)
+// Author: Serge Steer, Copyright INRIA
+ D1=H1.iodelay
+ D2=H2.iodelay
+ if or(D1<>D2) then error('Delay mismatch'),end
+ H=mlist(['rd','H','iodelay'],H1.H+H2.H,D1)
+endfunction
+function H=%rd_a_r(H1,H2)
+// Author: Serge Steer, Copyright INRIA
+ D1=H1.iodelay
+ if or(D1<>0) then error('Delay mismatch'),end
+ H=mlist(['rd','H','iodelay'],H1.H+H2,D1)
+endfunction
+function H=%rd_a_s(H1,H2)
+// Author: Serge Steer, Copyright INRIA
+ D1=H1.iodelay
+ if or(D1<>0) then error('Delay mismatch'),end
+ H=mlist(['rd','H','iodelay'],H1.H+H2,D1)
+endfunction
+function H=%r_a_rd(H1,H2)
+// Author: Serge Steer, Copyright INRIA
+ D2=H2.iodelay
+ if or(D2<>0) then error('Delay mismatch'),end
+ H=mlist(['rd','H','iodelay'],H1+H2.H,D2)
+endfunction
+
+//Substraction overloading functions
+function H=%rd_a_rd(H1,H2)
+// Author: Serge Steer, Copyright INRIA
+ D1=H1.iodelay
+ D2=H2.iodelay
+ if or(D1<>D2) then error('Delay mismatch'),end
+ H=mlist(['rd','H','iodelay'],H1.H-H2.H,D1)
+endfunction
+function H=%rd_a_r(H1,H2)
+// Author: Serge Steer, Copyright INRIA
+ D1=H1.iodelay
+ if or(D1<>0) then error('Delay mismatch'),end
+ H=mlist(['rd','H','iodelay'],H1.H-H2,D1)
+endfunction
+function H=%rd_a_s(H1,H2)
+// Author: Serge Steer, Copyright INRIA
+ D1=H1.iodelay
+ if or(D1<>0) then error('Delay mismatch'),end
+ H=mlist(['rd','H','iodelay'],H1.H-H2,D1)
+endfunction
+function H=%r_a_rd(H1,H2)
+// Author: Serge Steer, Copyright INRIA
+ D2=H2.iodelay
+ if or(D2<>0) then error('Delay mismatch'),end
+ H=mlist(['rd','H','iodelay'],H1-H2.H,D2)
+endfunction
+
+//extraction overloading functions
+function H=%rd_e(varargin)
+// Author: Serge Steer, Copyright INRIA
+ H=varargin($)
+ Hh= H.H;Hh.num=Hh.num(varargin(1:$-1));Hh.den=Hh.den(varargin(1:$-1));
+ H.H=Hh
+ H.iodelay=H.iodelay(varargin(1:$-1))
+endfunction
+
+//insertion overloading functions
+function H=%rd_i_rd(varargin)
+// Author: Serge Steer, Copyright INRIA
+ H=varargin($)
+ Hfrom=varargin($-1)
+
+ Hh= H.H
+ Hh.num(varargin(1:$-2))=Hfrom.H.num
+ Hh.den(varargin(1:$-2))=Hfrom.H.den
+ H.H=Hh
+ H.iodelay(varargin(1:$-2))=Hfrom.iodelay
+endfunction
+function H=%r_i_rd(varargin)
+// Author: Serge Steer, Copyright INRIA
+ H=varargin($)
+ Hfrom=varargin($-1)
+
+ Hh= H.H
+ Hh.num(varargin(1:$-2))=Hfrom.num
+ Hh.den(varargin(1:$-2))=Hfrom.den
+ H.H=Hh
+ H.iodelay(varargin(1:$-2))=zeros(Hfrom.num)
+endfunction
+function H=%s_i_rd(varargin)
+// Author: Serge Steer, Copyright INRIA
+ H=varargin($)
+ Hfrom=varargin($-1)
+
+ Hh= H.H
+ Hh.num(varargin(1:$-2))=Hfrom
+ Hh.den(varargin(1:$-2))=ones(Hfrom)
+ H.H=Hh
+ H.iodelay(varargin(1:$-2))=zeros(Hfrom)
+endfunction
+function H=%rd_i_r(varargin)
+// Author: Serge Steer, Copyright INRIA
+ Hh=varargin($)
+ Hfrom=varargin($-1)
+ Hh.num(varargin(1:$-2))=Hfrom.H.num
+ Hh.den(varargin(1:$-2))=Hfrom.H.den
+ D=zeros(Hh.num)
+ D(varargin(1:$-2))=Hfrom.iodelay
+ H=mlist(['rd','H','iodelay'],Hh,D)
+endfunction
+function H=%rd_i_s(varargin)
+// Author: Serge Steer, Copyright INRIA
+ num=varargin($);den=ones(num)
+ Hfrom=varargin($-1)
+
+ num(varargin(1:$-2))=Hfrom.H.num
+ den(varargin(1:$-2))=Hfrom.H.den
+ D=zeros(num)
+ D(varargin(1:$-2))=Hfrom.iodelay
+ H=mlist(['rd','H','iodelay'],rlist(num,den,'c'),D)
+endfunction
+
+//transpostion overloading function
+function H=%rd_t(H)
+// Author: Serge Steer, Copyright INRIA
+ H.H=H.H'
+ H.iodelay=H.iodelay'
+endfunction
+
+//string overloading function
+function txt=%rd_string(H)
+// Author: Serge Steer, Copyright INRIA
+ r=H.H
+ N=string(r.num)
+ D=string(r.den)
+ ln=max(matrix(length(N),2,-1),'r')
+ ld=max(matrix(length(D),2,-1),'r')
+ l=max(ln,ld)
+ [m,n]=size(r.num);
+ S=emptystr(m,n)
+
+ kz=find(H.iodelay==0);//zero delay entries
+ w='exp('+string(-H.iodelay)+'*s)*';w(kz)='';
+
+ for i=1:m*n
+ s=2*i-1:2*i
+ pw=part(' ',1:length(w(i)))
+ N(s)=pw+part(' ',1:(l(i)-ln(i))/2)+N(s)
+ D(s)=pw+part(' ',1:(l(i)-ld(i))/2)+D(s)
+ S(i) =w(i)+part('-',ones(1,l(i)))
+ end
+ txt=emptystr(5*m,n);
+ txt(1:5:$,:)=N(1:2:$,:)
+ txt(2:5:$,:)=N(2:2:$,:)
+ txt(3:5:$,:)=S(1:$,:)
+ txt(4:5:$,:)=D(1:2:$,:)
+ txt(5:5:$,:)=D(2:2:$,:)
+endfunction
+
+
+//Display overloading function
+function %rd_p(H)
+// Author: Serge Steer, Copyright INRIA
+//used to display rational fraction with complex coefficients
+//The real case is hard coded
+// Copyright INRIA
+ T=string(H)
+ l=max(length(T),'r')
+ Te=emptystr(size(T,1),1)
+ for k=1:size(T,2)
+ Te=Te+part(T(:,k),1:l(k)+1)+' '
+ end
+ mprintf("%s\n",Te)
+endfunction
+
+
+//frequency response computation overloading
+function [frq,repf,splitf]=repfreq(varargin)
+// Author: Serge Steer, Copyright INRIA
+ H=varargin(1)
+ autolib.repfreq
+ if typeof(H)=='rd' then
+ D=H.iodelay
+ varargin(1)=H.H
+ [frq,repf,splitf]=repfreq(varargin(:))
+
+ w=-2*%i*%pi*frq;
+ for k=1:size(D,'*')
+ repf(k,:)=repf(k,:).*exp(D(k)*w)
+ end
+ else
+ [frq,repf,splitf]=repfreq(varargin(:))
+ end
+endfunction
+
+//bode plot computation overloading
+function bode(varargin)
+// Author: Serge Steer, Copyright INRIA
+ H=varargin(1)
+ xdesslib.bode
+ if typeof(H)=='rd' then
+ if type(varargin($))==10 then //a comment
+ cm=varargin($);varagin($)=null()
+ else
+ cm=''
+ end
+ D=H.iodelay
+ varargin(1)=H.H
+ [frq,repf,splitf]=repfreq(varargin(1:$))
+ w=-2*%i*%pi*frq;
+ for k=1:size(D,'*')
+ repf(k,:)=repf(k,:).*exp(D(k)*w)
+ end
+ bode(frq,repf)
+ else
+ bode(varargin(:))
+ end
+endfunction
+
+//nyquist plot computation overloading
+function nyquist(varargin)
+// Author: Serge Steer, Copyright INRIA
+ H=varargin(1)
+ xdesslib.nyquist
+ if typeof(H)=='rd' then
+ if type(varargin($))==10 then //a comment
+ cm=varargin($);varagin($)=null()
+ else
+ cm=''
+ end
+ D=H.iodelay
+ varargin(1)=H.H
+ [frq,repf,splitf]=repfreq(varargin(1:$))
+ w=-2*%i*%pi*frq;
+ for k=1:size(D,'*')
+ repf(k,:)=repf(k,:).*exp(D(k)*w)
+ end
+ nyquist(frq,repf)
+ else
+ nyquist(varargin(:))
+ end
+endfunction
+
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