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//Author: Parthasarathi Panda
//parthasarathipanda314@gmail.com
//Convert digital filter second-order section parameters to state-space form
//Calling Sequence
//[A,B,C,D] = sos2ss(sos)
//[A,B,C,D] = sos2ss(sos,g)
//
//sos2ss converts a second-order section representation of a digital filter to an equivalent state-space representation.
//A,B,C,D:Steady state parameters
//sos:6 column second order section matrix
//g:gain
//EXAMPLES:
//sos = [1 1 1 1 0 -1 ;
// -2 3 1 1 10 1];
//[A,B,C,D] = sos2ss(sos,2);
//
//EXPECTED OUTPUT:
//D =- 4.
//C =42. 4. - 32. - 2.
//B =[1. 0. 0. 0. 0.]'
//A =[- 10. 0. 10. 1. ; 1. 0. 0. 0. ; 0. 1. 0. 0. ; 0. 0. 1. 0. ]
function [A,B,C,D]=sos2ss(sos,g)
[nargout,nargin]=argn();
if nargin==1 then
g=1;
end
if type(sos)~=1 | type(g)~=1 then
error('check the data type of input'); //to check if the inputs are real/complex arrays
end
if size(g)~=[1,1] then
error('check the data type of input'); //to check that n is single dimensional
end
//checking if sos is a 6 column matrix
[d,j]=size(sos);
if j~=6 then
error('sos should be a 6-column matrix');
end
num=[1];
den=[1];
//convolving the numerator and denominator to get the coefficient of the numerator and the denominator at the top and bottom
for i=[1:d]
num=convol(num,sos(i,1:3));
den=convol(den,sos(i,4:6));
end
t=2*d+1; //polynomial degree must be defined here
if den(t)==0 then
error('improper transfer function check input');
end
// t=2*d+1; //polynomial degree
A=zeros(t-1,t-1);
if t>2 then
A(2:(t-1),1:(t-2))=eye(t-2,t-2);
end
A(1,:)=-1*den(2:t)/den(1);
B=zeros(t,1);
B(1)=1/den(1); //constructing (A,B) in canonical controllable form
C=g*(num(2:t)-den(2:t)*num(1)/den(1));//appropiate C and D
D=g*num(1)/den(1);
endfunction
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