| | | Scilab Reference Manual | |
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arl2 — SISO model realization by L2 transfer approximation
h=arl2(y,den0,n [,imp]) h=arl2(y,den0,n [,imp],'all') [den,num,err]=arl2(y,den0,n [,imp]) [den,num,err]=arl2(y,den0,n [,imp],'all')
| y | : real vector or polynomial in z^-1, it contains the coefficients of the Fourier's series of the rational system to approximate (the impulse response) |
| den0 | : a polynomial which gives an initial guess of the solution, it may be poly(1,'z','c') |
| n | : integer, the degree of approximating transfer function (degree of den) |
| imp | : integer in (0,1,2) (verbose mode) |
| h | : transfer function num/den or transfer matrix (column vector) when flag 'all' is given. |
| den | : polynomial or vector of polynomials, contains the denominator(s) of the solution(s) |
| num | : polynomial or vector of polynomials, contains the numerator(s) of the solution(s) |
| err | : real constant or vector , the l2-error achieved for each solutions |
[den,num,err]=arl2(y,den0,n [,imp]) finds a pair of polynomials num and den such that the transfer function num/den is stable and its impulse response approximates (with a minimal l2 norm) the vector y assumed to be completed by an infinite number of zeros.
If y(z) = y(1)(1/z)+y(2)(1/z^2)+ ...+ y(ny)(1/z^ny)
then l2-norm of num/den - y(z) is err.
n is the degree of the polynomial den.
The num/den transfer function is a L2 approximant of the Fourier's series of the rational system.
Various intermediate results are printed according to imp.
[den,num,err]=arl2(y,den0,n [,imp],'all') returns in the vectors of polynomials num and den a set of local optimums for the problem. The solutions are sorted with increasing errors err. In this case den0 is already assumed to be poly(1,'z','c')
v=ones(1,20);
xbasc();
plot2d1('enn',0,[v';zeros(80,1)],2,'051',' ',[1,-0.5,100,1.5])
[d,n,e]=arl2(v,poly(1,'z','c'),1)
plot2d1('enn',0,ldiv(n,d,100),2,'000')
[d,n,e]=arl2(v,d,3)
plot2d1('enn',0,ldiv(n,d,100),3,'000')
[d,n,e]=arl2(v,d,8)
plot2d1('enn',0,ldiv(n,d,100),5,'000')
[d,n,e]=arl2(v,poly(1,'z','c'),4,'all')
plot2d1('enn',0,ldiv(n(1),d(1),100),10,'000')
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