Scilab 5.5.1
Please note that the recommended version of Scilab is 2025.0.0. This page might be outdated.
See the recommended documentation of this function
sfact
discrete time spectral factorization
Calling Sequence
F=sfact(P)
Arguments
- P
real polynomial matrix
Description
Finds F, a spectral factor of
P. P is a polynomial matrix such that
each root of P has a mirror image w.r.t the unit
circle. Problem is singular if a root is on the unit circle.
sfact(P) returns a polynomial matrix
F(z) which is antistable and such that
P = F(z)* F(1/z) *z^n
For scalar polynomials a specific algorithm is implemented. Algorithms are adapted from Kucera's book.
Examples
//Simple polynomial example z=poly(0,'z'); p=(z-1/2)*(2-z) w=sfact(p); w*numer(horner(w,1/z)) //matrix example F1=[z-1/2,z+1/2,z^2+2;1,z,-z;z^3+2*z,z,1/2-z]; P=F1*gtild(F1,'d'); //P is symmetric F=sfact(P) roots(det(P)) roots(det(gtild(F,'d'))) //The stable roots roots(det(F)) //The antistable roots clean(P-F*gtild(F,'d')) //Example of continuous time use s=poly(0,'s'); p=-3*(s+(1+%i))*(s+(1-%i))*(s+0.5)*(s-0.5)*(s-(1+%i))*(s-(1-%i));p=real(p); //p(s) = polynomial in s^2 , looks for stable f such that p=f(s)*f(-s) w=horner(p,(1-s)/(1+s)); // bilinear transform w=p((1-s)/(1+s)) wn=numer(w); //take the numerator fn=sfact(wn);f=numer(horner(fn,(1-s)/(s+1))); //Factor and back transform f=f/sqrt(horner(f*gtild(f,'c'),0));f=f*sqrt(horner(p,0)); //normalization roots(f) //f is stable clean(f*gtild(f,'c')-p) //f(s)*f(-s) is p(s)
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