polystab (Signal Processing Toolbox)

Stabilize polynomial.

Syntax

b = polystab(a)

Description

polystab stabilizes a polynomial with respect to the unit circle; it reflects roots with magnitudes greater than 1 inside the unit circle.

b = polystab(a)

where a is a vector of polynomial coefficients normally in the z-domain:

returns a row vector containing the stabilized polynomial.

Example

polystab can convert a linear-phase filter into a minimum-phase filter with the same magnitude response:

h = fir1(25,0.4);
hmin = polystab(h)*norm(h)/norm(polystab(h));

Algorithm

polystab finds the roots of the polynomial and maps those roots found outside the unit circle to the inside of the unit circle:

v = roots(a);
vs = 0.5*(sign(abs(v)-1)+1);
v = (1-vs).*v + vs./conj(v);
b = a(1)*poly(v);