Signal Processing Toolbox

polystab

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) returns a row vector b containing the stabilized polynomial, where a is a vector of polynomial coefficients, normally in the z-domain.

Examples

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);
  

See Also

roots

polyscale

prony