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. a is
a vector of polynomial coefficients, normally in the z-domain:
Examples
Convert Linear-Phase Filter to Minimum-Phase
Use the window method to design a 25th-oder FIR filter with normalized cutoff frequency rad/sample. Verify that it has linear phase but not minimum phase.
h = fir1(25,0.4); h_linphase = islinphase(h)
h_linphase = logical
1
h_minphase = isminphase(h)
h_minphase = logical
0
Use polystab to convert the linear-phase filter into a minimum-phase filter. Plot the phase responses of the filters.
hmin = polystab(h)*norm(h)/norm(polystab(h)); hmin_linphase = islinphase(hmin)
hmin_linphase = logical
0
hmin_minphase = isminphase(hmin)
hmin_minphase = logical
1
hfvt = fvtool(h,1,hmin,1,'Analysis','phase'); legend(hfvt,'h','hmin')
Verify that the two filters have identical magnitude responses.
hfvt = fvtool(h,1,hmin,1); legend(hfvt,'h','hmin')
Algorithms
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);