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:

A(z)=a(1)+a(2)z1++a(m+1)zm.

Examples

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Convert Linear-Phase Filter to Minimum-Phase

Use the window method to design a 25th-oder FIR filter with normalized cutoff frequency $0.4\pi$ rad/sample. Verify that it has linear phase but not minimum phase.

h = fir1(25,0.4);

h_linphase = islinphase(h)
h_minphase = isminphase(h)
h_linphase =

     1


h_minphase =

     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_minphase = isminphase(hmin)

hfvt = fvtool(h,1,hmin,1,'Analysis','phase');
legend(hfvt,'h','hmin')
hmin_linphase =

     0


hmin_minphase =

     1

Verify that the two filters have identical magnitude responses.

hfvt = fvtool(h,1,hmin,1);
legend(hfvt,'h','hmin')

More About

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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);

See Also

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