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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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Use the window method to design a 25th-oder FIR filter with normalized cutoff frequency 0.4π 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')

Figure Filter Visualization Tool - Phase Response contains an axes object and other objects of type uitoolbar, uimenu. The axes object with title Phase Response contains 2 objects of type line. These objects represent h, hmin.

Verify that the two filters have identical magnitude responses.

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

Figure Filter Visualization Tool - Magnitude Response (dB) contains an axes object and other objects of type uitoolbar, uimenu. The axes object with title Magnitude Response (dB) contains 2 objects of type line. These objects represent 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);

See Also

Introduced before R2006a