POLYSTAB

Purpose:

Reflects polynomial roots located outside the unit circle to the inside.

Syntax:

POLYSTAB(a)

A series or matrix. The polynomial coefficients in descending order.

Returns:

A series, the coefficients of the reflected polynomial.

Example:

W1: {1, -2, 5}

W2: polystab(W1)

W3: zplane({1}, W1)

W4: zplane({1}, W2)

W1 represents the coefficients of the polynomial:

$image\polys01.gif$

The roots of the polynomial are 1 + 2i and 1 – 2i, outside the unit circle. If these coefficients represent the denominator polynomial of a digital system, the system is unstable.

W2 == {1, -.4, .2}, the coefficients of the reflected polynomial. The roots of this polynomial are 0.2 + 4i, 0.2 - 4i, inside the unit circle. If the coefficients represent the denominator polynomial of a digital system, the system is stable.

W3 and W4 graphically show the pole locations with respect to the unit circle.

Remarks:

POLYSTAB replaces the roots of a polynomial that lie outside the unit circle with roots that are inside the unit circle. Typically, the input series represents the coefficients of the following digital system:

$image\polys02.gif$