Topic 10.5: Polynomials (Engineering Application)

Suppose a linear system which takes an input signal x(t) and converts it into an output signal y(t) according to the ordinary differential equation:

y⁽²⁾(t) + 2y⁽¹⁾(t) + 3y(t) = 4x⁽¹⁾(t) + 5x(t)

then the transfer function is defined by the rational polynomial (a ratio of two polynomials):

The properties of this linear system are defined by the location of the roots of the denominator of this polynomial, in this case, -1 ± 1.414213562j.