Question

The denominator polynomial in a transfer function may not have any missing terms between the highest and the lowest degree, unless?

(a) all odd terms are missing

(b) all even terms are missing

(c) all even or odd terms are missing

(d) all even and odd terms are missing

The question was posed to me by my school teacher while I was bunking the class.

I'd like to ask this question from Hurwitz Polynomials in division Elements of Realizability and Synthesis of One-Port Networks of Network Theory

Answer 1

Correct answer is (c) all even or odd terms are missing

Explanation: All the quotients in the polynomial P(s) are positive. The denominator polynomial in a transfer function may not have any missing terms between the highest and the lowest degree, unless all even or odd terms are missing.For example P(s) = s^3+3s is Hurwitz because all quotient terms are positive and all even terms are missing.