Question

The roots of the polynomial H(z) are identical to the roots of the polynomial H(z^-1).

(a) True

(b) False

The question was asked in an online interview.

The doubt is from Design of FIR Filters topic in section Digital Filters Design of Digital Signal Processing

Answer 1

Correct answer is (a) True

To explain: We know that z^-(M-1).H(z^-1)=±H(z). This result implies that the roots of the polynomial H(z) are identical to the roots of the polynomial H(z^-1).