Question

If the unit sample response h(n) of the filter is real, complex valued roots need not occur in complex conjugate pairs.

(a) True

(b) False

I got this question by my college director while I was bunking the class.

My query is from Design of FIR Filters in section Digital Filters Design of Digital Signal Processing

Answer 1

Correct choice is (b) False

Easy explanation: We know that the roots of the polynomial H(z) are identical to the roots of the polynomial H(z^-1). This implies that if the unit sample response h(n) of the filter is real, complex valued roots must occur in complex conjugate pairs.