Question

What is the condition on the system function of a linear phase filter?

(a) H(z)=\(z^{-N} H(z^{-1})\)

(b) H(z)=\(z^N H(z^{-1})\)

(c) H(z)=\(±z^N H(z^{-1})\)

(d) H(z)=\(±z^{-N} H(z^{-1})\)

The question was posed to me during an interview for a job.

Question is from Design of IIR Filters from Analog Filters topic in section Digital Filters Design of Digital Signal Processing

Answer 1

The correct answer is (d) H(z)=\(±z^{-N} H(z^{-1})\)

The best I can explain: A linear phase filter must have a system function that satisfies the condition

H(z)=\(±z^{-N} H(z^{-1})\)

where z^(-N) represents a delay of N units of time.