Question

If the filter is in linear phase, then filter would have a mirror-image pole outside the unit circle for every pole inside the unit circle.

(a) True

(b) False

I had been asked this question in an interview.

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

Answer 1

The correct option is (a) True

For explanation: For a linear phase filter, we know that

H(z)=\(±z^{-N} H(z^{-1})\)

where z^(-N) represents a delay of N units of time. But if this were the case, the filter would have a mirror image pole outside the unit circle for every pole inside the unit circle. Hence the filter would be unstable.