Take the 2-minute tour ×
Signal Processing Stack Exchange is a question and answer site for practitioners of the art and science of signal, image and video processing. It's 100% free, no registration required.

Please tell me. Also I dont know why phase is linear with FIR filters. I would like quantitative analysis. And why linear phase is not achieved by IIR filters ?

share|improve this question
Causal IIR filters cannot have linear phase, non-causal IIR filters can. As in $H(e^{j\omega})=e^{-j\omega\alpha}$ –  Parsa Oct 29 '14 at 2:46

2 Answers 2

The impulse response of a linear phase filter must be symmetric. If the impulse response is infinitely long, then the center of the impulse is an infinite distance away from the beginning, giving the symmetric IIR filter infinite delay.

share|improve this answer

For digital filters, linear phase places the following requirement on the transfer function:

$$ H(z) = H(z^{-1}).$$

That restriction implies a linear phase IIR filter would need to have poles both inside and outside the unit circle, making it unstable. Similar arguments apply for analog filters.

That being said, there are any number of approximations which may be "close enough" to linear phase, depending on the application--especially if the causality of filter is sacrificed. For a review of techniques, see the introduction to this paper:

S.R. Powell, P.M.Chau, A Technique for Realizing Linear-Phase IIR Filters, IEEE Trans. Signal Processing, Vol 39, No 11, Nov 1991, pp 2425-2435.

The algorithm in that paper achieves linear phase with acausal block processing, rather than the usual offline "Forward-Backward" zero-phase approach.

share|improve this answer

Your Answer


By posting your answer, you agree to the privacy policy and terms of service.

Not the answer you're looking for? Browse other questions tagged or ask your own question.