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linear phase IIR filter

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royvn

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Condition for a FIR filter to be linear phase is very popular, i.e. its coefficients must be symmetric or antisymmetric, but for IIR filters it's not so obvious.

Could anyone tell me what makes an IIR filter linear phase?

Thanx.
 

Theoretically IIR filter can not have linear phase.
But there are many papers about designing near-linear phase IIR filters.
 

although IIR filter is not linear phase, but in face you only care your interested band. And most IIR filter can keep near linear in your interested band, although tthere must be nonlinear in all band.

You can see a bessel IIR filter, in 0 to fs/s band it is not linear, but in 0 to fs/10 it can be looked as linear.
 

Thanks guys.

More specifically, I will limit the filters to real coefficients ones. It is obvious that if numerator and denominator (of the IIR transfer function) are linear phase FIRs, then the resulting IIR is linear phase (I don't want to talk about stability or causality at this moment).

But I don't think the inverse is correct, a linear IIR transfer function may consists of 2 nonlinear FIR polynomials (in a way such that the phase difference between them is linear). Anyone knows the GENERAL sufficient condition for an IIR filter being linear phase?

Thans a bunch.
 

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