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From: itsh11 on 18 Jun 2008 08:34
I want to design an IIR notch filter with linear phase. It is pretty
straight forward to design the IIR notch filter but I am not sure how to
design the phase compensator(all pass IIR filter) that makes the overall
phase of the system linear phase. Can someone throw a few pointers on this
design? Many thanks


From: Andor on 18 Jun 2008 08:44
itsh11 wrote:
> I want to design an IIR notch filter with linear phase. It is pretty
> straight forward to design the IIR notch filter but I am not sure how to
> design the phase compensator(all pass IIR filter) that makes the overall
> phase of the system linear phase. Can someone throw a few pointers on this
> design? Many thanks

It depends how linear the phase response has to be. There are
approximative rational transfer function phase-equalizers (IIR and
FIR), but stability and accuracy is usually a problem.

One approach is forwards-backwards filtering. This squares the
amplitude response and cancels the phase response of the filter. It is
particularly simple to implement for offline filtering applications.
For an online implementation search for the Powell / Chau algorithm.
You will need lots of memory because notch filters typically have long
impulse responses. At this point you might consider the FIR
alternative, with about equal memory constraints, higher
computational cost but much lower algorithm complexity (a DSP one
liner :-).

Regards,
Andor

From: Rune Allnor on 18 Jun 2008 08:51
On 18 Jun, 14:34, "itsh11" <its...(a)yahoo.com> wrote:
> I want to design an IIR notch filter with linear phase.

Can't be done.

> It is pretty
> straight forward to design the IIR notch filter but I am not sure how to
> design the phase compensator(all pass IIR filter) that makes the overall
> phase of the system linear phase.

That's no surprise, because it can't be done. For a
filter to be linear phase, the impulse response has
to be symmetric. Since your notch filter is IIR,
it measn that you will need an IIR anticausal
component of the impulse response.

The best you can do with your aproach, is to make
an allpass filter which corrects for the phase
'sufficiently well' but which does *not* give an
exactly linear phase.

Another option is to make FIR notch filter. It can
be made linear phase, but you will not have much
control over the shape of the notch.

Rune
From: Jerry Avins on 18 Jun 2008 12:50
itsh11 wrote:
> I want to design an IIR notch filter with linear phase. It is pretty
> straight forward to design the IIR notch filter but I am not sure how to
> design the phase compensator(all pass IIR filter) that makes the overall
> phase of the system linear phase. Can someone throw a few pointers on this
> design? Many thanks

You can at best approximate what you want. Sharp notch filters have
steep phase characteristics. How wide a useful band do you need?

Jerry
--
Engineering is the art of making what you want from things you can get.
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