Data-path accuracy in IIR filters?
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From: Rune Allnor on 31 Jul 2010 03:11 On 30 Jul, 18:31, spop...(a)speedymail.org (Steve Pope) wrote: > Rune Allnor <all...(a)tele.ntnu.no> wrote: > > > > > > >On 30 Jul, 01:42, Tim Wescott <t...(a)seemywebsite.com> wrote: > >> On 07/29/2010 12:47 PM, Steve Pope wrote: > >> > You can do this, or you can use a lattice topology > >> I did a quick search on "digital lattice filter" and didn't come up with > >> any really coherent discussion. There was lots of stuff about how to > >> use this or that lattice filter in this or that specialized application, > >> but not "this is DF1, this is DF2, this is a digital lattice filter...". > >> Got any references? > >These filters are treated in medium / advanced level > >DSP books, like Proakis & Manolakis. Don't think the > >term 'lattice filter' is too common, though; rather > >'lattice structure' or 'lattice ladder structure'. > >I am not sure they are worth a general discussion: > >The problem is that the lattice structure fuses both > >the FIR and its IIR inverse, so if the FIR has zeros on > >or outside the unit circle, the computations blow up. > > I do not think this is a problem in practice. The FIR > form of any topology is stable; the IIR form of the lattice > topology is unconditionally stable if the coefficients are > in the range (-1,1) My library is unavailable for the moment, so I can't look it up, but as I remember it this constraint is equivalent to the zeros of the FIR being inside the unit circle. The lattice factors are equivalent to the reflection coefficients that pop out from the Levinson recursion, right? > and you are using saturating arithmetic. > This latter fact makes them very useful in implementation, > because (almost) any IIR filter you would want to implement > satisfies this constraint. Would *want* to implement? If I am right about the zeros, that would require a competent designer / user of the filter. Would you risk a design of yours, on some of your students or clients making that call...? Rune
From: Steve Pope on 31 Jul 2010 04:05 Rune Allnor <allnor(a)tele.ntnu.no> wrote: >On 30 Jul, 18:31, spop...(a)speedymail.org (Steve Pope) wrote: >> I do not think this is a problem in practice. �The FIR >> form of any topology is stable; the IIR form of the lattice >> topology is unconditionally stable if the coefficients are >> in the range (-1,1) >My library is unavailable for the moment, so I can't look it >up, but as I remember it this constraint is equivalent to >the zeros of the FIR being inside the unit circle. The lattice >factors are equivalent to the reflection coefficients that pop >out from the Levinson recursion, right? Yes, they are. >> and you are using saturating arithmetic. >> This latter fact makes them very useful in implementation, >> because (almost) any IIR filter you would want to implement >> satisfies this constraint. >Would *want* to implement? If I am right about the zeros, >that would require a competent designer / user of the filter. >Would you risk a design of yours, on some of your students >or clients making that call...? I think you're referring to the filter being user-programmable. If the range of the coefficients is limited to (-1,1), then it is stable. It's pretty straightforward to build this range limit into an implementation. This may not keep the user from programming a useless transfer function into the filter, but it will keep them from creating an unstable filter that oscillates. (You may be addressing some other aspect of the situation, but if so, I'm not picking up on what you're saying.) Steve
From: Rune Allnor on 31 Jul 2010 05:09 On 31 Jul, 10:05, spop...(a)speedymail.org (Steve Pope) wrote: > Rune Allnor <all...(a)tele.ntnu.no> wrote: > > >On 30 Jul, 18:31, spop...(a)speedymail.org (Steve Pope) wrote: > >> I do not think this is a problem in practice. The FIR > >> form of any topology is stable; the IIR form of the lattice > >> topology is unconditionally stable if the coefficients are > >> in the range (-1,1) > >My library is unavailable for the moment, so I can't look it > >up, but as I remember it this constraint is equivalent to > >the zeros of the FIR being inside the unit circle. The lattice > >factors are equivalent to the reflection coefficients that pop > >out from the Levinson recursion, right? > > Yes, they are. > > >> and you are using saturating arithmetic. > >> This latter fact makes them very useful in implementation, > >> because (almost) any IIR filter you would want to implement > >> satisfies this constraint. > >Would *want* to implement? If I am right about the zeros, > >that would require a competent designer / user of the filter. > >Would you risk a design of yours, on some of your students > >or clients making that call...? > > I think you're referring to the filter being user-programmable. > If the range of the coefficients is limited to (-1,1), then > it is stable. It's pretty straightforward to build this range > limit into an implementation. This may not keep the user > from programming a useless transfer function into the filter, > but it will keep them from creating an unstable filter > that oscillates. > > (You may be addressing some other aspect of the situation, but > if so, I'm not picking up on what you're saying.) I'm referring to what I interpret to be the constraint of FIR zeros to stay inside the unit circle. Being able to use such a filter requires an amount of knowledge and competence on behalf of the user that I would not rely on. The xonstraint only changes the questionfrom "Why is my lattice structure linear phase FIR numerically unstable?" to "Why can't I implement the linear phase FIR as a lattice structure?" OK, you as system designer might have prevented your client from cooking up a disaster, but you are still left with a wining client. Rune
From: gretzteam on 31 Jul 2010 13:12 >Rune Allnor <allnor(a)tele.ntnu.no> wrote: > >>These filters are treated in medium / advanced level >>DSP books, like Proakis & Manolakis. Don't think the >>term 'lattice filter' is too common, though; rather >>'lattice structure' or 'lattice ladder structure'. > >Also, I'm pretty sure the "wave filters" or "wave lattice filters" >are not closely related to (what I am calling) a lattice filter >or lattice structure. > >"lattice-ladder" specifically refers to the topology of this >family that gives you both poles and zeros. > > >Steve > Hmmm now I realize that the wave filter is not the same as what is commonly called a 'lattice-structure' filter. I always think of a 'wave' filter as being a sum of parallel/series connections of 1st or 2nd order allpass section. It would be nice to have a good textbook reference that covers all those structures with their differences. Dave
From: Rune Allnor on 31 Jul 2010 13:28
On 31 Jul, 19:12, "gretzteam" <gretzteam(a)n_o_s_p_a_m.yahoo.com> wrote: > Hmmm now I realize that the wave filter is not the same as what is commonly > called a 'lattice-structure' filter. I always think of a 'wave' filter as > being a sum of parallel/series connections of 1st or 2nd order allpass > section. > It would be nice to have a good textbook reference that covers all those > structures with their differences. This one should get you started: http://www.amazon.com/Digital-Signal-Processing-ebook/dp/B0013OOD5U/ref=sr_1_3?ie=UTF8&m=A19GEMKTSHS1KO&s=digital-text&qid=1280597142&sr=8-3 My copy is unavailable these days so I can't look it up, but the amazon page suggests it contains a dicussion of wave filters. Rune |