Data-path accuracy in IIR filters?
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From: Steve Pope on 1 Aug 2010 14:42 Rune Allnor <allnor(a)tele.ntnu.no> wrote: >On 1 Aug, 09:50, spop...(a)speedymail.org (Steve Pope) wrote: >> Personally I am satisfied with this well-known fact from filter theory, >> I feel that the literature is strong enough, and I do not feel on the >> hook to come up with a proof. >Again, I obviously had you wrong. This is a bout maths and >engineering, >not emotions. If you don't 'feel' up to substantiating your position, >don't challenge the points made. Sorry, Rune, but it is you who has provided zero backup for your unsupported negative statements about the lattice filter topology. All I did was tell the OP it would be useful in his case. You haven't come close to explaining to us what, if any, problems there might be with it. >> You haven't supported these statements. �If there is a lattice >> topology whose stability depends upon the zero locations, please >> provide a cite for it. �(I'm sure such a think might exist. >> But it is not a mainstream topology I would think.) >This is well-known from statistichal DSP. I can't come up >with specifc citations, as my library is is storage and >will remain there for a few weeks to come, Ha! >but I will >tell you what to look for. I know this is treated in the >Proakis & Manolakis general DSP text: > >When dealing with AR models, one can solve the Yule-Walker >equations (or rather, and estimator for these equations) >in any number of ways. Direct solutions through linear algebra >will give you the straight-forward FIR prediction filter; the >Levinson recursion will also give you the reflection coefficients >that go directly into the lattice representation. > >As one would expect, there exist conversion formulae between >the FIR and lattice representations for the AR model: Insert a >set of FIR coefficients and crank out a set of lattice coefficients. >And vice versa. > >The problem is the implicit constraints. In the AR application >the FIR filter is guaranteed to be minimum phase, so its IIR >inverse is causal stable. This translates directly to the >lattice reflection coefficients being constrained to the >interval <-1,1>. > >However, the unsuspecting incompetent user who stumbles across >these conversion formulae and tries to convert a linear phase >FIR to lattice form - don't ask *why* one would want to do this; >I assume the user to be *incompetent* - would end up with a >numerically unstable FIR. Which is a contradiction in terms, >given the entry-level indoctrination matra of DSP. > >Which will only come back to haunt the designer, who exposed >the incompetent user to the lattice structure in the first place. Good, finally some information. The OP was designing a sixth-order Butterworth, not a linear phase FIR, but no matter. Steve
From: Rune Allnor on 1 Aug 2010 14:58 On 1 Aug, 20:42, spop...(a)speedymail.org (Steve Pope) wrote: > Rune Allnor <all...(a)tele.ntnu.no> wrote: > > >On 1 Aug, 09:50, spop...(a)speedymail.org (Steve Pope) wrote: > >> Personally I am satisfied with this well-known fact from filter theory, > >> I feel that the literature is strong enough, and I do not feel on the > >> hook to come up with a proof. > >Again, I obviously had you wrong. This is a bout maths and > >engineering, > >not emotions. If you don't 'feel' up to substantiating your position, > >don't challenge the points made. > > Sorry, Rune, but it is you who has provided zero backup for your > unsupported negative statements about the lattice filter topology. > All I did was tell the OP it would be useful in his case. You > haven't come close to explaining to us what, if any, problems there > might be with it. > > >> You haven't supported these statements. If there is a lattice > >> topology whose stability depends upon the zero locations, please > >> provide a cite for it. (I'm sure such a think might exist. > >> But it is not a mainstream topology I would think.) > >This is well-known from statistichal DSP. I can't come up > >with specifc citations, as my library is is storage and > >will remain there for a few weeks to come, > > Ha! Send me your credit card info, and I will order a copy of P&M - on your expense - to be delivered overnight. Everything is in there. One only needs to read it. > >but I will > >tell you what to look for. I know this is treated in the > >Proakis & Manolakis general DSP text: > > >When dealing with AR models, one can solve the Yule-Walker > >equations (or rather, and estimator for these equations) > >in any number of ways. Direct solutions through linear algebra > >will give you the straight-forward FIR prediction filter; the > >Levinson recursion will also give you the reflection coefficients > >that go directly into the lattice representation. > > >As one would expect, there exist conversion formulae between > >the FIR and lattice representations for the AR model: Insert a > >set of FIR coefficients and crank out a set of lattice coefficients. > >And vice versa. > > >The problem is the implicit constraints. In the AR application > >the FIR filter is guaranteed to be minimum phase, so its IIR > >inverse is causal stable. This translates directly to the > >lattice reflection coefficients being constrained to the > >interval <-1,1>. > > >However, the unsuspecting incompetent user who stumbles across > >these conversion formulae and tries to convert a linear phase > >FIR to lattice form - don't ask *why* one would want to do this; > >I assume the user to be *incompetent* - would end up with a > >numerically unstable FIR. Which is a contradiction in terms, > >given the entry-level indoctrination matra of DSP. > > >Which will only come back to haunt the designer, who exposed > >the incompetent user to the lattice structure in the first place. > > Good, finally some information. ....which is utterly trivial to come by if one is even moderately eductaed on DSP. > The OP was designing a sixth-order Butterworth, not a linear > phase FIR, but no matter. That was what the OP talekd about, yes. Somebody else started wining about lattice structures only being explained on a per application basis. There are very good reasons for that - one needs to know *exactly* what they are used for and why. Rune
From: Steve Pope on 2 Aug 2010 17:49 Rune Allnor <allnor(a)tele.ntnu.no> wrote: [lattice filters] >but I will >tell you what to look for. I know this is treated in the >Proakis & Manolakis general DSP text: It is. I'm back in my office today so I have Proakis & Manolakis right in front of me. In the summary at the end of Chapter 9 these authors state: "Finally we mention that lattice and lattice-ladder filter structures are known to be robust in fixed-point implementations." The is what I was attempting to commuicate to the OP for his filter problem, before the discussion got sidetracked. Steve
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