Data-path accuracy in IIR filters?
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From: robert bristow-johnson on 1 Aug 2010 09:34 On Aug 1, 5:53 am, Rune Allnor <all...(a)tele.ntnu.no> wrote: > On 1 Aug, 09:53, spop...(a)speedymail.org (Steve Pope) wrote: > > > Rune Allnor <all...(a)tele.ntnu.no> wrote: > > > >On 1 Aug, 05:10, spop...(a)speedymail.org (Steve Pope) wrote: > > >> "latticema" -- all-zero filter > > >> "latticear" -- all-pole filter > > >> "latticearma" -- filter with both poles and zeros > > >> Steve > > >Sorry - I got you wrong from the start. I had you down as knowing > > >your DSP. This reveals your true guise as a mere matlab user. > > > Sigh. You're grasping at straws. > > I'm not. Matlab has a very poor repurtation as academic > reference. They used to estimate the length / duration of > the impulse response of IIR filters as the number of > numerator coefficients in the transfer functions (which > works for FIR filters). Their IIR filter design procedures > were screwed up to the point where one needed to 'unteach' > students the matlab blunders before one could teach how > things really were doing. Iterative methods like the > Levinson recursion required users to supply 'true' AR > orders up front, as opposed to supplying a *maximum* order > and then use some order estimator within those constraints. > > At least that was the status when I last used the SP > toolbox around 2004, and had been the status in the 15 years > prior to that time. I know the SP toolbox has been reworked > since then, but I doubdt that more than two decades worth > of flaws, blunders and mistakes are corrected in a hurry. they could begin to fix the blunder of putting the DC component of the fft into X(1). r b-j
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: Steve Pope on 1 Aug 2010 14:48 Rune Allnor <allnor(a)tele.ntnu.no> wrote: >On 1 Aug, 09:53, spop...(a)speedymail.org (Steve Pope) wrote: >> Rune Allnor �<all...(a)tele.ntnu.no> wrote: >> >On 1 Aug, 05:10, spop...(a)speedymail.org (Steve Pope) wrote: >> >> "latticema" -- all-zero filter >> >> "latticear" -- all-pole filter >> >> "latticearma" -- filter with both poles and zeros >> >Sorry - I got you wrong from the start. I had you down as knowing >> >your DSP. This reveals your true guise as a mere matlab user. >> Sigh. �You're grasping at straws. >I'm not. Matlab has a very poor repurtation as academic >reference. Possibly, but their descriptions of these topologies (which which you were unfamiliar despite your claimed experience in filter design) are correct, which is why I referred to them. >They used to estimate the length / duration of >the impulse response of IIR filters as the number of >numerator coefficients in the transfer functions (which >works for FIR filters). Their IIR filter design procedures >were screwed up to the point where one needed to 'unteach' >students the matlab blunders before one could teach how >things really were doing. Iterative methods like the >Levinson recursion required users to supply 'true' AR >orders up front, as opposed to supplying a *maximum* order >and then use some order estimator within those constraints. > >At least that was the status when I last used the SP >toolbox around 2004, and had been the status in the 15 years >prior to that time. I know the SP toolbox has been reworked >since then, but I doubdt that more than two decades worth >of flaws, blunders and mistakes are corrected in a hurry. This is nice background material, but you are sidestepping acknowledging that the particular topology I referred to, the "lattice ARMA" with both poles and zeros, it not unstable based on the location of the zeros. It seems you've painted yourself into a corner dude. 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 1 Aug 2010 15:33
Rune Allnor <allnor(a)tele.ntnu.no> wrote: >On 1 Aug, 20:42, spop...(a)speedymail.org (Steve Pope) wrote: >> Rune wrote, >>>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. I just found it a bit amusing that you wanted me to furnish a proof of my statements, but for your statements it's okay for you to point to a textbook. >> 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. It was Tim who asked about where this topology was documented since it didn't seems to be in the textbooks he had at hand. It was then that I committed the Evil of pointing to a Mathworks document. I did not give them an unqualified endorsement; I said "something like the Mathworks Filter Design Toolbox has a passable explanation of this topology." I then later posted an exact link. I now feel like I'm in a "no good deed goes unpunished" situation. :-) Tangentially, many textbooks are full of errors also. Steve |