From: Steve Pope on
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
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
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