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From: Steve Pope on 31 Jul 2010 15:03 Rune Allnor <allnor (a)tele.ntnu.no> wrote:[Lattice filter topology] >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. I must say that I'm just not getting your point here. Firstly, the FIR part of such a filter is not unstable. The IIR part cannot be unstable if the coefficients are constrained within the range (-1,1), a constraint that is easily imposed by the implementation whether it be in RTL, or gates, or software/firmware. Other topologies have similar regions of instabilities for their coefficient; but they are not stated as simply. You seem to be fishing for problems specific to the lattice topology that, so far as I know, just aren't there. This is useful, normal, mundane, everday filter topology. Steve
From: Rune Allnor on 31 Jul 2010 16:20 On 31 Jul, 21:03, spop... (a)speedymail.org (Steve Pope) wrote:> Rune Allnor <all... (a)tele.ntnu.no> wrote:> > [Lattice filter topology] > > >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. > > I must say that I'm just not getting your point here. > > Firstly, the FIR part of such a filter is not unstable. > > The IIR part cannot be unstable if the coefficients are > constrained within the range (-1,1), a constraint that is > easily imposed by the implementation whether it be in RTL, > or gates, or software/firmware. Sure. You know that. I know that. But is that konwledge wide-spread? Would you trust users to depend on knowing these things? > Other topologies have similar regions of instabilities for > their coefficient; but they are not stated as simply. Wrong. The IIRs are stable subject to poles staying strictly inside the unit circle. Zeros might be everywhere, no restrictions there. FIRs are unconditionally stable, at the outset. The lattice structure represents a dobule obfuscation in that it 1) Places restrictions on FIR filter stability 2) Depends on zero locations Ano one of those restrictions would mess up the amateur's mind; the two together would play havoc with anyone in two seconds flat. Remember, the days when people actually read up on DSP before attempting to use the techniques are long since gone. You have to deal with the "Matlab does all the thinking" (TM) generation. > You seem to be fishing for problems specific to the lattice topology > that, so far as I know, just aren't there. This is useful, > normal, mundane, everday filter topology. Again, I don't have my books easily available, so with the caveat that I'm writing off years-old memories: The FIR and IIR parts are tightly coupled in the lattice structure. In effect the N'th order lattice filter does the computations in N stages, with cross-copleing between each stage: The output after *both* n'th stage filters are fed (with different scaling) as input to *both* the n+1'th stages in the lattice. As there are the same number of stages as there are poles (IIR) / zeros (FIR), the IIR part will be unconditionally unstable if there are two zeros on or outside the unit circle. Concequently, the FIR will be unstable, as input from one M order unstable IIR will be used as input to the FIR computations somewhere in the lattice. The only way I can see where one might get away ith this, is if there is exactky one unstable zero of the IIR (reflection coefficient >=1) and that the corresponding lattice section is the very last, where its output is not used as input to the FIR. If you think I am wrong, you are welcome to provide proofs to show that the lattice structure is unconditionally stable. Rune
From: Steve Pope on 31 Jul 2010 16:49 Rune Allnor <allnor (a)tele.ntnu.no> replies to my post,>> I must say that I'm just not getting your point here. >> Firstly, the FIR part of such a filter is not unstable. >> The IIR part cannot be unstable if the coefficients are >> constrained within the range (-1,1), a constraint that is >> easily imposed by the implementation whether it be in RTL, >> or gates, or software/firmware. >Sure. You know that. I know that. But is that konwledge >wide-spread? Would you trust users to depend on knowing >these things? Yes, it's as widespread as any stability criteria for any other filter topology. >> Other topologies have similar regions of instabilities for >> their coefficient; but they are not stated as simply. >Wrong. The IIRs are stable subject to poles staying >strictly inside the unit circle. Zeros might be everywhere, >no restrictions there. The same is true for a lattice topology, and for any other common topologies. >FIRs are unconditionally stable, at the outset. >The lattice structure represents a dobule obfuscation in that it >1) Places restrictions on FIR filter stability I have NO idea what you are talking about here. >2) Depends on zero locations Again, you've lost me. Your statements 1) and 2) are not true, so far as I know. >Again, I don't have my books easily available, so with the caveat >that >I'm writing off years-old memories: >The FIR and IIR parts are tightly coupled in the lattice structure. Please look at the figure on page 11-28 of this document: http://www.busim.ee.boun.edu.tr/~resources/fdq.pdf The zero location are controlled by the coefficients v1, v2.... These coefficients do not make the filter unstable. There is no "obfuscation" much less "double obfuscation". This is a perfectly normal, everyday, widely used filter with better stability behavior than most. Steve
From: Steve Pope on 31 Jul 2010 23:10 Steve Pope <spope33 (a)speedymail.org> wrote:>Please look at the figure on page 11-28 of this document: > >http://www.busim.ee.boun.edu.tr/~resources/fdq.pdf Actually, there is a somewhat better Mathworks document on the subject here: http://www.mathworks.com/access/helpdesk_r13/help/toolbox/filterdesign/propref7.html#20164 In my experience, the most useful and well behaved forms of lattice filters are termed as follows in the above: "latticema" -- all-zero filter "latticear" -- all-pole filter "latticearma" -- filter with both poles and zeros Steve
From: Rune Allnor on 1 Aug 2010 03:34
On 31 Jul, 22:49, spop... (a)speedymail.org (Steve Pope) wrote:> Rune Allnor <all... (a)tele.ntnu.no> replies to my post,> > >> I must say that I'm just not getting your point here. > >> Firstly, the FIR part of such a filter is not unstable. > >> The IIR part cannot be unstable if the coefficients are > >> constrained within the range (-1,1), a constraint that is > >> easily imposed by the implementation whether it be in RTL, > >> or gates, or software/firmware. > >Sure. You know that. I know that. But is that konwledge > >wide-spread? Would you trust users to depend on knowing > >these things? > > Yes, it's as widespread as any stability criteria for any > other filter topology. The other topologies only matter as the established baseline. We are focusing on the lattice topology here. > >> Other topologies have similar regions of instabilities for > >> their coefficient; but they are not stated as simply. > >Wrong. The IIRs are stable subject to poles staying > >strictly inside the unit circle. Zeros might be everywhere, > >no restrictions there. > > The same is true for a lattice topology, The pleas prove this statement mathematically. Up to this point you have been very persistent in restricting the reflection coefficients to the range [-1,1]. Could you pelase elaborate on what happens if the reflection coefficients stray outside that range? > >FIRs are unconditionally stable, at the outset. > >The lattice structure represents a dobule obfuscation in that it > >1) Places restrictions on FIR filter stability > > I have NO idea what you are talking about here. A lattice implementation fuses the IIR and the FIR into a common structure. That's why it is used in the AR-type perdictors: You get *both* the perdicted signal, as computed by the FIR AR predictor *and* the prediction error (as computed by the IIR predictor inverse) for a minimum ofcomputations. One constraint for this to work is that the IIR is stable. > >2) Depends on zero locations > > Again, you've lost me. Your statements 1) and 2) are not true, > so far as I know. "As far as you know." Check it out. > >Again, I don't have my books easily available, so with the caveat > >that > >I'm writing off years-old memories: > >The FIR and IIR parts are tightly coupled in the lattice structure. > > Please look at the figure on page 11-28 of this document: > > http://www.busim.ee.boun.edu.tr/~resources/fdq.pdf > > The zero location are controlled by the coefficients v1, v2.... > These coefficients do not make the filter unstable. > > There is no "obfuscation" much less "double obfuscation". This > is a perfectly normal, everyday, widely used filter with better > stability behavior than most. So why isn't it mentioned in every textbook out there? Why bother with DF I and II if the lattice works so well? Rune |