On 13 Jun, 20:22, robert bristow-johnson <r...@audioimagination.com> wrote:> On Jun 13, 11:53�am, Rune Allnor <all...@tele.ntnu.no> wrote:> > So what is *your* contribution here? You started out by > > claiming that you and RBJ have shown that the 1/sqrt(1+jw) > > filter is minimum phase. Now you refer everything to this > > paper by Kasdin. > > i'm not making any claims for discovery.I know, and please note that I don't address you or your opinions here, nor do I look for any quarrel or skirmish with you. I address Andor's various claims. As much as I would like to keep others out of this, I had to mention your name because he did.>�i don't even know if Andor > is, but i don't speak for him. �Well, he both makes the claim as well as speaks for you. In one of his first posts in this thread, http://groups.google.no/group/comp.dsp/msg/7443e0ed644b858f?hl=no he writes "The fact that the operator H [=1/sqrt(jw)] is minimum- phase was pieced together by rb-j and me here in comp.dsp." As for my own opinions on minimum phase properties for H(w) on irrational form, I can not express them any clearer than I did in my first reply in the thread you referred to. Rune
Determing whether or not a filter is minimum phase
Started by ●June 11, 2008
Reply by ●June 13, 20082008-06-13
Reply by ●June 13, 20082008-06-13
On Jun 13, 2:47�pm, Rune Allnor <all...@tele.ntnu.no> wrote:> On 13 Jun, 20:22, robert bristow-johnson <r...@audioimagination.com> > wrote:...> > >�i don't even know if Andor > > is, but i don't speak for him. � > > Well, he both makes the claim as well as speaks for you. > In one of his first posts in this thread, > > http://groups.google.no/group/comp.dsp/msg/7443e0ed644b858f?hl=no > > he writes > > "The fact that the operator H [=1/sqrt(jw)] is minimum- > phase was pieced together by rb-j and me here in comp.dsp."well, as far as i can tell, Andor is accurate in saying this, but i had to go back to the Nov 2007 thread and re-read it because my brain is mush and i can't seem to remember anything. i didn't take that for Andor "speaking for me". ocassionally, when the topic becomes oversampling and linear (or polynomial) interpolation, i have referred to a paper that Duane Wise and i did. Duane has never hung around here (that i know of), but i don't think in me referring to something Duane and i did together a decade ago counts as me "speaking for" him. back then, he posed a question about the minimum-phasiness of this "half-pole" filter, and with a crude, hand-wavey, not-very-rigorous "proof", i think we came to the conclusion that yes, it is min phase (even though i don't know where the poles and zeros are, but if it had 'em, they would be in the left half-plane). i just wanted to make it clear that i, for one, do not take any credit for any originality (or even salience) of what Andor and i "pieced together". but that's me, Andor is free to make a different claim, i don't speak for him. i try to mean only what i say and i try to say only what i mean (but i don't always succeed). r b-j
Reply by ●June 16, 20082008-06-16
robert bristow-johnson wrote:> On Jun 13, 2:47�pm, Rune Allnor wrote: > > > > > > > On 13 Jun, 20:22, robert bristow-johnson > > wrote: > ... > > > >�i don't even know if Andor > > > is, but i don't speak for him. � > > > Well, he both makes the claim as well as speaks for you. > > In one of his first posts in this thread, > > >http://groups.google.no/group/comp.dsp/msg/7443e0ed644b858f?hl=no > > > he writes > > > "The fact that the operator H [=1/sqrt(jw)] is minimum- > > phase was pieced together by rb-j and me here in comp.dsp." > > well, as far as i can tell, Andor is accurate in saying this, but i > had to go back to the Nov 2007 thread and re-read it because my brain > is mush and i can't seem to remember anything. �i didn't take that for > Andor "speaking for me". �ocassionally, when the topic becomes > oversampling and linear (or polynomial) interpolation, i have referred > to a paper that Duane Wise and i did. �Duane has never hung around > here (that i know of), but i don't think in me referring to something > Duane and i did together a decade ago counts as me "speaking for" him. > > back then, he posed a question about the minimum-phasiness of this > "half-pole" filter, and with a crude, hand-wavey, not-very-rigorous > "proof", i think we came to the conclusion that yes, it is min phase > (even though i don't know where the poles and zeros are, but if it had > 'em, they would be in the left half-plane).I guess one of Rune's problem is the definition of a minimum-phase system. Is it one where all the poles and zeros have to lie in the left half-plane (as Rune suggests and consequently complains that thus minimum-phasedness does not apply to non-rational systems), or is a system minimum-phase iff the log magnitude and the phase are a Hilbert transform pair? The latter definition, as my example shows, is more general. When applied to rational type systems, it reduces to the first.> > i just wanted to make it clear that i, for one, do not take any credit > for any originality (or even salience) of what Andor and i "pieced > together". �but that's me, Andor is free to make a different claim, i > don't speak for him. �i try to mean only what i say and i try to say > only what i mean (but i don't always succeed).Nobody is making any claims to originality, and this "result" is too trivial to publish. But it might be worth it to compress the whole thread into a neatly written "homework" format for later reference. There are quite a few characterizations of minimum-phaseedness (remember the energy concentration in the impulse response?), and there are discrete- and continuous-time systems to consider. There is also the P&M definition of a discrete-time minimum-phase system over the values of the phase response at w=0 and pi. Perhaps it would be worth a blog entry... Regards, Andor
Reply by ●June 16, 20082008-06-16
On 16 Jun, 10:07, Andor <andor.bari...@gmail.com> wrote:> robert bristow-johnson wrote: > > On Jun 13, 2:47�pm, Rune Allnor wrote: > > > > On 13 Jun, 20:22, robert bristow-johnson > > > wrote: > > ... > > > > >�i don't even know if Andor > > > > is, but i don't speak for him. � > > > > Well, he both makes the claim as well as speaks for you. > > > In one of his first posts in this thread, > > > >http://groups.google.no/group/comp.dsp/msg/7443e0ed644b858f?hl=no > > > > he writes > > > > "The fact that the operator H [=1/sqrt(jw)] is minimum- > > > phase was pieced together by rb-j and me here in comp.dsp." > > > well, as far as i can tell, Andor is accurate in saying this, but i > > had to go back to the Nov 2007 thread and re-read it because my brain > > is mush and i can't seem to remember anything. �i didn't take that for > > Andor "speaking for me". �ocassionally, when the topic becomes > > oversampling and linear (or polynomial) interpolation, i have referred > > to a paper that Duane Wise and i did. �Duane has never hung around > > here (that i know of), but i don't think in me referring to something > > Duane and i did together a decade ago counts as me "speaking for" him. > > > back then, he posed a question about the minimum-phasiness of this > > "half-pole" filter, and with a crude, hand-wavey, not-very-rigorous > > "proof", i think we came to the conclusion that yes, it is min phase > > (even though i don't know where the poles and zeros are, but if it had > > 'em, they would be in the left half-plane). > > I guess one of Rune's problem is the definition of a minimum-phase > system. Is it one where all the poles and zeros have to lie in the > left half-plane (as Rune suggests and consequently complains that thus > minimum-phasedness does not apply to non-rational systems),That's the context where 'minimum phase' is discussed in all the textbooks I have seen. If you can come up with a reference to suggest otherwise I would like to know of it.> or is a > system minimum-phase iff the log magnitude and the phase are a Hilbert > transform pair?That may or may not be the case. I have only seen this approach in comp.dsp posts by RBJ. Again, if somebody can come up with a reference to where this result is *proved*, I would like to see it.> The latter definition, as my example shows, is more > general. When applied to rational type systems, it reduces to the > first.Maybe so, but the hardly matters unless it can be proven to be correct?> > i just wanted to make it clear that i, for one, do not take any credit > > for any originality (or even salience) of what Andor and i "pieced > > together". �but that's me, Andor is free to make a different claim, i > > don't speak for him. �i try to mean only what i say and i try to say > > only what i mean (but i don't always succeed). > > Nobody is making any claims to originality,You could have fooled me. Steven Smith asked for references to support a claim in your first post in this thread, your response was as quoted above. If you have other references I would like to know about them.> and this "result" is too > trivial to publish.Well, it breaks out of all the standard confinements in standard DSP and systems control texts, which only deal with rational systems. That means that one of two situations has appeared: 1) You have not seen some basic problem with your approach, which everybody else who have worked with such questions for at least half a century have noted 2) You have seen a way around some basic problem which have confined everybodye else who have worked with such questions for at least half a century If you are wrong, everybody who want to know about these things would like to be aware of it. If you are correct, it would mean that a whole new field of theory is open to exploitation, and so everybody who want to know about these things would like to be aware of it. Your result might be trivial, but it might still be worth publishing. Rune
Reply by ●June 16, 20082008-06-16
On 16 Jun, 10:29, Rune Allnor <all...@tele.ntnu.no> wrote:> On 16 Jun, 10:07, Andor <andor.bari...@gmail.com> wrote:> > or is a > > system minimum-phase iff the log magnitude and the phase are a Hilbert > > transform pair? > > That may or may not be the case. I have only seen this > approach in comp.dsp posts by RBJ. Again, if somebody > can come up with a reference to where this result is > *proved*, I would like to see it.I did some research and found a proof in the Oppenheim & Schafer 1975 book, section 10.5.3. They use the Hilbert transform relation between the Log Magnitude and Phase spectrum to find a causal minimum phase sequence from the real cepstrum. That makes a lot of sense, since that approach circumvents any messy dealings with the phase spectrum in che complex cepstrum.> > The latter definition, as my example shows, is more > > general.That's *your* claim which you will need to prove.> > When applied to rational type systems, it reduces to the > > first.Interestingly, O&S start out the discussion based on a system function on rational form (O&S, 1975, page 503, un-numbered equation above eq. 10.46a). So the rational system model is stated when deriving the Hilbert tranform approach, meaning that one can not just apply the approach to a irrational function and expect useful results. ...> Well, it breaks out of all the standard confinements > in standard DSP and systems control texts, which only > deal with rational systems. That means that one of two > situations has appeared: > > 1) You have not seen some basic problem with your > � �approach, which everybody else who have worked with > � �such questions for at least half a century have > � �noted > 2) You have seen a way around some basic problem > � �which have confined everybodye else who have > � �worked with such questions for at least half > � �a centuryJust to clarify a poor formulation: It is the research community as such which has addressed these questions for decades, not individuals. Rune
Reply by ●June 16, 20082008-06-16
Andor <andor.bariska@gmail.com> writes:> [...] > Perhaps it would be worth a blog entry...Or maybe a DSP Tips and Tricks article? -- % Randy Yates % "My Shangri-la has gone away, fading like %% Fuquay-Varina, NC % the Beatles on 'Hey Jude'" %%% 919-577-9882 % %%%% <yates@ieee.org> % 'Shangri-La', *A New World Record*, ELO http://www.digitalsignallabs.com
Reply by ●June 16, 20082008-06-16
On 16 Jun, 13:36, Randy Yates <ya...@ieee.org> wrote:> Andor <andor.bari...@gmail.com> writes: > > [...] > > Perhaps it would be worth a blog entry... > > Or maybe a DSP Tips and Tricks article?Rick would, of course, have the last word on that particular question, but I can't see that this discussion is at all relevant to that column: - The subject is too mathematical (which is an almost decisive argument against discussing this in that column) - The column is not peer reviewed (there is too much mathemathical fuzzyness to leave Andor's argument as is without serious scrutiny) - The 'result' is not practically useful (that I can see) - The result seems to be plain wrong (ref my post on the O&S 1975 treatise of the HT approach to minimum phase systems). Of course, I haven't looked into this in quite as much detail as Andor, which is why I still think he should publish his argument in the IEEE Transactions on Signal Processing, where the competent mathemathicians will have ample oportunity to review the arguments. Rune
Reply by ●June 16, 20082008-06-16
On Jun 11, 2:54 pm, "alexryu" <ryu.a...@gmail.com> wrote:> Hello all > I have a filter I inherited from someone else (long gone) that is supposed > to be minimum phase but I would like to make sure. Could someone please > tell me the best way to do this? The filter is rather long (~500). Is the > only method to use a generic polynomial root-finding algorithm, see where > the zeros lie, and pray for stability/convergence?What property of a minimum phase filter are you looking for? With 500 coefficients, even quad precision FP coefficients likely can not approximate the originally intended filter with sufficient accuracy for the actual resulting filter to meet any precise and exact minimum phase criteria. I would instead look for the desired properties that your requirement for minimum phase would imply, and see if your filter is close enough to that desired design criteria, given your existing numerical precision. . IMHO. YMMV. -- rhn A.T nicholson d.0.t C-o-M http://www.nicholson.com/rhn/dsp.html
