On Mar 8, 12:02 pm, Rune Allnor <all...@tele.ntnu.no> wrote:> On Mar 7, 11:18 pm, Andor <andor.bari...@gmail.com> wrote: > > > Interesting piece. Just a couple of questions: > > - Why not use the BLT to transfor to discrete-time domain? > I don't know Greg's stuff, I am familiar with the properties > of the BLT.I'm not sure it matters what the technique is? Surely all that matters is that a discrete-time filter is derived that has the key properties of its CT counterpart (approximately flat -ve group delay over a region with approximately flat magnitude response). The fact that the overall response is roughly the same is merely an aesthetic bonus.> - Why analyze in discrete-time domain at all? Your results > would have been seriously interesting if you could demonstrate > similar effects in continuos-time domain; here they are amusing. > - Why not use the impulse as test signal? You refer to 'some' who > 'claim' that system with negative group delays are noncausal, as > if you contest (or at least not support) such a view. I have > made such claims.How would you suggest performing the experiment in CT, short of actually building the circuit? Even circuit analysis tools have to operate in discrete time.> Your way of phrasing opens a whole new can of worms of semantic wars > etc - why not demonstarte once and for all that systems with negative > group delays exist and can be implemented in CT? (If that indeed is > your claim, of course; I could not find out from the article what > your stand on the issue is.)It would appear that he has. He's presented a circuit whose transfer function is easily derivable, and which clearly has a negative group delay over some region (as the graph demonstrates).> I would suggest the following: > > 1) Make a clear statement of the 'usual' views on the issue, > your own opinions, and exactly what this article aims > to demonstrate. > 2) Compute the phase response of the CT system function and > demonstrate that there is a negative group delay there. > If you have the tools, I would also suggest you simulate > the impulse response of that circuit in CT domain.I agree that graphs of the impulse responses would have been nice. But on the other hand, they're kind of irrelevant to the argument, as it is clear that both systems are causal!> 3) Use standard techniques in DT domain (BLT, Kronecker delta) > and repeat your analysis. > > If all the results persist (system functions show negative > group delays, anticausal behaviour) after such a re-work, I > will consider to spend some time looking into your article > in more detail.I believe the point of the article was precisely to counter the belief that -ve group delay equates to "anticausal behaviour".> > As the article stands, it only cretates confusion. A less > benevolent reviewer than me might sugest that the instability > caused by the truncated signal is caused by poles located > outside the unit circle, and thus suggest that there is a > fundamental flaw in the argument. As you know, if you can > repeat the results using standard analysis tools and from > multiple angles of attack, it will stop those sorts of > argument at the outset.Even if there were poles outside the unit circle, that wouldn't allow the system to become non-causal! The article already states that both CT and DT filters are minimum-phase. A trivial analysis of the transfer function polynomials demonstrates that they are stable. -- Oli
Negative Group Delay ... again!
Started by ●March 7, 2008
Reply by ●March 8, 20082008-03-08
Reply by ●March 8, 20082008-03-08
On Mar 8, 2:38�pm, Oli Charlesworth <ca...@olifilth.co.uk> wrote:> On Mar 8, 12:02 pm, Rune Allnor <all...@tele.ntnu.no> wrote: > > > On Mar 7, 11:18 pm, Andor <andor.bari...@gmail.com> wrote: > > > Interesting piece. Just a couple of questions: > > > - Why not use the BLT to transfor to discrete-time domain? > > � I don't know Greg's stuff, I am familiar with the properties > > � of the BLT. > > I'm not sure it matters what the technique is?It does to me. A result derived with a known, well-udnerstood technique has a far greater impact than a unfamiliar, possibly novel technique applied to a tricky question.>�Surely all that > matters is that a discrete-time filter is derived that has the key > properties of its CT counterpart (approximately flat -ve group delay > over a region with approximately flat magnitude response). �The fact > that the overall response is roughly the same is merely an aesthetic > bonus.Wrong. If the claim applies to the CT cirquit, it is the CT cirquit which must be analyzed.> > - Why analyze in discrete-time domain at all? Your results > > � would have been seriously interesting if you could demonstrate > > � similar effects in continuos-time domain; here they are amusing. > > - Why not use the impulse as test signal? You refer to 'some' who > > � 'claim' that system with negative group delays are noncausal, as > > � if you contest (or at least not support) such a view. I have > > � made such claims. > > How would you suggest performing the experiment in CT, short of > actually building the circuit? �Even circuit analysis tools have to > operate in discrete time.Derive and analyze the Laplace transform for the cirquit? All analytical, should be easy.> > Your way of phrasing opens a whole new can of worms of semantic wars > > etc - why not demonstarte once and for all that systems with negative > > group delays exist and can be implemented in CT? (If that indeed is > > your claim, of course; I could not find out from the article what > > your stand on the issue is.) > > It would appear that he has. �He's presented a circuit whose transfer > function is easily derivable, and which clearly has a negative group > delay over some region (as the graph demonstrates).Well, that's *not* what the article says. The statement "We will now proceed to find a discrete filter with comparable characteristics in order to be able to reproduce the experiment in Matlab world." can only be interpreted as if the subsequent analysis applies to the DT "comparable" system.> > I would suggest the following: > > > 1) Make a clear statement of the 'usual' views on the issue, > > � �your own opinions, and exactly what this article aims > > � �to demonstrate. > > 2) Compute the phase response of the CT system function and > > � �demonstrate that there is a negative group delay there. > > � �If you have the tools, I would also suggest you simulate > > � �the impulse response of that circuit in CT domain. > > I agree that graphs of the impulse responses would have been nice. > But on the other hand, they're kind of irrelevant to the argument, as > it is clear that both systems are causal!That's what confuses me: - I can't figure out what the claim in the article is; what is the 'usual' stand on the question and how is it contested? - What is the premise for the debate? Are we talking about CT or DT systems? Online or offline in case of DT? Causal? Stable? - What are the arguments? I don't know the Berchin method for CT->DT transform; if the claims are valid they should work just as well with the well-known BLT. - What are the conclusions? I see some graphs but because I'm completely lost in earlier stages I don't understand what they signify or what the impact is.> > 3) Use standard techniques in DT domain (BLT, Kronecker delta) > > � �and repeat your analysis. > > > If all the results persist (system functions show negative > > group delays, anticausal behaviour) after such a re-work, I > > will consider to spend some time looking into your article > > in more detail. > > I believe the point of the article was precisely to counter the belief > that -ve group delay equates to "anticausal behaviour".If so, the article would benefit greatly from a better structure and presentation.> > As the article stands, it only cretates confusion. A less > > benevolent reviewer than me might sugest that the instability > > caused by the truncated signal is caused by poles located > > outside the unit circle, and thus suggest that there is a > > fundamental flaw in the argument. As you know, if you can > > repeat the results using standard analysis tools and from > > multiple angles of attack, it will stop those sorts of > > argument at the outset. > > Even if there were poles outside the unit circle, that wouldn't allow > the system to become non-causal! �The article already states that both > CT and DT filters are minimum-phase. �A trivial analysis of the > transfer function polynomials demonstrates that they are stable.Again, that may be the case but I am not able to follow the chain of arguments to reach that conclusion. Rune
Reply by ●March 8, 20082008-03-08
On Mar 8, 2:38=A0pm, Oli Charlesworth <ca...@olifilth.co.uk> wrote:> On Mar 8, 12:02 pm, Rune Allnor <all...@tele.ntnu.no> wrote: > > > On Mar 7, 11:18 pm, Andor <andor.bari...@gmail.com> wrote: > > > Interesting piece. Just a couple of questions: > > > - Why not use the BLT to transfor to discrete-time domain? > > =A0 I don't know Greg's stuff, I am familiar with the properties > > =A0 of the BLT. > > I'm not sure it matters what the technique is?It does to me. A result derived with a known, well-udnerstood technique has a far greater impact than a unfamiliar, possibly novel technique applied to a tricky question.>=A0Surely all that > matters is that a discrete-time filter is derived that has the key > properties of its CT counterpart (approximately flat -ve group delay > over a region with approximately flat magnitude response). =A0The fact > that the overall response is roughly the same is merely an aesthetic > bonus.Wrong. If the claim applies to the CT cirquit, it is the CT cirquit which must be analyzed.> > - Why analyze in discrete-time domain at all? Your results > > =A0 would have been seriously interesting if you could demonstrate > > =A0 similar effects in continuos-time domain; here they are amusing. > > - Why not use the impulse as test signal? You refer to 'some' who > > =A0 'claim' that system with negative group delays are noncausal, as > > =A0 if you contest (or at least not support) such a view. I have > > =A0 made such claims. > > How would you suggest performing the experiment in CT, short of > actually building the circuit? =A0Even circuit analysis tools have to > operate in discrete time.Derive and analyze the Laplace transform for the cirquit? All analytical, should be easy.> > Your way of phrasing opens a whole new can of worms of semantic wars > > etc - why not demonstarte once and for all that systems with negative > > group delays exist and can be implemented in CT? (If that indeed is > > your claim, of course; I could not find out from the article what > > your stand on the issue is.) > > It would appear that he has. =A0He's presented a circuit whose transfer > function is easily derivable, and which clearly has a negative group > delay over some region (as the graph demonstrates).Well, that's *not* what the article says. The statement "We will now proceed to find a discrete filter with comparable characteristics in order to be able to reproduce the experiment in Matlab world." can only be interpreted as if the subsequent analysis applies to the DT "comparable" system.> > I would suggest the following: > > > 1) Make a clear statement of the 'usual' views on the issue, > > =A0 =A0your own opinions, and exactly what this article aims > > =A0 =A0to demonstrate. > > 2) Compute the phase response of the CT system function and > > =A0 =A0demonstrate that there is a negative group delay there. > > =A0 =A0If you have the tools, I would also suggest you simulate > > =A0 =A0the impulse response of that circuit in CT domain. > > I agree that graphs of the impulse responses would have been nice. > But on the other hand, they're kind of irrelevant to the argument, as > it is clear that both systems are causal!That's what confuses me: - I can't figure out what the claim in the article is; what is the 'usual' stand on the question and how is it contested? - What is the premise for the debate? Are we talking about CT or DT systems? Online or offline in case of DT? Causal? Stable? - What are the arguments? I don't know the Berchin method for CT->DT transform; if the claims are valid they should work just as well with the well-known BLT. - What are the conclusions? I see some graphs but because I'm completely lost in earlier stages I don't understand what they signify or what the impact is.> > 3) Use standard techniques in DT domain (BLT, Kronecker delta) > > =A0 =A0and repeat your analysis. > > > If all the results persist (system functions show negative > > group delays, anticausal behaviour) after such a re-work, I > > will consider to spend some time looking into your article > > in more detail. > > I believe the point of the article was precisely to counter the belief > that -ve group delay equates to "anticausal behaviour".If so, the article would benefit greatly from a better structure and presentation.> > As the article stands, it only cretates confusion. A less > > benevolent reviewer than me might sugest that the instability > > caused by the truncated signal is caused by poles located > > outside the unit circle, and thus suggest that there is a > > fundamental flaw in the argument. As you know, if you can > > repeat the results using standard analysis tools and from > > multiple angles of attack, it will stop those sorts of > > argument at the outset. > > Even if there were poles outside the unit circle, that wouldn't allow > the system to become non-causal! =A0The article already states that both > CT and DT filters are minimum-phase. =A0A trivial analysis of the > transfer function polynomials demonstrates that they are stable.Again, that may be the case but I am not able to follow the chain of arguments to reach that conclusion. Rune
Reply by ●March 8, 20082008-03-08
On Mar 8, 2:38=A0pm, Oli Charlesworth <ca...@olifilth.co.uk> wrote:> On Mar 8, 12:02 pm, Rune Allnor <all...@tele.ntnu.no> wrote: > > > On Mar 7, 11:18 pm, Andor <andor.bari...@gmail.com> wrote: > > > Interesting piece. Just a couple of questions: > > > - Why not use the BLT to transfor to discrete-time domain? > > =A0 I don't know Greg's stuff, I am familiar with the properties > > =A0 of the BLT. > > I'm not sure it matters what the technique is?It does to me. A result derived with a known, well-udnerstood technique has a far greater impact than a unfamiliar, possibly novel technique applied to a tricky question.>=A0Surely all that > matters is that a discrete-time filter is derived that has the key > properties of its CT counterpart (approximately flat -ve group delay > over a region with approximately flat magnitude response). =A0The fact > that the overall response is roughly the same is merely an aesthetic > bonus.Wrong. If the claim applies to the CT cirquit, it is the CT cirquit which must be analyzed.> > - Why analyze in discrete-time domain at all? Your results > > =A0 would have been seriously interesting if you could demonstrate > > =A0 similar effects in continuos-time domain; here they are amusing. > > - Why not use the impulse as test signal? You refer to 'some' who > > =A0 'claim' that system with negative group delays are noncausal, as > > =A0 if you contest (or at least not support) such a view. I have > > =A0 made such claims. > > How would you suggest performing the experiment in CT, short of > actually building the circuit? =A0Even circuit analysis tools have to > operate in discrete time.Derive and analyze the Laplace transform for the cirquit? All analytical, should be easy.> > Your way of phrasing opens a whole new can of worms of semantic wars > > etc - why not demonstarte once and for all that systems with negative > > group delays exist and can be implemented in CT? (If that indeed is > > your claim, of course; I could not find out from the article what > > your stand on the issue is.) > > It would appear that he has. =A0He's presented a circuit whose transfer > function is easily derivable, and which clearly has a negative group > delay over some region (as the graph demonstrates).Well, that's *not* what the article says. The statement "We will now proceed to find a discrete filter with comparable characteristics in order to be able to reproduce the experiment in Matlab world." can only be interpreted as if the subsequent analysis applies to the DT "comparable" system.> > I would suggest the following: > > > 1) Make a clear statement of the 'usual' views on the issue, > > =A0 =A0your own opinions, and exactly what this article aims > > =A0 =A0to demonstrate. > > 2) Compute the phase response of the CT system function and > > =A0 =A0demonstrate that there is a negative group delay there. > > =A0 =A0If you have the tools, I would also suggest you simulate > > =A0 =A0the impulse response of that circuit in CT domain. > > I agree that graphs of the impulse responses would have been nice. > But on the other hand, they're kind of irrelevant to the argument, as > it is clear that both systems are causal!That's what confuses me: - I can't figure out what the claim in the article is; what is the 'usual' stand on the question and how is it contested? - What is the premise for the debate? Are we talking about CT or DT systems? Online or offline in case of DT? Causal? Stable? - What are the arguments? I don't know the Berchin method for CT->DT transform; if the claims are valid they should work just as well with the well-known BLT. - What are the conclusions? I see some graphs but because I'm completely lost in earlier stages I don't understand what they signify or what the impact is.> > 3) Use standard techniques in DT domain (BLT, Kronecker delta) > > =A0 =A0and repeat your analysis. > > > If all the results persist (system functions show negative > > group delays, anticausal behaviour) after such a re-work, I > > will consider to spend some time looking into your article > > in more detail. > > I believe the point of the article was precisely to counter the belief > that -ve group delay equates to "anticausal behaviour".If so, the article would benefit greatly from a better structure and presentation.> > As the article stands, it only cretates confusion. A less > > benevolent reviewer than me might sugest that the instability > > caused by the truncated signal is caused by poles located > > outside the unit circle, and thus suggest that there is a > > fundamental flaw in the argument. As you know, if you can > > repeat the results using standard analysis tools and from > > multiple angles of attack, it will stop those sorts of > > argument at the outset. > > Even if there were poles outside the unit circle, that wouldn't allow > the system to become non-causal! =A0The article already states that both > CT and DT filters are minimum-phase. =A0A trivial analysis of the > transfer function polynomials demonstrates that they are stable.Again, that may be the case but I am not able to follow the chain of arguments to reach that conclusion. Rune
Reply by ●March 8, 20082008-03-08
On Mar 8, 2:38=A0pm, Oli Charlesworth <ca...@olifilth.co.uk> wrote:> On Mar 8, 12:02 pm, Rune Allnor <all...@tele.ntnu.no> wrote: > > > On Mar 7, 11:18 pm, Andor <andor.bari...@gmail.com> wrote: > > > Interesting piece. Just a couple of questions: > > > - Why not use the BLT to transfor to discrete-time domain? > > =A0 I don't know Greg's stuff, I am familiar with the properties > > =A0 of the BLT. > > I'm not sure it matters what the technique is?It does to me. A result derived with a known, well-udnerstood technique has a far greater impact than a unfamiliar, possibly novel technique applied to a tricky question.>=A0Surely all that > matters is that a discrete-time filter is derived that has the key > properties of its CT counterpart (approximately flat -ve group delay > over a region with approximately flat magnitude response). =A0The fact > that the overall response is roughly the same is merely an aesthetic > bonus.Wrong. If the claim applies to the CT cirquit, it is the CT cirquit which must be analyzed.> > - Why analyze in discrete-time domain at all? Your results > > =A0 would have been seriously interesting if you could demonstrate > > =A0 similar effects in continuos-time domain; here they are amusing. > > - Why not use the impulse as test signal? You refer to 'some' who > > =A0 'claim' that system with negative group delays are noncausal, as > > =A0 if you contest (or at least not support) such a view. I have > > =A0 made such claims. > > How would you suggest performing the experiment in CT, short of > actually building the circuit? =A0Even circuit analysis tools have to > operate in discrete time.Derive and analyze the Laplace transform for the cirquit? All analytical, should be easy.> > Your way of phrasing opens a whole new can of worms of semantic wars > > etc - why not demonstarte once and for all that systems with negative > > group delays exist and can be implemented in CT? (If that indeed is > > your claim, of course; I could not find out from the article what > > your stand on the issue is.) > > It would appear that he has. =A0He's presented a circuit whose transfer > function is easily derivable, and which clearly has a negative group > delay over some region (as the graph demonstrates).Well, that's *not* what the article says. The statement "We will now proceed to find a discrete filter with comparable characteristics in order to be able to reproduce the experiment in Matlab world." can only be interpreted as if the subsequent analysis applies to the DT "comparable" system.> > I would suggest the following: > > > 1) Make a clear statement of the 'usual' views on the issue, > > =A0 =A0your own opinions, and exactly what this article aims > > =A0 =A0to demonstrate. > > 2) Compute the phase response of the CT system function and > > =A0 =A0demonstrate that there is a negative group delay there. > > =A0 =A0If you have the tools, I would also suggest you simulate > > =A0 =A0the impulse response of that circuit in CT domain. > > I agree that graphs of the impulse responses would have been nice. > But on the other hand, they're kind of irrelevant to the argument, as > it is clear that both systems are causal!That's what confuses me: - I can't figure out what the claim in the article is; what is the 'usual' stand on the question and how is it contested? - What is the premise for the debate? Are we talking about CT or DT systems? Online or offline in case of DT? Causal? Stable? - What are the arguments? I don't know the Berchin method for CT->DT transform; if the claims are valid they should work just as well with the well-known BLT. - What are the conclusions? I see some graphs but because I'm completely lost in earlier stages I don't understand what they signify or what the impact is.> > 3) Use standard techniques in DT domain (BLT, Kronecker delta) > > =A0 =A0and repeat your analysis. > > > If all the results persist (system functions show negative > > group delays, anticausal behaviour) after such a re-work, I > > will consider to spend some time looking into your article > > in more detail. > > I believe the point of the article was precisely to counter the belief > that -ve group delay equates to "anticausal behaviour".If so, the article would benefit greatly from a better structure and presentation.> > As the article stands, it only cretates confusion. A less > > benevolent reviewer than me might sugest that the instability > > caused by the truncated signal is caused by poles located > > outside the unit circle, and thus suggest that there is a > > fundamental flaw in the argument. As you know, if you can > > repeat the results using standard analysis tools and from > > multiple angles of attack, it will stop those sorts of > > argument at the outset. > > Even if there were poles outside the unit circle, that wouldn't allow > the system to become non-causal! =A0The article already states that both > CT and DT filters are minimum-phase. =A0A trivial analysis of the > transfer function polynomials demonstrates that they are stable.Again, that may be the case but I am not able to follow the chain of arguments to reach that conclusion. Rune
Reply by ●March 8, 20082008-03-08
On Mar 8, 2:38�pm, Oli Charlesworth <ca...@olifilth.co.uk> wrote:> On Mar 8, 12:02 pm, Rune Allnor <all...@tele.ntnu.no> wrote: > > > On Mar 7, 11:18 pm, Andor <andor.bari...@gmail.com> wrote: > > > Interesting piece. Just a couple of questions: > > > - Why not use the BLT to transfor to discrete-time domain? > > � I don't know Greg's stuff, I am familiar with the properties > > � of the BLT. > > I'm not sure it matters what the technique is?It does to me. A result derived with a known, well-udnerstood technique has a far greater impact than a unfamiliar, possibly novel technique applied to a tricky question.>�Surely all that > matters is that a discrete-time filter is derived that has the key > properties of its CT counterpart (approximately flat -ve group delay > over a region with approximately flat magnitude response). �The fact > that the overall response is roughly the same is merely an aesthetic > bonus.Wrong. If the claim applies to the CT cirquit, it is the CT cirquit which must be analyzed.> > - Why analyze in discrete-time domain at all? Your results > > � would have been seriously interesting if you could demonstrate > > � similar effects in continuos-time domain; here they are amusing. > > - Why not use the impulse as test signal? You refer to 'some' who > > � 'claim' that system with negative group delays are noncausal, as > > � if you contest (or at least not support) such a view. I have > > � made such claims. > > How would you suggest performing the experiment in CT, short of > actually building the circuit? �Even circuit analysis tools have to > operate in discrete time.Derive and analyze the Laplace transform for the cirquit? All analytical, should be easy.> > Your way of phrasing opens a whole new can of worms of semantic wars > > etc - why not demonstarte once and for all that systems with negative > > group delays exist and can be implemented in CT? (If that indeed is > > your claim, of course; I could not find out from the article what > > your stand on the issue is.) > > It would appear that he has. �He's presented a circuit whose transfer > function is easily derivable, and which clearly has a negative group > delay over some region (as the graph demonstrates).Well, that's *not* what the article says. The statement "We will now proceed to find a discrete filter with comparable characteristics in order to be able to reproduce the experiment in Matlab world." can only be interpreted as if the subsequent analysis applies to the DT "comparable" system.> > I would suggest the following: > > > 1) Make a clear statement of the 'usual' views on the issue, > > � �your own opinions, and exactly what this article aims > > � �to demonstrate. > > 2) Compute the phase response of the CT system function and > > � �demonstrate that there is a negative group delay there. > > � �If you have the tools, I would also suggest you simulate > > � �the impulse response of that circuit in CT domain. > > I agree that graphs of the impulse responses would have been nice. > But on the other hand, they're kind of irrelevant to the argument, as > it is clear that both systems are causal!That's what confuses me: - I can't figure out what the claim in the article is; what is the 'usual' stand on the question and how is it contested? - What is the premise for the debate? Are we talking about CT or DT systems? Online or offline in case of DT? Causal? Stable? - What are the arguments? I don't know the Berchin method for CT->DT transform; if the claims are valid they should work just as well with the well-known BLT. - What are the conclusions? I see some graphs but because I'm completely lost in earlier stages I don't understand what they signify or what the impact is.> > 3) Use standard techniques in DT domain (BLT, Kronecker delta) > > � �and repeat your analysis. > > > If all the results persist (system functions show negative > > group delays, anticausal behaviour) after such a re-work, I > > will consider to spend some time looking into your article > > in more detail. > > I believe the point of the article was precisely to counter the belief > that -ve group delay equates to "anticausal behaviour".If so, the article would benefit greatly from a better structure and presentation.> > As the article stands, it only cretates confusion. A less > > benevolent reviewer than me might sugest that the instability > > caused by the truncated signal is caused by poles located > > outside the unit circle, and thus suggest that there is a > > fundamental flaw in the argument. As you know, if you can > > repeat the results using standard analysis tools and from > > multiple angles of attack, it will stop those sorts of > > argument at the outset. > > Even if there were poles outside the unit circle, that wouldn't allow > the system to become non-causal! �The article already states that both > CT and DT filters are minimum-phase. �A trivial analysis of the > transfer function polynomials demonstrates that they are stable.Again, that may be the case but I am not able to follow the chain of arguments to reach that conclusion. Rune
Reply by ●March 8, 20082008-03-08
On Mar 8, 2:38�pm, Oli Charlesworth <ca...@olifilth.co.uk> wrote:> On Mar 8, 12:02 pm, Rune Allnor <all...@tele.ntnu.no> wrote: > > > On Mar 7, 11:18 pm, Andor <andor.bari...@gmail.com> wrote: > > > Interesting piece. Just a couple of questions: > > > - Why not use the BLT to transfor to discrete-time domain? > > � I don't know Greg's stuff, I am familiar with the properties > > � of the BLT. > > I'm not sure it matters what the technique is?It does to me. A result derived with a known, well-udnerstood technique has a far greater impact than a unfamiliar, possibly novel technique applied to a tricky question.>�Surely all that > matters is that a discrete-time filter is derived that has the key > properties of its CT counterpart (approximately flat -ve group delay > over a region with approximately flat magnitude response). �The fact > that the overall response is roughly the same is merely an aesthetic > bonus.Wrong. If the claim applies to the CT cirquit, it is the CT cirquit which must be analyzed.> > - Why analyze in discrete-time domain at all? Your results > > � would have been seriously interesting if you could demonstrate > > � similar effects in continuos-time domain; here they are amusing. > > - Why not use the impulse as test signal? You refer to 'some' who > > � 'claim' that system with negative group delays are noncausal, as > > � if you contest (or at least not support) such a view. I have > > � made such claims. > > How would you suggest performing the experiment in CT, short of > actually building the circuit? �Even circuit analysis tools have to > operate in discrete time.Derive and analyze the Laplace transform for the cirquit? All analytical, should be easy.> > Your way of phrasing opens a whole new can of worms of semantic wars > > etc - why not demonstarte once and for all that systems with negative > > group delays exist and can be implemented in CT? (If that indeed is > > your claim, of course; I could not find out from the article what > > your stand on the issue is.) > > It would appear that he has. �He's presented a circuit whose transfer > function is easily derivable, and which clearly has a negative group > delay over some region (as the graph demonstrates).Well, that's *not* what the article says. The statement "We will now proceed to find a discrete filter with comparable characteristics in order to be able to reproduce the experiment in Matlab world." can only be interpreted as if the subsequent analysis applies to the DT "comparable" system.> > I would suggest the following: > > > 1) Make a clear statement of the 'usual' views on the issue, > > � �your own opinions, and exactly what this article aims > > � �to demonstrate. > > 2) Compute the phase response of the CT system function and > > � �demonstrate that there is a negative group delay there. > > � �If you have the tools, I would also suggest you simulate > > � �the impulse response of that circuit in CT domain. > > I agree that graphs of the impulse responses would have been nice. > But on the other hand, they're kind of irrelevant to the argument, as > it is clear that both systems are causal!That's what confuses me: - I can't figure out what the claim in the article is; what is the 'usual' stand on the question and how is it contested? - What is the premise for the debate? Are we talking about CT or DT systems? Online or offline in case of DT? Causal? Stable? - What are the arguments? I don't know the Berchin method for CT->DT transform; if the claims are valid they should work just as well with the well-known BLT. - What are the conclusions? I see some graphs but because I'm completely lost in earlier stages I don't understand what they signify or what the impact is.> > 3) Use standard techniques in DT domain (BLT, Kronecker delta) > > � �and repeat your analysis. > > > If all the results persist (system functions show negative > > group delays, anticausal behaviour) after such a re-work, I > > will consider to spend some time looking into your article > > in more detail. > > I believe the point of the article was precisely to counter the belief > that -ve group delay equates to "anticausal behaviour".If so, the article would benefit greatly from a better structure and presentation.> > As the article stands, it only cretates confusion. A less > > benevolent reviewer than me might sugest that the instability > > caused by the truncated signal is caused by poles located > > outside the unit circle, and thus suggest that there is a > > fundamental flaw in the argument. As you know, if you can > > repeat the results using standard analysis tools and from > > multiple angles of attack, it will stop those sorts of > > argument at the outset. > > Even if there were poles outside the unit circle, that wouldn't allow > the system to become non-causal! �The article already states that both > CT and DT filters are minimum-phase. �A trivial analysis of the > transfer function polynomials demonstrates that they are stable.Again, that may be the case but I am not able to follow the chain of arguments to reach that conclusion. Rune
Reply by ●March 8, 20082008-03-08
On Mar 8, 2:01 pm, Rune Allnor <all...@tele.ntnu.no> wrote:> On Mar 8, 2:38 pm, Oli Charlesworth <ca...@olifilth.co.uk> wrote: > > > I'm not sure it matters what the technique is? > > It does to me. A result derived with a known, well-udnerstood > technique has a far greater impact than a unfamiliar, possibly > novel technique applied to a tricky question.Perhaps.> > Surely all that > > matters is that a discrete-time filter is derived that has the key > > properties of its CT counterpart (approximately flat -ve group delay > > over a region with approximately flat magnitude response). The fact > > that the overall response is roughly the same is merely an aesthetic > > bonus. > > Wrong. If the claim applies to the CT cirquit, it is the CT > cirquit which must be analyzed.Not necessarily. See further down...> > How would you suggest performing the experiment in CT, short of > > actually building the circuit? Even circuit analysis tools have to > > operate in discrete time. > > Derive and analyze the Laplace transform for the cirquit? > All analytical, should be easy.Yes, we could analyse via the Laplace domain by putting in a signal with a known equation, and examining the output signal's equation. But given that the group delay and magnitude responses aren't completely flat (over the bandlimited region of interest), there will clearly be some distortion, so it's not going to be a case of y(t) = x(t + T). As far as I can see, the next logical step in analysing the "delay" would be to graph both input and output signals. But clearly, the graphing process requires discretising the time axis.> > It would appear that he has. He's presented a circuit whose transfer > > function is easily derivable, and which clearly has a negative group > > delay over some region (as the graph demonstrates). > > Well, that's *not* what the article says. The statement > > "We will now proceed to find a discrete filter with > comparable characteristics in order to be able to > reproduce the experiment in Matlab world." > > can only be interpreted as if the subsequent analysis > applies to the DT "comparable" system.Figure 2 shows the group delay of the CT system (in blue); i.e. it has already been demonstrated that the CT system has -ve group delay.> > I agree that graphs of the impulse responses would have been nice. > > But on the other hand, they're kind of irrelevant to the argument, as > > it is clear that both systems are causal! > > That's what confuses me: > > - I can't figure out what the claim in the article is; what is > the 'usual' stand on the question and how is it contested? > - What is the premise for the debate? Are we talking about > CT or DT systems? Online or offline in case of DT? Causal? > Stable? > - What are the arguments? I don't know the Berchin method for > CT->DT transform; if the claims are valid they should work > just as well with the well-known BLT. > - What are the conclusions? I see some graphs but because > I'm completely lost in earlier stages I don't understand > what they signify or what the impact is.Andor would be able to answer these questions better than I, but here is my guess. I think it is clear that the article is discussing causal, stable systems, given that the two systems presented are both causal and stable, and that the typical confusion about -ve group delay is that it somehow violates causality in practical (i.e. stable) systems. Whether we're talking about online or offline processing is irrelevant, as this doesn't affect the property of causality (at least, not as far as analysing an impulse response is concerned). In my opinion, the abstract states what the article is trying to address (i.e. its "arguments"). Namely, the surpise/confusion that many people exhibit when confronted with the topic of -ve group delay. I believe the purpose of the article was to demonstrate that -ve group delay is possible; the experiments in the DT domain clearly demonstrate this, along with the apparently non-intuitive illusion of non-causality. The article concludes with an explanation for this illusion. Although there is no proof, surely it is logical to conclude that if the apparent paradox has been cleared up in the DT domain, it also serves to clear up any apparent paradox in the CT domain? Therefore, I'm not sure that it matters what the specific discretisation technique was.> > I believe the point of the article was precisely to counter the belief > > that -ve group delay equates to "anticausal behaviour". > > If so, the article would benefit greatly from a better structure > and presentation.Perhaps.> > Even if there were poles outside the unit circle, that wouldn't allow > > the system to become non-causal! The article already states that both > > CT and DT filters are minimum-phase. A trivial analysis of the > > transfer function polynomials demonstrates that they are stable. > > Again, that may be the case but I am not able to follow > the chain of arguments to reach that conclusion.I'm not sure the chain of arguments affects a numerical analysis of the transfer function polynomials... -- Oli
Reply by ●March 8, 20082008-03-08
On Mar 8, 2:43 pm, Oli Charlesworth <ca...@olifilth.co.uk> wrote:> On Mar 8, 2:01 pm, Rune Allnor <all...@tele.ntnu.no> wrote: > > > > How would you suggest performing the experiment in CT, short of > > > actually building the circuit? Even circuit analysis tools have to > > > operate in discrete time. > > > Derive and analyze the Laplace transform for the cirquit? > > All analytical, should be easy. > > Yes, we could analyse via the Laplace domain by putting in a signal > with a known equation, and examining the output signal's equation. > But given that the group delay and magnitude responses aren't > completely flat (over the bandlimited region of interest), there will > clearly be some distortion, so it's not going to be a case of y(t) = > x(t + T). As far as I can see, the next logical step in analysing the > "delay" would be to graph both input and output signals. But clearly, > the graphing process requires discretising the time axis. >Just realised that this is irrelevant, and should be ignored! You are right, a CT analysis would be tractable. -- Oli
Reply by ●March 8, 20082008-03-08
On Mar 8, 3:43�pm, Oli Charlesworth <ca...@olifilth.co.uk> wrote:> On Mar 8, 2:01 pm, Rune Allnor <all...@tele.ntnu.no> wrote: > > > On Mar 8, 2:38 pm, Oli Charlesworth <ca...@olifilth.co.uk> wrote: > > > > I'm not sure it matters what the technique is? > > > It does to me. A result derived with a known, well-udnerstood > > technique has a far greater impact than a unfamiliar, possibly > > novel technique applied to a tricky question. > > Perhaps.Certainly. If a conclusion depends on using a novel method to do a standard computation, the first awkward questions will inevitably concern the soundness of this new method. It will only strengthen the conclusion if it can be demonstrated that the conclusion is independent of numerical methods used.> > > Surely all that > > > matters is that a discrete-time filter is derived that has the key > > > properties of its CT counterpart (approximately flat -ve group delay > > > over a region with approximately flat magnitude response). �The fact > > > that the overall response is roughly the same is merely an aesthetic > > > bonus. > > > Wrong. If the claim applies to the CT cirquit, it is the CT > > cirquit which must be analyzed. > > Not necessarily. �See further down... > > > > How would you suggest performing the experiment in CT, short of > > > actually building the circuit? �Even circuit analysis tools have to > > > operate in discrete time. > > > Derive and analyze the Laplace transform for the cirquit? > > All analytical, should be easy. > > Yes, we could analyse via the Laplace domain by putting in a signal > with a known equation, and examining the output signal's equation.No. The LT describes the linear system regardless of input and output signals. If the LP is invalid, then the system is nonlinear and thus the concept of group delay is undefined. Thanks for pointing out another item for my list of points that ought to be clarified. Rune
