How to get envelope from AM signal without phase shift
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From: Eric Jacobsen on 27 Mar 2010 12:10 On 3/27/2010 3:47 AM, WWalker wrote: > Eric, > > Since a pulse distorts in the nearfield, one can not determin it's group > speed in the nearfield. But if you take the same pulse and send it through > a low pass filter, mix it with a carrier, and send it though a dipole you > get the same superluminal results. Because the filtered pulse is narrow > band, it propagates undistorted and arrives sooner than a light propagated > pulse. I'm not following this argument, especially the last statement. > I have done a Vee Pro simulation and it clearly shows this. In this program > I used a pulse with the following characteristics: 1Hz Freq, 50ns pulse > width, 10ns rise and fall time, 1V amplitude. the Lowpass filter had the > following characteristics: 50MHz cutoff frequency (fc), 6th order, Transfer > function: 1/(j(f/fc)+1)^6. Then I multiplied this narrowbanded signal with > a 500MHz carrier and sent it though a light speed propagating transfer > function [e^(ikr)] and though the magnetic component of a electric dipole > transfer function [e^(ikr)*(-kr-i)]. Finally I extracted the modulation > envelopes of the tranmitted signal, light speed signal, and the dipole > signal. To extract the envelopes I squared the signal and then passed it > through a 300MHz cutoff (fc), 12th order LPF with the following transfer > function [1/(j(f/fc)+1)^12]. The pulse envelope from the dipole arrives > 0.16ns earlier than the light speed propagated pulse. This corresponds > exactly with theoretical expectations (0.08/fc=0.16ns). > > I think perhaps this is the evidence you have all been looking for. > > William Although I probably shouldn't be, I was thinking about this a bit more and wanted to add some thoughts. Although the following is certainly not a rigorous analysis, in general as the signal bandwidth goes up the time resolution one can achieve in correlation measurements gets smaller. The information update rate for typical comm systems is the symbol period, Ts, and generally Ts = 1/BW where BW is the 3dB signal bandwidth. It is possible to resolve time more finely than Ts and synchronization systems have to do this to recover the symbols, but a reasonable benchmark for how fast information is updating is Ts = 1/BW. I think it is arguable that if one wants to measure how fast information is propagating with very fine time resolution one needs to use a signal with a very wide bandwidth. Otherwise one risks measuring a phase offset due to phenomena like negative group delay rather than accelerated information propagation. You said: > The pulse envelope from the dipole arrives > 0.16ns earlier than the light speed propagated pulse. This corresponds > exactly with theoretical expectations (0.08/fc=0.16ns). What theory creates an expectation that the signal propagates faster than light? I don't know of any. Since you've filtered your signal to 50 MHz BW there will be no significant frequency components with periods shorter than 20ns. You're claiming that a time difference of 0.16ns (or 1/125th of the length of the smallest period in the signal) is a difference in information propagation. I think it's far more likely to be a phase shift due to the dispersion (as shown in the Sten paper), since that is only 360/125 = 2.88 degrees of phase advance. A signal experiencing 2.88 degrees of phase advance through a dispersive medium is far more believable than propagation faster than light. This is what I've been saying, what Andor's blog demonstrates, and what my reading of the Sten paper indicates. As mentioned long ago, I think a good experiment would be to interrupt the input signal at some point, perhaps even the modulated signal at a carrier zero crossing. The propagation of the interruption (which has infinite bandwidth if it's a hard stop) should be revealing. -- Eric Jacobsen Minister of Algorithms Abineau Communications http://www.abineau.com
From: Vladimir Vassilevsky on 27 Mar 2010 13:05 Eric Jacobsen wrote: > As mentioned long ago, I think a good experiment would be to interrupt > the input signal at some point, perhaps even the modulated signal at a > carrier zero crossing. The propagation of the interruption (which has > infinite bandwidth if it's a hard stop) should be revealing. Interesting question. What should be a good narrowband test signal to demonstrate the information propagation speed in dispersive media? Obviously it should not be an eigenfunction of linear system; i.e. sinusoids and exponentials are not suitable. I suggest windowed sinc or RRC pulse modulated BPSK. But, you may have to put the equalization filter into the picture as well. Vladimir Vassilevsky DSP and Mixed Signal Design Consultant http://www.abvolt.com
From: glen herrmannsfeldt on 27 Mar 2010 13:59 Eric Jacobsen <eric.jacobsen(a)ieee.org> wrote: (snip) > Although the following is certainly not a rigorous analysis, in general > as the signal bandwidth goes up the time resolution one can achieve in > correlation measurements gets smaller. The information update rate for > typical comm systems is the symbol period, Ts, and generally Ts = 1/BW > where BW is the 3dB signal bandwidth. It is possible to resolve time > more finely than Ts and synchronization systems have to do this to > recover the symbols, but a reasonable benchmark for how fast information > is updating is Ts = 1/BW. I think it is arguable that if one wants to > measure how fast information is propagating with very fine time > resolution one needs to use a signal with a very wide bandwidth. > Otherwise one risks measuring a phase offset due to phenomena like > negative group delay rather than accelerated information propagation. I agree. I was indirectly mentioning this a few days ago, with the suggestion of very low bandwidth, and so low information transmission rates. Also, for efficient communication, you have to make good use of the bandwidth that you do have. There should be signal components throughout the whole bandwidth. As Jerry was mentioning, with a single sinewave modulating the carrier there is pretty much zero information flowing. > You said: > > The pulse envelope from the dipole arrives > > 0.16ns earlier than the light speed propagated pulse. This corresponds > > exactly with theoretical expectations (0.08/fc=0.16ns). > What theory creates an expectation that the signal propagates faster > than light? I don't know of any. > Since you've filtered your signal to 50 MHz BW there will be no > significant frequency components with periods shorter than 20ns. You're > claiming that a time difference of 0.16ns (or 1/125th of the length of > the smallest period in the signal) is a difference in information > propagation. With enough averaging, it can be done. The average should be over a wide distribution of input signals, though. > I think it's far more likely to be a phase shift due to > the dispersion (as shown in the Sten paper), since that is only 360/125 > = 2.88 degrees of phase advance. A signal experiencing 2.88 degrees of > phase advance through a dispersive medium is far more believable than > propagation faster than light. This is what I've been saying, what > Andor's blog demonstrates, and what my reading of the Sten paper indicates. This was done optically some years ago, but the experimenters knew exactly what was happening. If you have a narrow bandwidth system, then it is pretty much resonant at that frequency. As the beginning of the Gaussian envelope wave comes through, it excites the resonant system and generates an output with a peak earlier than you would expect due to the velocity of light. If you change the shape of the pulse, then the resulting time is different. I don't know the reference anymore, though. > As mentioned long ago, I think a good experiment would be to interrupt > the input signal at some point, perhaps even the modulated signal at a > carrier zero crossing. The propagation of the interruption (which has > infinite bandwidth if it's a hard stop) should be revealing. Well, you can't really do that with a narrow band system. The modulation has to be within the bandwidth, which limits how fast you can change the signal. -- glen
From: Eric Jacobsen on 27 Mar 2010 14:16 On 3/27/2010 10:59 AM, glen herrmannsfeldt wrote: > Eric Jacobsen<eric.jacobsen(a)ieee.org> wrote: > (snip) > >> Although the following is certainly not a rigorous analysis, in general >> as the signal bandwidth goes up the time resolution one can achieve in >> correlation measurements gets smaller. The information update rate for >> typical comm systems is the symbol period, Ts, and generally Ts = 1/BW >> where BW is the 3dB signal bandwidth. It is possible to resolve time >> more finely than Ts and synchronization systems have to do this to >> recover the symbols, but a reasonable benchmark for how fast information >> is updating is Ts = 1/BW. I think it is arguable that if one wants to >> measure how fast information is propagating with very fine time >> resolution one needs to use a signal with a very wide bandwidth. >> Otherwise one risks measuring a phase offset due to phenomena like >> negative group delay rather than accelerated information propagation. > > I agree. I was indirectly mentioning this a few days ago, with > the suggestion of very low bandwidth, and so low information > transmission rates. Also, for efficient communication, you have > to make good use of the bandwidth that you do have. There should > be signal components throughout the whole bandwidth. As Jerry was > mentioning, with a single sinewave modulating the carrier there > is pretty much zero information flowing. > >> You said: > >>> The pulse envelope from the dipole arrives >>> 0.16ns earlier than the light speed propagated pulse. This corresponds >>> exactly with theoretical expectations (0.08/fc=0.16ns). > >> What theory creates an expectation that the signal propagates faster >> than light? I don't know of any. > >> Since you've filtered your signal to 50 MHz BW there will be no >> significant frequency components with periods shorter than 20ns. You're >> claiming that a time difference of 0.16ns (or 1/125th of the length of >> the smallest period in the signal) is a difference in information >> propagation. > > With enough averaging, it can be done. The average should be over > a wide distribution of input signals, though. > >> I think it's far more likely to be a phase shift due to >> the dispersion (as shown in the Sten paper), since that is only 360/125 >> = 2.88 degrees of phase advance. A signal experiencing 2.88 degrees of >> phase advance through a dispersive medium is far more believable than >> propagation faster than light. This is what I've been saying, what >> Andor's blog demonstrates, and what my reading of the Sten paper indicates. > > This was done optically some years ago, but the experimenters > knew exactly what was happening. If you have a narrow bandwidth > system, then it is pretty much resonant at that frequency. As the > beginning of the Gaussian envelope wave comes through, it excites > the resonant system and generates an output with a peak earlier than > you would expect due to the velocity of light. If you change the > shape of the pulse, then the resulting time is different. > I don't know the reference anymore, though. > >> As mentioned long ago, I think a good experiment would be to interrupt >> the input signal at some point, perhaps even the modulated signal at a >> carrier zero crossing. The propagation of the interruption (which has >> infinite bandwidth if it's a hard stop) should be revealing. > > Well, you can't really do that with a narrow band system. > The modulation has to be within the bandwidth, which limits how > fast you can change the signal. > > -- glen Yes, but turning the signal off abruptly at the input to the antenna provide the widest bandwidth stimulus that you're going to get, and therefore, I think, a good reference signal. An wideband impulse at the input to the antenna would be better, but some don't seem to like doing this analysis with a pulse. The Sten paper did, and showed the dispersion with it. That seems logical to me. -- Eric Jacobsen Minister of Algorithms Abineau Communications http://www.abineau.com
From: Eric Jacobsen on 27 Mar 2010 14:24
On 3/27/2010 10:05 AM, Vladimir Vassilevsky wrote: > > > Eric Jacobsen wrote: > >> As mentioned long ago, I think a good experiment would be to interrupt >> the input signal at some point, perhaps even the modulated signal at a >> carrier zero crossing. The propagation of the interruption (which has >> infinite bandwidth if it's a hard stop) should be revealing. > > Interesting question. What should be a good narrowband test signal to > demonstrate the information propagation speed in dispersive media? > Obviously it should not be an eigenfunction of linear system; i.e. > sinusoids and exponentials are not suitable. > I suggest windowed sinc or RRC pulse modulated BPSK. > But, you may have to put the equalization filter into the picture as well. > > Vladimir Vassilevsky > DSP and Mixed Signal Design Consultant > http://www.abvolt.com Yeah, it's an interesting problem. I now see why Ander referred to his blog article as "pouring oil in the fire and causing yet more confusion." I've not thought this out completely, but I'm starting to think you just can't get there with a narrowband signal if you want good time resolution and you don't want to get fooled by group delay hijinks. Clearly an impulse is a preferrable stimulus, and any filtering in the system will degrade that to a sinc of some sort, so starting with a windowed sinc isn't a bad idea. Likewise a BPSK signal, with the highest symbol rate possible, and then compare the phases of the transmit and recovered symbol clocks, would work. The time resolution would be no better than the clock jitter window, but if the symbol rate was high enough that could be made pretty small. But, as you mention, whether or not the signal was equalized would affect the result as the clock may lock somewhere other than the center of the eye. Tough problem. -- Eric Jacobsen Minister of Algorithms Abineau Communications http://www.abineau.com |