How to get envelope from AM signal without phase shift
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From: robert bristow-johnson on 31 Mar 2010 19:44 On Mar 31, 6:03 pm, Clay <c...(a)claysturner.com> wrote: > On Mar 31, 4:17 pm, robert bristow-johnson <r...(a)audioimagination.com> > wrote: > > > to simplify things, the thought experiment i prefer is instead of a > > single moving charge moving on the Z-axis, what one should consider is > > an infinite line of uniform charge (also having a non-zero lineal mass > > density) moving along the Z-axis. actually, it should be two parallel > > infinite lines of uniform charge (parallel to the Z-axis) of known > > spacing moving together in the Z direction. > > > for the observer moving along with the two parallel lines of charge, > > there is no motion relative to that observer and the problem is simple > > electrostatics and, knowing the distance between the two lines, the > > repulsive acceleration (sideways) of the two lines can be determined > > purely from electrostatics. > > > now there's a "stationary" observer that watches the two lines of > > charge (and the "moving" observer) whiz by him and also notices that, > > due to time dilation, the moving observer's clock is ticking more > > slowly, so the outward acceleration of the moving lines of charge > > appears to be slower than what is observed if they are not moving (as > > the first observer sees). > > > the rate of outward acceleration of the moving lines of charge, when > > considering *only* electrostatics together with special relativity is > > exactly the same outward acceleration of the same two moving lines of > > charge when considering both static and magnetic forces in a classical > > context (no relativistic effect). > > > that thought experiment, first introduced to me by a physics prof (who > > now is at Analog Devices) in the 70s, was sufficient to convince me > > that the electromagnetic interaction (in the classical context) is > > none other than just the sole electrostatic interaction with > > relativistic effects applied. > > > i s'pose the same can be done with lines of mass and the static > > Newtonian gravitational interaction, also applying special relativity > > and what you'll get out would be consistent with GEM (gravito-electro- > > magnetism) where Maxwell's and Lorentz equations have mass (or mass > > density) replacing charge (or charge density) and the Coulomb > > constant, 1/(4*pi*epsilon_0), is replaced with -G (the minus sign is > > because like-signed charges repel while like-signed masses attract). > > for some reason (that i don't really get), the gravito-magnetic force > > has an extra factor of 2 tossed into it (at least that's what the lit > > seems to say). > > > but, i think either classical EM or GEM can both be sorta understood > > by considering the simple Coulomb or Newtonian static model with > > relativistic effects. that's why we know that the magnetic > > interaction is really just a consequence of the static interaction and > > not a separate fundamental interaction. .... > > The quick and easy way is via 4-vectors. > i might call that "the formal and general and legitimate way". and i don't see how you would teach that to college sophomores after they have first learned about classical EM and later about special relativity. engineering/physics/chem majors in their sophomore year should know how to derive the electrostatic field due to an infinite line of charge and how that field will act on a little segment (of given length) of another infinite line of charge (where nothing is moving). and they should know how to derive the electromagnetic field of an identical line of charge that is moving (co-linearly) at some known velocity and how that magnetic field would act on a short segment of another similar line of charge that is moving with a know velocity. and, once they accept the postulates (i really think that only one postulate is needed) of special relativity, they should understand where time dilation comes from and how to apply that to an observer in motion relative to another observer. it's a special case. it does not prove it in the general case, but i think it can be used to persuade a student who hasn't yet (and may never) learned about Minkowski spacetime, tensors, and 4-vectors, that the classical magnetic interaction is nothing more than the electrostatic interaction with special relativity considered. and, being an EE into DSP and being a third of a century away from any formal physics class, it's about where my atrophied neurons regarding all of this are stuck. and i never had a physics class where anything other than the basics of special relativity had been taught (in "General Physics"). i never had a course in formal SR (with Minkowki constructs) or in GR (but i think i am okay about the postulates of both). r b-j
From: Jerry Avins on 31 Mar 2010 20:17 On 3/31/2010 6:42 PM, WWalker wrote: ... > In terms of quantum mechanics I think the following might be happening in > this system. If a photon is created a t=0 then as it propagates, because of > the uncertainty principle, the uncertainty of the velocity of the photon is > much larger than c in the nearfield and much less than c in the farfield. > Which means the photon can be much faster than light in the nearfield but > reduces to the speed of light as it propagates into the farfield. Below is > the argument that shows this. So an uncertain velocity is, at least on average, faster? Why? ... Jerry -- "It does me no injury for my neighbor to say there are 20 gods, or no God. It neither picks my pocket nor breaks my leg." Thomas Jefferson to the Virginia House of Delegates in 1776. ���������������������������������������������������������������������
From: Eric Jacobsen on 31 Mar 2010 21:08 On 3/31/2010 4:09 PM, WWalker wrote: > r b-j, > > The dicussion here has been very helpful with signal processing and > understanding the information in the signals I use in my simulations. The > topic has been discussed theoretically over dacades without proving or > disproving the superluminal behavior of the the dipole system (i.e. Speed > of Gravity etc). I do not believe theoretical evidence will ever prove it > one way or another. > > My hope is that an experiment might be able to prove or disprove the > superluminal behavior of this system, that is why I am discussing > simulations here to see if a good experimental setup and signal processing > method can be developed. > > William It's going to be difficult to prove or disprove it either way. I think it would have been done by now if it was straightforward, and the discussions here seem to indicate how that comes to be. A physicist who doesn't understand signal processing can be (and have been) tripped up by misinterpreting the results, as you seem inclined to do. To use your button-push bomb trigger example again, a step or impulse that has been bandlimited spreads out in time. The impulse (or step, but the impulse is easier to follow), which can be defined very specifically in time, gets spread out over time by the bandlimiting filter. This can be seen easily in your plots, in Andor's paper, anywhere a plot of a bandlimited "impulse" exists. In high-snr cases the temptation is to use the peak of the spread pulse to indicate the arrival of the impulse. At low SNR it may be necessary to integrate over the entire pulse length time in order to reliably detect the "arrival of the impulse". Clearly the rising edge of the spread pulse doesn't anticipate the arrival of the peak, so from a causality point of view the beginning traces of the initial arrival of the leading edge of the pulse may be most indicative of the actual arrival time of the earliest portion of information associated with the impulse. Unless, as I mentioned, the SNR is low, in which case one has to wait longer to integrate the energy for reliable detection. So when does the actual, narrow, "impulse" arrive? It is ambiguous. At high SNR it could be argued that detection of initial energy (which is why Vladimir suggested you start with zero-input-zero-output, put in energy, and see when energy comes out) defines the actual propagation, since the system is necessarily causal. I'm hoping you're beginning to see why a small phase advance that is much narrower than the pulse length is NOT reliably indicative of accelerated propagation. It is just a phase advance, and the mechanisms by which those can happen are real. It does not indicate propagation faster than c, but people who see the phase advance are sorely tempted to continue to point to it and claim either noncausality or propagation faster than c. If you measure from the initial stimulus, i.e., the button push, or the arrival of the wideband impulse into the bandlimiting filter, then you have a hope of measuring the actual propagation through the system. Filter delays can then be observed reliably. If you just compare the relative phases of the signals after bandlimiting and the difference is small compared to the length of the impulse response, then it is extremely difficult to distinguish phase advance due to dispersive effects or negative group delay from accelerated propagation. Phase advance due to bandlimited prediction is the far more likely explanation than propagation faster than c, and continuing to point to the phase differences as evidence does nothing to resolve the issue. You could still simulate disconnection of the signal from the Tx antenna input by interrupting the signal and see how that affects the output. That's a wideband stimulus and it should be much easier to see how fast that propagates through the system. -- Eric Jacobsen Minister of Algorithms Abineau Communications http://www.abineau.com
From: glen herrmannsfeldt on 1 Apr 2010 05:23 Clay <clay(a)claysturner.com> wrote: (snip) > The quick and easy way is via 4-vectors. > Here the scalar electric potential and the magnetic vector potential > form a 4-vector. It isn't that quick and easy, but it does work. Feynman does it after he does it the other way. Or maybe in the middle. > It is interesting to note that the fields themselves do not transform > nicely. In fact it is the potentials that affect things and not the > fields. This is well demonstrated by the Aharonov-Boehm effect. Yes > there are cases where you have non zero potentials with zero fields > and can observe the quantum interference being affected by varying the > potential! Anyway, in Feynman's description there are three terms, one due to the position of a charge (Coulomb's term except delayed by r/c), the second is a velocity dependent correction to the first. The result of the second term is that in the near field the electric field vector is radial from (or to) the current position of the charge in the constant velocity case. It is just as Jerry mentioned a long time ago: in the case of a predictable motion, nature knows how to fix it. It might be that is necessary for special relativity and frame invariance, but it is surprising. Using that term, in the case of a slowly oscillating charge, it wouldn't be surprising if the field wasn't what you would expect from an appropriately delayed Coulomb field. The third term is the acceleration term, the only one you see in the far field, especially for neutral sources. > But start with a single stationary charge in one frame of reference > (in this frame the potentials are trivial) and then view the charge > from a moving frame and using 4-vector calculus you get the new > potentials. The curl of the magnetic vector potential will give you > the B fields resulting from a single moving charge. A lot of Physics > books will start with the Biot-Savart law and work from there avoiding > the relativity approach. But it makes it much easier to calculate. My college class used the Berkely book, which does get into the relativistic form pretty fast, but not quite the same as Feynman does it. We did have the whole 4-vector explanation, but I don't think we had homework problems using it. -- glen
From: WWalker on 1 Apr 2010 06:22
Jerry, In my last post (argument pasted again below) I presented an analysis which showed in the nearfield dv>>c in the nearfield and dv<<c in the farfield. Once the photon is created, it is propagating in one direction away from the creation point with, lets assume, a possitive velocity. Lets say in the nearfield dv=10c therefore, the velocity of the photon will range between: 0-10c, with an average of 5c, which is much faster than light. "Lets calculate the uncertainty of the velocity of a photon that propagates one wavelength after it is created: According to the Heisenberg uncertainty principle, the relation between the uncertainty in Energy (dE) and the uncertainty in time (dt) is: dE*dt >= h. The time for a photon to cross one wavelength distance is: dt = lambda/c. Since dE = h*df and df=dv/lambda then dE*dt=h*dv/c, but dE*dt <= h therefore: dv >= c For smaller distances the uncertianty will be greater and for larger distances the uncertainty will be much smaller. " William >On 3/31/2010 6:42 PM, WWalker wrote: > > ... > >> In terms of quantum mechanics I think the following might be happening in >> this system. If a photon is created a t=0 then as it propagates, because of >> the uncertainty principle, the uncertainty of the velocity of the photon is >> much larger than c in the nearfield and much less than c in the farfield. >> Which means the photon can be much faster than light in the nearfield but >> reduces to the speed of light as it propagates into the farfield. Below is >> the argument that shows this. > >So an uncertain velocity is, at least on average, faster? Why? > > ... > >Jerry >-- >"It does me no injury for my neighbor to say there are 20 gods, or no >God. It neither picks my pocket nor breaks my leg." > Thomas Jefferson to the Virginia House of Delegates in 1776. >��������������������������������������������������������������������� > |