[Date Prev][Date Next][Thread Prev][Thread Next][Date Index][Thread Index]

Narrowband frequency estimation was Re: 7.1Hz, how the heck did Tesla succeed?

Original poster: Jim Lux <jimlux@xxxxxxxxxxxxx>

At 07:05 AM 7/19/2005, Tesla list wrote: 
Original poster: William Beaty <billb@xxxxxxxxxx>

On Sat, 16 Jul 2005, Tesla list wrote:

> >What goes wrong is that the received signal is way down in the noise,
> >therefore exotic antenna techniques become useful.
>
> If the signal is in the noise no exotic antenna will help you.

If the noise is mostly thermal noise from the wire, then it would help if
we can somehow crank up the amount of EM energy being received.  I think
this was the whole point of their paper.   I'll have to look it up.


> >Another problem is that the bandwidth of a detector varies in inverse
> >proportion to sampling time, so a narrowband signal which wanders randomly
> >will be wrongly interpreted as a wideband signal .  Regardless of whether
> >the detection is performed live, or via sofware w/files, if (say) you
> >sample at 1Hz but only for 0.1 second, the instrument will have chopped
> >the signal and therefore falsely receives it as a wide band signal.
>
>
> But, that's not that was suggested.  what was suggested was sampling @
> 100 %  for a very Long time.


I think you don't understand.  Do you propose to measure the shape of a
signal's spectral line ...without using any narrowband filters?

Precisely so. This is what a PLL tracker does, for instance. There's also a lot of these being used in speech processing, for formant tracking.


The
measured spectrum of any signal is convolved with the shape of the
sampling filter, so if you don't use a narrow filter, a very narrow signal
spectrum will look like your wide filter.


A narrow signal convolved with a wide filter is still a narrow signal.


  But if you *do* use a narrow
filter and long sampling times, then if the frequency of that narrowband
signal wanders around, it will be measured as having a wide spectrum.
But we don't know if that signal is actually wandering around in
frequency, or actually has a wide spectrum, since it's buried in noise.
And in order to extract it from noise, we have to sample for a long time
using narrow filters.  But this method of extracting it from noise is bad
if the signal is moving around: it gives out an entirely wrong spectrum.
What you're really interested in doing is finding the "instantaneous frequency" (confusingly called the IF in the literature). I have a paper in front of me by Kumaresan and Rao describing precisely this. I don't particularly agree with the algorithm they've described, but the concept is there. There's also some papers by Costas, and Boashash, as well as whole books on the spectral estimation problem.

As long ago as 1795 folks like Baron Gaspard de Prony were analysing tide data to find the basis sinusoids.


Get it?  We can't SEE the signal except through "lenses" of long sampling
times which distort a certain type of signal.   Making long measurements
in order to pull a signal up from noise...  this technique can't tell the
difference between a signal with a wide spectrum and a narrow signal that
moves in frequency.


Actually it can.


   So the true value for Earth cavity Q is possibly
unknown.

But this is all somewhat beside the point, since the Sutton/Spaniol paper
said that these measurements were all done decades ago with lousy
equipment using sampling filters with too wide a band.  The calculated Q
is caused by the wide filters on the equipment, and the true Q of the
Earth cavity MIGHT be very different...  yet everyone has been relying on
the wrong published data ever since those old measurements.


> >To
> >make narrowband measurements you have to make longterm measurements.  If
> >the signal frequency is changing, then you can't measure it with
> >narrowband filters unless you know just how it's changing.
>
> Sure you Can. Simple example is a phase locked loop tracking a sine wave
> that's slowly varying.

BUT THESE SIGNALS ARE BURIED DEEP IN NOISE!  Jeeze.  What is going ON
here?!!!  A PLL doesn't work.  If we could see the darn things on a scope
or measure them with a frequency counter or lock them to a PLL, then we'd
instantly know if the frequency was stable or varying.

Sure you can, but not with a frequency counter, which, as you point out, doesn't work well with signals in the presence of noise (because the frequency counter has a limiter or thresholder in the front end). A simple first order PLL won't find it (since it assumes that the frequency is constant), but a higher order loop might. As a practical matter, PLLs aren't necessarily the best way to find a sinusoid in noise, although they do a fine job tracking once you've found it.

  But if all we have
is extremely noisy data, then spectrum analysers need long integration
time, and this prevents us from knowing if a particular signal's spectral
line is as wide as measured, or perhaps the line is actually narrow, but
is wandering during the (necessary) long measurement.

Yes, you need long integration time, but that doesn't mean that the frequency you're trying to find has to remain constant for the whole time.
What you effectively wind up doing is finding some sort of optimum estimator for a generalized function y(t) = a(t) * cos( omega(t)*t + phasezero), where a(t) and omega(t) are slowly varying functions.

Consider that if you were trying to find the frequency rate, frequency and phase of a linear ramp, buried in noise. One can build a set of matched filters with different frequency rates, frequencies, and phases, and try all of them to see which one gives the largest output. Turns out that you don't have to do an exhaustive search, especially if you have a-priori information about the signal (i.e. you can bound the search space). For instance, you might have good reason to believe that the instantaneous frequency cannot vary faster than a certain rate (e.g. from the underlying physics).

This is much like how direct sequence spread spectrum systems acquire the initial code phase (e.g. in GPS, where the signal is well below the thermal noise floor at the input to the receiver). Your GPS receiver basically tries all possible codes and code phases until it finds one where the incoming signal and the trial code/code phase matches.

Mind you, the concept of "bandwidth" or "Q"for a matched filter may not be quite as straightforward as it might for a simple LC resonance.


If the line is narrow, then the Earth cavity Q is high.



>
> >  That's why
> >spread spectrum comm is used: the frequency hopping is a *huge* problem
> >unless you know the code.
> >
> > > and exact Fo frequency "jumping around" is not problem at all...
> >
> >Totally wrong because the jumping around, combined with the narrowband
> >filters, will chop the signal and add a wideband artifact.  Or do you have
> >an explanation for how a spread spectrum signal which is deep down in the
> >noise can be easily received when you don't know the random sequence of
> >frequencies?  If frequency jumps caused no problems, then spread spectrum
> >transmissions would give no security at all.  It's the same physics.
>
> Let's be careful here. There's two distinct problems you've described. The
> first is just detecting a spread spectrum signal.

In this "cell phone" analogy, just detecting the presence of a wideband
noiselike spread-spectrum signal is totally beside the point, it's
useless, it has no bearing on the problem.  I thought this was obvious.

What we want is this:

   Observe the true shape of a spectral peak


The problem is this:

   The peak is buried deep in noise


The solution is this:

  Use a spectrum analyzer (or software.)  Sample with many narrow
  frequency channels, and integrate over a long sample time in order to
  build up a high S/N ratio.

This approach works ONLY if the tone is fixed in frequncy, and hence, does not work for us. One needs to use a bit more sophistication, as outlined above.

I might point out that the problem of finding a moving narrow band signal buried in noise is one that is solved every day for a variety of applications. Deep space communications is one such application.



Next solution?

  Don't rely on natural lightning signals, instead drive the Earth cavity
  with a huge CW signal that's easily detected far above the noise level,
  then turn off the transmitter and measure the ringdown waveform.

As far as I know, nobody except perhaps Tesla has ever done this down
at the frequencies we're talking about (below 1KHz or even 100Hz.)

I would imagine that there is a fair amount of research on the propagation properties of signals in the sub 100 Hz range. It's an area of interest to geophysical prospectors, for instance. And, of course, there's ELF communications systems.