simultaneous frequence and phase estimation

Jerry Avins wrote:

(snip)

> I wasn't addressing you at all. Negative frequencies arise when
> replacing xin(wt) and cos(wt) with e^+jwt and e^-jwt, which it is
> mathematically convenient to do. The price we pay for that convenience
> is either using negative frequency or imagining that time marches
> backward as well as forward. (Almost invariably, we chose the former.)

> As for my plea to Randy, he assigns physical meaning to negative
> frequencies. I don't, but I can if I want to, just as I can compute with
> them.

Randy's ideas about complex numbers do seem a little strong
to me sometimes, but as far as negative time and physical
convenience, Feynman might disagree with you.

With certain conditions, Feynman describes antiparticles
(antimatter) as normal matter traveling backwards in time.

In one of the "Feynman lectures on Physics" he explores complex
numbers, instead of computing exp(i x) he computes 10**(i x),
finding that the results are sinusoidal with a period that
is not 2pi, and then does the derivation backwards to show that
if you use e instead of 10 as the base you find a period
of 2pi.

Still, my favorite of the lectures is the last one in the
first volume on the non-conservation of parity.

-- glen

glen herrmannsfeldt wrote:

   ...

> With certain conditions, Feynman describes antiparticles
> (antimatter) as normal matter traveling backwards in time.

My fuzzy recollection is that there was a lot of "as if" to that. His 
time-line drawings are simple and descriptive. "Simply wonderful" is a 
suitable double entendre.

   ...

Jerry
-- 
Engineering is the art of making what you want from things you can get.
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Jerry Avins wrote:

> glen herrmannsfeldt wrote:

>> With certain conditions, Feynman describes antiparticles
>> (antimatter) as normal matter traveling backwards in time.

> My fuzzy recollection is that there was a lot of "as if" to that. His 
> time-line drawings are simple and descriptive. "Simply wonderful" is a 
> suitable double entendre.

Well, in combination with the also quoted (in a different thread)
"Nobody understands quantum theory", maybe we really don't know.

-- glen

glen herrmannsfeldt wrote:
> Jerry Avins wrote:
> 
> (snip)
> 
>> Negative frequencies arise when
>> replacing xin(wt) and cos(wt) with e^+jwt and e^-jwt, which it is
>> mathematically convenient to do. The price we pay for that convenience
>> is either using negative frequency or imagining that time marches
>> backward as well as forward. (Almost invariably, we chose the former.)

This is only the half truth. Actually, we are using Heaviside's trick.
In other words, there physically exists only a function of negative 
time, and we are tacitly adding two mutually cancelling mirrored copies 
by padding the imagined  time to come with zeros.
I consider this somewhat self-cheating mathematics the reason for 
Feynmans stunning outline to be formally correct.


> Randy's ideas about complex numbers do seem a little strong
> to me sometimes, but as far as negative time and physical
> convenience, Feynman might disagree with you.
> 
> With certain conditions, Feynman describes antiparticles
> (antimatter) as normal matter traveling backwards in time.

Yes, Feynman is correct but perhaps pointless.

Mr. or Dr. Blumschein 

Please put up a website with the Matlab code you've written for natural 
spectrogram and some demos. Then we can download it and see for ourselves.
Please comment the code well, as sometimes it is easier to understand the
numerical process by looking at the program code.

Thank you.

glen herrmannsfeldt wrtoe:
...
> With certain conditions, Feynman describes antiparticles
> (antimatter) as normal matter traveling backwards in time.

I thought that particles traveling backwards in time necesserily need
to be moving at speed above the speed of light in vacuum which
immediately implies imaginary mass (insert a speed v > c into a
Lorentz boost equation) and inverted kinetic energy (the infinum of
kinetic energy is reached at speed of light, and they have zero
kinetic energy when moving infinitely fast)  - why resort to such
esoterics when you can simply invert the sign of the electric charge
of the elementary particles?

As far as I remember, particles moving backwards in time (tachyions)
and antimatter have nothing to do with each other. Then again, I'm
defnitely no physicist.

Regards,
Andor

HelpRaptor wrote:
> Dr. Blumschein 
> 
> Please put up a website with the Matlab code you've written for natural 
> spectrogram and some demos. Then we can download it and see for ourselves.
> Please comment the code well, as sometimes it is easier to understand the
> numerical process by looking at the program code.

Thank you for this suggestion. While I didn't yet resume after a long 
break my forum on AuditoryFunction at
http://iesk.et.uni-magdeburg.de/~blumsche/AuditoryFunction.html
I already sent a manuscript of mine (4pages only) and a longish ppt file 
(nearly 40 pages, 5 MB) to those who asked me for that, and I will 
continue to do so.
Presumably, the main problem is not the code but openeness for the quite 
unusual principles.

I was in contact with Eckard before I left for my holidays because I
too was curious about his proposition of the Fourier Cosine Transform
being somehow linked to a "natural spectrogram" (to be honest, mostly
because I don't believe it), and he seemed eloquent enough to suggest
that he might be competent in that area. After several emails,
however, and after re-reading them I decided that it isn't really
worth the effort for now, since his replies don't provide the
necessary facts for me to really understand what he's talking about.
Either he's constantly evading my questions, or it's me being
incapable to express myself properly so he can answer them.

I'm not saying he's a fraud (although some of his assertions are
substantially untenable - such as the claim his Fourier Cosine
Transform "natural spectrogram" would not be subject to the Heisenberg
restrictions), but from what I have gained from our correspondence so
far (no precise answers to my questions, a lot of gibberish about the
Fourier Cosine Transform and some general allusions to mathematical
concepts and people that he did not care to back up with the necessary
explanations) I think I'll also wait to see more tangible *facts*
before I invest more time in reading this thread.

Btw., his web page is a collection of emails from other people
generally talking about auditory topics (something of a collection of
wild theories, too, but fun to read), nothing that really helps
getting a handle on any of his assertions and claims, especially not
on his "natural spectrogram".

That's my 2 cents worth about this guy - and, Eckard, no pun intended!
--smb


Eckard Blumschein <blumschein@et.uni-magdeburg.de> wrote in message news:<40AA271C.5040001@et.uni-magdeburg.de>...
> HelpRaptor wrote:
> > Dr. Blumschein 
> > 
> > Please put up a website with the Matlab code you've written for natural 
> > spectrogram and some demos. Then we can download it and see for ourselves.
> > Please comment the code well, as sometimes it is easier to understand the
> > numerical process by looking at the program code.
> 
> Thank you for this suggestion. While I didn't yet resume after a long 
> break my forum on AuditoryFunction at
> http://iesk.et.uni-magdeburg.de/~blumsche/AuditoryFunction.html
> I already sent a manuscript of mine (4pages only) and a longish ppt file 
> (nearly 40 pages, 5 MB) to those who asked me for that, and I will 
> continue to do so.
> Presumably, the main problem is not the code but openeness for the quite 
> unusual principles.

Stephan M. Bernsee wrote:

> I'm not saying he's a fraud (although some of his assertions are
> substantially untenable - such as the claim his Fourier Cosine
> Transform "natural spectrogram" would not be subject to the Heisenberg
> restrictions), 

Distrust against my claim is understandable in this case. However, it 
does not substitute relevant arguments.
Even our own ears do better resolve than everybody would expect who 
applies Heisenberg's principle in the usual but unjustified manner.
(Temporal resolution goes down to less than 10 microseconds, frequency 
resolution reaches less than 1 Hz).
There is a quite simple explanation for this paradox:
We may analyse high as well as low frequencies at a time, using 
different parts of the organ of Corti and massively parallel signal 
processing within brain. The natural spectrogram performs in principle 
similar but even better.
Natural solutions are subject to real restrictions not to wrong 
conclusions.


> Btw., his web page is a collection of emails from other people
> generally talking about auditory topics 
....
> nothing that really helps getting a handle on any of his assertions and claims, especially not
> on his "natural spectrogram".

Unfortunately, this is correct. So far, I only recommend looking at it 
to those who are interested in the special field of auditory perception 
or to those who wonder what led me to the natural spectrogram.

>>I already sent a manuscript of mine (4pages only) and a longish ppt file 
>>(nearly 40 pages, 5 MB) to those who asked me for that, and I will 
>>continue to do so.
>>Presumably, the main problem is not the code but openeness for the quite 
>>unusual principles.

I would like to add that those of you are correct to some extend who 
know that FCT is usually just the real part of complex FT and therefore 
do not expect any change.
On the other hand, they overlook that use of FCT in IR+ removes 
Hermitian redundancy in case of the only physically relevant positive 
elapsed time. As a rule, they are also not aware of the pros and cons of 
this simplification. While renunciation of Heaviside's trick requires to 
add complex calculus later on, if necessary, causality of the theory is 
made sure from the very beginning. Neither Bode's relations nor Kramers 
Kronig relations are necessary for that.
Do not try to subordinate the real-valued world to the complex-valued 
one as a subset. They are about as different from each other but 
nonetheless equally important as sphere and cube.
One may put IR into IR+ and vice versa. Do not worry about counting time 
backwards always from actual now.

Eckard Blumschein

Eckard Blumschein <blumschein@et.uni-magdeburg.de> wrote:
>
> Distrust against my claim is understandable in this case. However, it 
> does not substitute relevant arguments.

Right - that would be your part!

> Even our own ears do better resolve than everybody would expect who 
> applies Heisenberg's principle in the usual but unjustified manner.
> (Temporal resolution goes down to less than 10 microseconds, frequency 
> resolution reaches less than 1 Hz).

I don't think so, Eckard.
As Scotty said: "Can't change the law of physics, captain" ;-)

> There is a quite simple explanation for this paradox:
> We may analyse high as well as low frequencies at a time, using 
> different parts of the organ of Corti and massively parallel signal 
> processing within brain. The natural spectrogram performs in principle 
> similar but even better.

Show me how, and why, please!

> Natural solutions are subject to real restrictions not to wrong 
> conclusions.

From what I've read so far, conclusions are not yet possible based on
the facts (or lack thereof) presented.

> I would like to add that those of you are correct to some extend who 
> know that FCT is usually just the real part of complex FT and therefore 
> do not expect any change.

Why should we?

> On the other hand, they overlook that use of FCT in IR+ removes 
> Hermitian redundancy in case of the only physically relevant positive 
> elapsed time. 

Time, as any other unit that you could put into interpreting the
result of the FCT, DFT, whatever, is totally arbitrary. The conclusion
that the direction of time makes any difference here for the result,
IMHO, is wrong.

--smb