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ETS
Guest
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 Posted:
Fri Dec 10, 2004 9:48 pm Post subject:
Re: Impossible sampling theory! |
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Airy R. Bean wrote:
| Quote: | ooo = "of the order of"
I have described that finite width in my Lesson 3.
It is interesting that you seem to agree with me on that
basis - that the sinc roll-off implies the real width of
the processed signal is a function of the input sampling
and not of the output DAC.
The mathematics, does not, however, work out because the
Diracian is orders of magnitude greater than the signals that
we deal with.
"ETS" <emale80919@yahoo.com> wrote in message
news:10rh8gtjlcpbk47@corp.supernews.com...
Airy R. Bean wrote:
2. The area of the sampled pulse is very much less than unity,
the volts being ooo unity and the time being typically ooo usecs.
Not sure what u mean about time being ooo usecs. In a real ckt,
the sample pulse does have a finite width which introduces a sinc
rolloff of the sampled data. A dirac has infinite height and 0 width.
Check the math above, it does work out.
True, it is also orders of magnitude narrower than the signals we deal |
with :-)
You can't take a dirac in pieces, you have to take the amplitude (oo)
and the width 0 for a dirac to work. Also, the dirac should be viewed
as a limit, not at an absolute time. A similar problem exists in
probability. The probability at a point is zero for a continuous pdf.
In order to use it properly, it must be integrated. That was one that
threw me for a loop when I first encountered it. Sorry I have not seen
your lesson 3, not sure what you mean by finite width. A dirac by
definition has zero width, and the integral only exists in the limit. |
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ETS
Guest
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| Posted:
Fri Dec 10, 2004 10:01 pm Post subject:
Re: Impossible sampling theory! |
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Airy R. Bean wrote:
| Quote: | It doesn't "simplify" it because it is not
related to it. They are orders of magnitude
in difference.
If the real samples are taken to be single points in time,
then the signal they represent is zero-integrable. If they're
then being treated as variations on the Diracian so that they can
be analysed, then there has to be some (unmentioned) scaling
factor involved in the model.
The issue of spectral droop is a red herring because
the action of any LPF on the output is to null out the
higher harmonics of the sampling frequency and their
sidebands, and so their amplitudes are irrelevant.
What about this, do you believe the dirac impulse is a real function or |
not? I look at it as a mathematical tool, that is all. Think about
this, all continuous time functions exist as a collection of single
points (unless we can argue that time is discrete :-)) No matter how
small the time scale, a continuous time function is represented as a
point with zero width at that instant of time. So a continuous function
can be viewed as a function sampled with an (oo) sample rate. Kinda
interesting way to view it, that in the limit all signals are sampled ;-)
Not sure about you second paragraph there, the spectral droop is a
funtion of the sample aperture. With a dirac, zero aperture means no
droop. Real world sampled signal do experience this because no one has
built a diracian sampler. The LPF is used for antialiasing, not for
spectral droop. |
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ETS
Guest
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| Posted:
Fri Dec 10, 2004 10:03 pm Post subject:
Re: Impossible sampling theory! |
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Airy R. Bean wrote:
| Quote: | There's no confusion here - all mathematical descriptions
of engineering processes are models of those processes.
The use of the Diracian is not a model because it does not
model the values of the engineering process.
"ETS" <emale80919@yahoo.com> wrote in message
news:10rh8gtjlcpbk47@corp.supernews.com...
Airy R. Bean wrote:
How do you come to terms with the attributes of your claimed model
being orders of magnitude different from the signals of the real world?
Don't confuse real world with mathematical modeling. Obviously diracs
do not exist in the real world, they are a mathematical model that is
not attainable with real world circuits.
Well, let's not get too hung up on nomenclature. Let's call it an |
idealized mathematical analog of a real world event. |
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Eric Jacobsen
Guest
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| Posted:
Fri Dec 10, 2004 11:42 pm Post subject:
Re: Impossible sampling theory! |
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On Fri, 10 Dec 2004 10:02:59 -0000, "Airy R. Bean" <me@privacy.net>
wrote:
| Quote: | Why not cite some of those responses and show
how they answered the questions?
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Gareth, this really is ridiculous. So many people have posted answers
to you that it isn't practical to even know where to start. You, on
the other hand, are the one claiming they're incorrect, so the burden
really is on you to explain why you think so.
| Quote: | The answer is, that they did not, and merely repeated
parrot-fashion (or religionist fashion if you prefer) what
could be read from the text books. As I referred to such
textbook context initially, then those responses were meaningless,
other than, perhaps, to serve as an ego-trip for the posters.
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This just oozes irony. Gushes. Floods.
| Quote: | "Andrew Reilly" <andrew-newspost@areilly.bpc-users.org> wrote in message
news:pan.2004.12.09.21.51.51.348184@areilly.bpc-users.org...
You have provided no coherent or correct refutation of any of the
responses that were provided in the previous discussions.
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Eric Jacobsen
Minister of Algorithms, Intel Corp.
My opinions may not be Intel's opinions.
http://www.ericjacobsen.org |
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Eric Jacobsen
Guest
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| Posted:
Fri Dec 10, 2004 11:44 pm Post subject:
Re: Impossible sampling theory! |
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On Fri, 10 Dec 2004 10:10:12 -0000, "Airy R. Bean" <me@privacy.net>
wrote:
| Quote: | (You're a CBer, so you won't have a clue about what the
above means, and so I append a short article to assist you.)
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Better watch out, Gareth, there's a guy here who hates it when people
post childish personal insults. You don't want to get on his bad
side.
Eric Jacobsen
Minister of Algorithms, Intel Corp.
My opinions may not be Intel's opinions.
http://www.ericjacobsen.org |
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David Bernier
Guest
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| Posted:
Sat Dec 11, 2004 3:55 am Post subject:
Re: Impossible sampling theory! |
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Airy R. Bean wrote:
| Quote: | A number of texts suggest that sampling can be modelled
by multiplying the incoming waveform by a comb of
Diracian Delta Functions.
How can this be?
[snip] |
You might be interested in the idea of
windowed Fourier transforms, which are down to earth.
I did a search with Google, and to sample around time T0 one
can multiply the signal by a box of area 1 of this type:
_____------.--------______
t=T0
and then do the usual Fourier Transform of the resulting product.
[ The width of the box has to be chosen carefully to
give "nice" or "usable" results ]
This is described in course notes by William J. Phillips
of Dalhousie University here:
http://www.engmath.dal.ca/courses/engm6610/notes/node3.html
The four figures at the end of
Section 2.1 "The Short Time Fourier Transform",
are quite enlightening.
David Bernier |
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Airy R. Bean
Guest
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| Posted:
Sat Dec 11, 2004 3:14 pm Post subject:
Re: Impossible sampling theory! |
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The parameters that you ascribe below show that the
Diracian is not identifiable in any practical sampling.
"ETS" <emale80919@yahoo.com> wrote in message
news:xrkud.20674$8S5.2284816@twister.southeast.rr.com...
| Quote: | You can't take a dirac in pieces, you have to take the amplitude (oo)
and the width 0 for a dirac to work. |
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Airy R. Bean
Guest
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| Posted:
Sat Dec 11, 2004 3:19 pm Post subject:
Re: Impossible sampling theory! |
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As indeed do I. All mathematics when applied to
engineering is a tool or a model.
Certainly, we use it as a tool in the Analogue
Signal Processing when we consider the Impulse
Response of our networks.
But in the case of sampling, we are not exciting
our circuit designs with a tool signal - we generate
a specific sampling waveform whose attributes
are not those of the Diracian, and therefore the
derivation is erroneous.
However, the Diracian is not a model of signal
that appears in real-world sampling circuits.
All other mathematics that the electronic engineer
encounters have values that represent those
measurable from the circuits under consideration.
"ETS" <emale80919@yahoo.com> wrote in message
news:ADkud.35028$Mu3.2413177@twister.southeast.rr.com...
| Quote: | What about this, do you believe the dirac impulse is a real function or
not? I look at it as a mathematical tool, that is all. |
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Airy R. Bean
Guest
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| Posted:
Sat Dec 11, 2004 3:20 pm Post subject:
Re: Impossible sampling theory! |
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Only when analysed under an integral sign.
"ETS" <emale80919@yahoo.com> wrote in message
news:ADkud.35028$Mu3.2413177@twister.southeast.rr.com...
| Quote: | ..... So a continuous function
can be viewed as a function sampled with an (oo) sample rate. Kinda
interesting way to view it, that in the limit all signals are sampled ;-) |
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Airy R. Bean
Guest
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| Posted:
Sat Dec 11, 2004 3:21 pm Post subject:
Re: Impossible sampling theory! |
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I was referring to the LPF following the DAC on the
output - a bit late to apply an anti-aliasing filter there!
"ETS" <emale80919@yahoo.com> wrote in message
news:ADkud.35028$Mu3.2413177@twister.southeast.rr.com...
| Quote: | Not sure about you second paragraph there, the spectral droop is a
funtion of the sample aperture. With a dirac, zero aperture means no
droop. Real world sampled signal do experience this because no one has
built a diracian sampler. The LPF is used for antialiasing, not for
spectral droop. |
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Airy R. Bean
Guest
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| Posted:
Sat Dec 11, 2004 3:22 pm Post subject:
Re: Impossible sampling theory! |
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It is not "ideal". It is not even representative.
"ETS" <emale80919@yahoo.com> wrote in message
news:bFkud.35030$Mu3.2413177@twister.southeast.rr.com...
| Quote: | Well, let's not get too hung up on nomenclature. Let's call it an
idealized mathematical analog of a real world event. |
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Airy R. Bean
Guest
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| Posted:
Sat Dec 11, 2004 3:27 pm Post subject:
Re: Impossible sampling theory! |
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Not disputed at all.
However, the sampling waveforms in practice
are not represented by an area of 1.
If anyone wishes to claim that their sampled
signals are represented in some way by the Diracian,
then they must mentally model an invisible scaling factor to
bring the magnitudes of their sampled waveforms
into the order of magnitude of the attributes of the
Dracaena.
I enquired as to how others came to terms with this
blatant discrepancy.
"David Bernier" <david250@videotron.ca> wrote in message
news:DPpud.32050$bD6.843615@wagner.videotron.net...
| Quote: | Airy R. Bean wrote:
A number of texts suggest that sampling can be modelled
by multiplying the incoming waveform by a comb of
Diracian Delta Functions.
How can this be?
You might be interested in the idea of
windowed Fourier transforms, which are down to earth.
I did a search with Google, and to sample around time T0 one
can multiply the signal by a box of area 1 of this type:
_____------.--------______
t=T0
and then do the usual Fourier Transform of the resulting product.
[ The width of the box has to be chosen carefully to
give "nice" or "usable" results ] |
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Airy R. Bean
Guest
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| Posted:
Sat Dec 11, 2004 3:38 pm Post subject:
Re: Impossible sampling theory! |
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"Dracaena"?? "Diracian"!!! The perils of using a
spell checker mechanically!
"Airy R. Bean" <me@privacy.net> wrote in message
news:3200rtF3fjpeeU11@individual.net...
| Quote: | Not disputed at all.
However, the sampling waveforms in practice
are not represented by an area of 1.
If anyone wishes to claim that their sampled
signals are represented in some way by the Diracian,
then they must mentally model an invisible scaling factor to
bring the magnitudes of their sampled waveforms
into the order of magnitude of the attributes of the
Dracaena. |
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Nimrod
Guest
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| Posted:
Sat Dec 11, 2004 5:23 pm Post subject:
Re: Impossible sampling theory! |
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"Airy R. Bean" <me@privacy.net> wrote in message
news:32017gF3dmk1aU1@individual.net...
| Quote: | "Dracaena"?? "Diracian"!!! The perils of using a
spell checker mechanically!
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I just assumed it was the "Dracaena" that you thought you understood. You
sure as hell don't understand the "Diracian"!!!
I did some googling and tracked down the posts that have explained this to
you before. You didn't understand it then and still don't. |
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Randy Poe
Guest
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| Posted:
Sat Dec 11, 2004 5:48 pm Post subject:
Re: Impossible sampling theory! |
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Airy R. Bean wrote:
| Quote: | If anyone wishes to claim that their sampled
signals are represented in some way by the Diracian,
then they must mentally model an invisible scaling factor to
bring the magnitudes of their sampled waveforms
into the order of magnitude of the attributes of the
Dracaena.
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No they must not.
| Quote: | I enquired as to how others came to terms with this
blatant discrepancy.
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It has been explained to you over and over why there is
no "blatant discrepancy", that nobody is using the model
you claim they are. You are arguing with a strawman and you
know it.
If the measurement process is modeled with delta-functions,
the model also includes an integration. The delta-functions
appear under integrals.
If the model is just using multiplication by a sampling
function, then it uses spikes of finite height, usually 1.
Nobody is modeling sampling as multiplication by a delta
function without integration. Your repeated questions about
how can this model work are pointless, since you are asking
about a model nobody is using.
And for the record, nobody is using the term "Diracian"
as far as I have ever seen.
- Randy |
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