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Airy R. Bean
Guest
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 Posted:
Thu Dec 09, 2004 8:29 pm Post subject:
Impossible sampling theory! |
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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?
1. The samples that you get are measured in the order
of single volts whereas the Diracian is infinitely tall. Surely,
if something of the order of unity were to be multiplied by
something of the order of infinity, the result would
be of the order of infinity?
How do you account for the difference? Do you have
some internal mental model where there is an invisible constant,
"Big K", perhaps, to account for the difference in scaling?
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.
How do you handle this mentally when the area of the Diracian
is unity?
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?
3. If you are one of those who claim that the sampled signal is a short
spike of zero width, then it is zero-integrable and not analysable by
any process involving Laplace Transforms.
How do you overcome the problem that your sampled signals are
not representable in the way that you claim? |
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James Bond
Guest
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| Posted:
Thu Dec 09, 2004 8:29 pm Post subject:
beanie |
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how old are you beanie?
you cause a lot of problems. thats my observation
interesting indeed. whats in it for you? do you learn from this group? do
you provide input that others appreciate?
dr. x
---
Outgoing mail is certified Virus Free.
Checked by AVG anti-virus system (http://www.grisoft.com).
Version: 6.0.808 / Virus Database: 550 - Release Date: 08/12/2004 |
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David C. Ullrich
Guest
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| Posted:
Thu Dec 09, 2004 9:12 pm Post subject:
Re: Impossible sampling theory! |
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On Thu, 9 Dec 2004 15:29:52 -0000, "Airy R. Bean" <me@privacy.net>
wrote:
| Quote: | A number of texts suggest that sampling can be modelled
by multiplying the incoming waveform by a comb of
Diracian Delta Functions.
|
Huh. A second ago you denied ever saying that every
text on the planet is wrong. Can you name a _relevant_
text, that being a text that discusses this issue,
that denies what you just said?
| Quote: | How can this be?
1. The samples that you get are measured in the order
of single volts whereas the Diracian is infinitely tall.
|
No, it's not infinitely tall. It's not a function.
| Quote: | Surely,
if something of the order of unity were to be multiplied by
something of the order of infinity, the result would
be of the order of infinity?
|
But it's true that after you do that sampling what's
left is no longer a function (at least not a function
defined on R).
| Quote: | How do you account for the difference? Do you have
some internal mental model where there is an invisible constant,
"Big K", perhaps, to account for the difference in scaling?
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.
How do you handle this mentally when the area of the Diracian
is unity?
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?
3. If you are one of those who claim that the sampled signal is a short
spike of zero width, then it is zero-integrable and not analysable by
any process involving Laplace Transforms.
How do you overcome the problem that your sampled signals are
not representable in the way that you claim?
|
How do you account for the fact that you ask us all these
silly questions, even though you're determined to pay no
attention if anyone tries to explain?
************************
David C. Ullrich |
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Stan Pawlukiewicz
Guest
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| Posted:
Thu Dec 09, 2004 9:22 pm 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?
|
About fifty years of carefully crafted theory from numerous estemed
| Quote: |
1. The samples that you get are measured in the order
of single volts whereas the Diracian is infinitely tall. Surely,
if something of the order of unity were to be multiplied by
something of the order of infinity, the result would
be of the order of infinity?
The information is in the area under the pulse. |
| Quote: | How do you account for the difference?
|
Don't need to.
Do you have
| Quote: | some internal mental model where there is an invisible constant,
"Big K", perhaps, to account for the difference in scaling?
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The delta function is used as method of representing discrete quantities
on a continuous axis. It's a form of embedding.
Its used in numerous disciplines such as probability, in representing
mixed discrete and continuous probability densities.
| Quote: |
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.
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Sampling theory is intrinsically unitless.
| Quote: |
How do you handle this mentally when the area of the Diracian
is unity?
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Handle what, when I multiply it, the quantity goes with the area.
| Quote: |
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?
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Its an abstraction, the information is in the area under the curve.
You want a real world approximation of the delta function, consider the
optical pulse created in nuclear fusion experiments that try to implode
deuterium pellets.
| Quote: |
3. If you are one of those who claim that the sampled signal is a short
spike of zero width, then it is zero-integrable and not analysable by
any process involving Laplace Transforms.
|
Its a generalized function, defined as the derivative of the unit step.
There is a Fourier pair delta(t) <-> 1
Look it up if you don't believe me.
| Quote: |
How do you overcome the problem that your sampled signals are
not representable in the way that you claim?
Not my problem, its your problem.
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Airy R. Bean
Guest
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| Posted:
Thu Dec 09, 2004 9:40 pm Post subject:
Re: Impossible sampling theory! |
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And I haven't said it below. Are you a troll?
And what I denied ever saying was that every
textBOOK was wrong.
You'ew changing your goalposts by the minute.
"David C. Ullrich" <ullrich@math.okstate.edu> wrote in message
news:27ugr0p24k1bhc3vj26nf6ep161p9b47io@4ax.com...
| Quote: | On Thu, 9 Dec 2004 15:29:52 -0000, "Airy R. Bean" <me@privacy.net
wrote:
A number of texts suggest that sampling can be modelled
by multiplying the incoming waveform by a comb of
Diracian Delta Functions.
Huh. A second ago you denied ever saying that every
text on the planet is wrong. |
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Tim Wescott
Guest
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| Posted:
Thu Dec 09, 2004 9:40 pm Post subject:
Don't Feed the Troll! (was Re: Impossible sampling theory!) |
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Airy R. Bean wrote:
essentially what he's been writing all along.
I've come to agree with Jerry. Don't feed the troll!
--
Tim Wescott
Wescott Design Services
http://www.wescottdesign.com |
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Airy R. Bean
Guest
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| Posted:
Thu Dec 09, 2004 9:44 pm Post subject:
Re: Impossible sampling theory! |
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Why would there be any texts that deny that "A number
of texts suggest that sampling can be modelled by multiplying
the incoming waveform by a comb of Diracian Delta Functions"?
What texts do you suggest would discuss other texts in that manner?
"David C. Ullrich" <ullrich@math.okstate.edu> wrote in message
news:27ugr0p24k1bhc3vj26nf6ep161p9b47io@4ax.com...
| Quote: | On Thu, 9 Dec 2004 15:29:52 -0000, "Airy R. Bean" <me@privacy.net
wrote:
A number of texts suggest that sampling can be modelled
by multiplying the incoming waveform by a comb of
Diracian Delta Functions.
Huh. A second ago you denied ever saying that every
text on the planet is wrong. Can you name a _relevant_
text, that being a text that discusses this issue,
that denies what you just said? |
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Airy R. Bean
Guest
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| Posted:
Thu Dec 09, 2004 9:52 pm Post subject:
Re: Don't Feed the Troll! (was Re: Impossible sampling theor |
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The only trolls in this NG would seem to be those
who clamour that the troll should not be fed. Often, as
in the case of Westcott below, their plaintiff moans
follow their showing themselves up with childish
outbursts which are then chastised without being risen
to.
Having been so chastised, they try to suggest that it is others
rather than they themselves as the originators of
childish posts who should be ostracised.
"Tim Wescott" <tim@wescottnospamdesign.com> wrote in message
news:10rgvvsidsjc6c3@corp.supernews.com...
| Quote: | Airy R. Bean wrote:
essentially what he's been writing all along.
I've come to agree with Jerry. Don't feed the troll! |
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deBaser
Guest
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| Posted:
Thu Dec 09, 2004 10:05 pm Post subject:
Re: Don't Feed the Troll! (was Re: Impossible sampling theor |
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Tim Wescott wrote:
| Quote: | Airy R. Bean wrote:
essentially what he's been writing all along.
I've come to agree with Jerry. Don't feed the troll!
|
Hey a troll is for life not just for xmas. Do you know there are starving
trolls out there so give him all your f@ckin' money. Feed the troll, let
him know its xmas time
Bob Geldoff |
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Airy R. Bean
Guest
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| Posted:
Thu Dec 09, 2004 10:07 pm Post subject:
Re: Impossible sampling theory! |
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How tall do you think it is for the multiplication
to take effect in a real circuit?
"David C. Ullrich" <ullrich@math.okstate.edu> wrote in message
news:27ugr0p24k1bhc3vj26nf6ep161p9b47io@4ax.com...
| Quote: | On Thu, 9 Dec 2004 15:29:52 -0000, "Airy R. Bean" <me@privacy.net
wrote:
1. The samples that you get are measured in the order
of single volts whereas the Diracian is infinitely tall.
No, it's not infinitely tall. It's not a function. |
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Kevin Neilson
Guest
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| Posted:
Thu Dec 09, 2004 10:11 pm 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?
1. The samples that you get are measured in the order
of single volts whereas the Diracian is infinitely tall. Surely,
if something of the order of unity were to be multiplied by
something of the order of infinity, the result would
be of the order of infinity?
|
One of my professors implied that the Dirac delta wasn't mathematically
rigorous but provides correct results so it's used nonetheless. |
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Torkel Franzen
Guest
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| Posted:
Thu Dec 09, 2004 10:19 pm Post subject:
Re: Don't Feed the Troll! (was Re: Impossible sampling theor |
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"Airy R. Bean" <me@privacy.net> writes:
| Quote: | in the case of Westcott below, their plaintiff moans
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You mean "plaintive". |
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Airy R. Bean
Guest
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| Posted:
Thu Dec 09, 2004 10:22 pm Post subject:
Re: Impossible sampling theory! |
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It can be mathematically rigorous if you were
to use the curve borrowed from the Normal
Distribution of statistics, but it cannot
produce the correct results for the simple
reason that the pulses obtained are several orders of
magnitude different from the pulses in real circuits.
(And if you regard the pulses produced in real circuits
as existing only at a point, then those pulses are
not analysable)
In all aspects of engineering, the numbers that you
analyse are the physical values that arise in your
equipment. I wonder how others come to terms
with the fact that the numbers produced by the claim
that sampling is the multiplication by a comb of
Diracian are simply far, far too large?
"Kevin Neilson" <kevin_neilson@removethiscomcast.net> wrote in message
news:cpa0vb$quo1@xco-news.xilinx.com...
| 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?
1. The samples that you get are measured in the order
of single volts whereas the Diracian is infinitely tall. Surely,
if something of the order of unity were to be multiplied by
something of the order of infinity, the result would
be of the order of infinity?
One of my professors implied that the Dirac delta wasn't mathematically
rigorous but provides correct results so it's used nonetheless. |
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Airy R. Bean
Guest
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| Posted:
Thu Dec 09, 2004 10:23 pm Post subject:
Re: Don't Feed the Troll! (was Re: Impossible sampling theor |
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Yes! I did!
"Torkel Franzen" <torkel@sm.luth.se> wrote in message
news:vcbvfbbl788.fsf@beta19.sm.ltu.se...
| Quote: | "Airy R. Bean" <me@privacy.net> writes:
in the case of Westcott below, their plaintiff moans
You mean "plaintive". |
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Randy Poe
Guest
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| Posted:
Thu Dec 09, 2004 10:27 pm Post subject:
Re: Impossible sampling theory! |
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Airy R. Bean wrote:
| Quote: | How tall do you think it is for the multiplication
to take effect in a real circuit?
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A real sample-and-hold circuit has a finite width and a
height of 1.
And the Fourier theory in actual DSP is based on discrete
Fourier series, which involves integrals over finite time
windows, not the continuous Fourier transform which involves
integrals over all time.
And the DFT of a comb function of height 1 is another comb
function of finite height.
But you knew all that already, didn't you?
- Randy |
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