Maker Pro
Maker Pro

Impossible sampling theory!

D

David Bernier

Airy said:
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
 
A

Airy R. Bean

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 said:
Airy said:
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 ]
 
A

Airy R. Bean

"Dracaena"?? "Diracian"!!! The perils of using a
spell checker mechanically!
 
N

Nimrod

Airy R. Bean said:
"Dracaena"?? "Diracian"!!! The perils of using a
spell checker mechanically!

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.
 
D

David Kastrup

Airy R. Bean said:
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.

Well, if you want to work with the Fourier transform of a sampled
signal, the integral over the sampled function must be non-zero, and
you just have isolated points with content. Something has to give,
and it turned out that it was easiest to sacrifice strict point-wise
defined functions since they don't survive integration and
differention unmolested, anyway. And if one wants to have an entity
that will do the right things under integral transforms, it is
probably easiest to define it by its behavior for integration in the
first place: distributions. Stieltjes integrals might be related,
though.
 
P

Peter

They were too busy
studying Machiavelli and Nietzsche with Strauss, Bloom, and their
acolytes from the University of Chicago. Chickenhawks to a man. Bush Jr.
too. I could file
this official U.S. government document with the International Court of
Justice in The Hague as proof-positive that it is now the official
policy of the United States government to wage criminal wars of
aggression against other U.N. member states in violation of the most
elementary principles of the contemporary international legal order that
would be too numerous t


I don't know how all the above got posted in my name but it certainly
wasn't me that posted it!

Peter, G3PHO
 
S

Spin Dryer

On Sat, 11 Dec 2004 21:08:16 GMT, [Peter] said :-
I don't know how all the above got posted in my name but it certainly
wasn't me that posted it!

Peter, G3PHO

Don't be a fool mate, check the headers of the post (H in Agent) - and
you'll see it's Dippy/Hipcrime/Dipslime; look it up.
 
R

Reg Edwards

To summarise - the Earth is over-populated. In conjunction with Aids we are
all doing our inadequate best to remedy the situation. But a rapid descent
into utter chaos is inevitable. It won't take as long as it took the
dinasaurs.

===========================================
 
P

Phil Scott

- or go shamefully to the frozen food section
of your favorite grocery and select 2 high quality pie crusts (you
will need one for the top also).
Boil the prepared delicacy until the meat starts to come off the bones.
Remove, de-bone and cube; continue to reduce the broth.
Brown the onions, peppers and celery.
Add the meat then season, continue browning.
De-glaze with sherry, add the reduced broth.
Finally, put in the root vegetables and simmer for 15 minutes.
Allow to cool slightly.
Place the pie pan in 375 degree oven for a few minutes so bottom crust is not soggy,
reduce oven to 325.
Fill the pie with stew, place top crust and with a fork, seal the crusts together
then poke holes in top.
Return to oven and bake for 30 minutes, or until pie crust is golden brown.



Sudden Infant Death Soup

SIDS: delicious in winter, comparable to old fashioned Beef and Vegetable Soup.
Its free, you can sell the crib, baby clothes, toys, stroller... and so easy to
procure if such a lucky find is at hand (just pick him up from the crib and
he?s good to go)!

SIDS victim, cleaned
½ cup cooking oil
Carrots
onions
broccoli
whole cabbage
fresh green beans
potato
turnip
celery
tomato
½ stick butter
1 cup cooked pasta (macaroni, shells, etc.)

Remove as much meat as possible, cube, and brown in hot oil.
Add a little water, season, then add the carcass.
Simmer for half an hour keeping the stock thick.
Remove the carcass and add the vegetables slowly to the stock,
so that it remains boiling the whole time.
Cover the pot and simmer till vegetables are tender
(2 hours approximately).
Continue seasoning to taste.
Before serving, add butter and pasta,
serve piping with hot bread and butter.



Offspring Rolls

Similar to Vietnamese style fried rolls, they have lots of meat
(of course this can consist of chicken, beef, pork, o
 
A

Airy R. Bean

But it doesn't provide correct results!

Kevin Neilson said:
One of my professors implied that the Dirac delta wasn't mathematically
rigorous but provides correct results so it's used nonetheless.
 
A

Airy R. Bean

Does the definition whose URL you quoted (and how much better
a form of debate if you present your own argument rather than seeking
to send your correspondents off somewhere else?) describe how the attributes
of area
and amplitude of the Diracian can possibly be representative of
real-world sampling pulses with "plenty of rigor"?
 
S

Spike

Does the definition whose URL you quoted (and how much better
a form of debate if you present your own argument rather than seeking
to send your correspondents off somewhere else?) describe how.....

For some reason you appear frightened of researching information, such
as following a url, and integrating the knowledge gained with what you
already know in order to take things into new territory. But this is
how science advances, and the study for a degree of PhD requires that
the current position be adequately researched as a prerequisite to
moving on to one's particular research topic. This is called the
Literature Survey, and it is a fundamental part of the PhD. Fail to
perform this adequately, and your PhD is doomed.

As you will not follow urls, I append a short article to help you, and
as you are prone to ISP failures, I may repost this from time-to-time.

Note particularly the paragraph headed "RESEARCH METHODS".

For the information of other readers, the url is
http://www.itacs.uow.edu.au/research/postgrad/comments.shtml

GENERAL COMMENTS ON RESEARCH

PREAMBLE:
Research, by its very nature, is a step into the unknown and therefore
open-ended; there are no guarantees. As such your supervisor(s) will
not know the answer to your research questions (research is not the
same as coursework). This step is usually guided by the results of
previous researchers in the field. Such previous work "sets the
scene"/points you in the right direction/tells you where to look.
Steady, methodical and persistent effort on your part is then
necessary to reach your research goal, often employing the
scientific/experimental method(s) (e.g. hypothesis testing). Of
itself, this might not be sufficient; genuine insight, serendipity and
unexpected "connections" from seemingly unrelated areas are often
necessary. These can neither be anticipated nor manifested at will.
Many scientific breakthroughs come from the most unexpected sources.

RESEARCH METHODS:
In order to (a) become familiar with your chosen area of research, and
(b) to ensure you don't "reinvent the wheel" and commence working on a
topic which has been previously researched, it is essential to become
familiar with the published literature in the field. A good way of
doing this is to write your own literature survey/review article,
perhaps even presenting a seminar/conference paper on your findings.
This helps you not only to familiarise yourself with previous work,
but also to highlight what has yet to be done/what problems remain to
be solved in your chosen field. It also helps to identify areas in
which you are perhaps weak and need to learn and/or improve your
skills.
The first six months of a 3-year PhD programme should be devoted to a
literature survey; the second six months to replicating previous work.
By the end of the first year, it should become clear as to how the
earlier work can be extended/improved, thus enabling a detailed
research proposal to be formulated. Naturally, the remaining two years
are spent in following these ideas (and periodically backtracking and
revising your research plan in the light of your findings).

NOTE:
For Research Masters (and undergraduate Honours), it is quite valid to
work on a topic which has been researched previously, but from a
different perspective/extending it in some manner. For a PhD, an
original contribution to knowledge is required - establishing what has
been done previously and identifying a substantial problem to tackle
is even more critical here. Successfully applying new/different (and
better) techniques to problems previously solved by other means is
still a valid approach for a PhD however.
In order to conduct a literature survey, you will need to hone your
library skills, specifically: (i) how to track down survey
papers/introductory books, (ii) developing the art of quickly reading
and evaluating abstracts (at least - entire papers if appropriate),
(iii) identification of the classic references in the field, and
subsequently tracking them down (in hard copy form, either within the
UoW Library, or via Inter-Library Loans), (iv) use of the UoW on-line
Library resources, as well as more general searching of the World Wide
Web, & (v) the ability to critically evaluate what's been done
previously. In short, who are the key researchers in the field? What
are the seminal works/books/survey papers? What are the most important
journals in your chosen area?

NOTE:
It is very important to keep abreast of the latest developments in the
field, especially if someone publishes what you are currently working
on. If this happens, you may need to take a significant change of
direction with your work. Thus periodic updates of your literature
survey will be necessary during the course of your study.
 
A

Alan

For some reason you appear frightened of researching information, such
as following a url, and integrating the knowledge gained with what you
already know in order to take things into new territory. But this is
how science advances, and the study for a degree of PhD requires that
the current position be adequately researched as a prerequisite to
moving on to one's particular research topic. This is called the
Literature Survey, and it is a fundamental part of the PhD. Fail to
perform this adequately, and your PhD is doomed.

The paraoid stalker and coward formerly known as RVMJ and Binary Era
continues his obsessive stalking.

[ rest of crap snipped ]
 
A

Airy R. Bean

Against whom is the spikeful Old Mother Hen Nugatory-RVMJ-Binaryera
venting her spleen on the occasion quoted below? Who do we know
who is studying for a PhD and who has thus invited her infantile
and obsessive bile?
 
F

Frank Turner-Smith G3VKI

Airy R. Bean said:
Against whom is the spikeful Old Mother Hen Nugatory-RVMJ-Binaryera
venting her spleen on the occasion quoted below? Who do we know
who is studying for a PhD and who has thus invited her infantile
and obsessive bile?
Well it's unlikely to be YOU, Beanie. I doubt you even passed the 11+
....(_!_)...
 
A

Alan

Against whom is the spikeful Old Mother Hen Nugatory-RVMJ-Binaryera
venting her spleen on the occasion quoted below? Who do we know
who is studying for a PhD and who has thus invited her infantile
and obsessive bile?

Who knows? Please cut him a little slack. Let us not forget that the
school kids are on holiday. As a noted coward and pedophobe Aero Spike
must be feeling awful at this time of year.
Do not forget that he was the one who gave us these gems....

'I was afraid to leave my home'
'I was too scared to take leave from work'

etc.

A person so cowardly can only really hit back by posting nonsense on the
NGs
 
N

Nimrod

James Bond said:
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

Unheard of for Gareth to post anything helpful.
 
Z

ZZZPK

: Unheard of for Gareth to post anything helpful.
:
:
5.6 on the cluckometer
 
Top