(too old to reply)
Chimera
8 years ago
Post by Airy R. Bean
If you have a mathematical function that has no width
and exists only at discrete points then it is zero-integrable,
with the exception of the contrivance of Dirac's Delta function.
The "contrivance of Dirac's Delta function"? As we are talking about Dirac'sIf you have a mathematical function that has no width
and exists only at discrete points then it is zero-integrable,
with the exception of the contrivance of Dirac's Delta function.
Delta function does that not make it rather relevant?
Your problem is that you don't understand even the basics of what you are
trying to study. Dirac's delta function has unit AREA and tends toward zero
width. The fact that it is defined as an AREA _repeat AREA _ then it is
intergrable. If not, then sampling would not work.
Do you have any technical qualifications in this field? Any at all?
Chimera
Airy R. Bean
8 years ago
1. The person masquerading as "Chimera" has latched onto
the attributes of the Delta Function, which were never in dispute.
However, taken with her infantile stance of name-calling, she is
best ignored for the irrelevance that she undoubtedly is.
Examples of her infantile stance may be seen below.
2. Whereas what you say is true, there is a problem with
real sampling taken as points in that it yields samples that are
zero-integrable
and therefore impossible to determine the frequency spectrum for
by conventional mathematical analysis.
3. The spectrum of real sampling changes dependant upon the
width of the sampling pulse, and we are only interested in the
value of the sampled waveform at the rising edge, and a spectrum that
is independent of the sampling pulse width.
4. So, to represent that rising edge only, we treat our real samples
as existing only at that edge
5. As such, those samples are isomorphic to the Unit Impulse but
because of their small size are zero-integrable.
6. Therefore, in order to achieve an analysis, we replace the unity
of one that is the characteristic of the real world with the unity
of infinity which is the amplitude of the Unit Impulse.
7. This is a contrivance for modelling only, and it is important
to stress that real sampling is NOT multiplying by a Unit Impulse,
for this raises so many valid mathematical objections.
Facts are inconvenient? Only to those who have swallowed the
religious lie that real sampling _IS_ multiplying by a comb of impulses
rather then _IS MODELLED_ by such.
something a bit more than twice the bandwidth of the initial waveform, it
can
the attributes of the Delta Function, which were never in dispute.
However, taken with her infantile stance of name-calling, she is
best ignored for the irrelevance that she undoubtedly is.
Examples of her infantile stance may be seen below.
2. Whereas what you say is true, there is a problem with
real sampling taken as points in that it yields samples that are
zero-integrable
and therefore impossible to determine the frequency spectrum for
by conventional mathematical analysis.
3. The spectrum of real sampling changes dependant upon the
width of the sampling pulse, and we are only interested in the
value of the sampled waveform at the rising edge, and a spectrum that
is independent of the sampling pulse width.
4. So, to represent that rising edge only, we treat our real samples
as existing only at that edge
5. As such, those samples are isomorphic to the Unit Impulse but
because of their small size are zero-integrable.
6. Therefore, in order to achieve an analysis, we replace the unity
of one that is the characteristic of the real world with the unity
of infinity which is the amplitude of the Unit Impulse.
7. This is a contrivance for modelling only, and it is important
to stress that real sampling is NOT multiplying by a Unit Impulse,
for this raises so many valid mathematical objections.
Facts are inconvenient? Only to those who have swallowed the
religious lie that real sampling _IS_ multiplying by a comb of impulses
rather then _IS MODELLED_ by such.
Post by Chimera
Delta function does that not make it rather relevant?
Your problem is that you don't understand even the basics of what you are
trying to study. Dirac's delta function has unit AREA and tends toward zero
width. The fact that it is defined as an AREA _repeat AREA _ then it is
intergrable. If not, then sampling would not work.
Do you have any technical qualifications in this field? Any at all?
Not to pile on here, but the fact is, if someone provides sampling data at
Post by Airy R. Bean
If you have a mathematical function that has no width
and exists only at discrete points then it is zero-integrable,
with the exception of the contrivance of Dirac's Delta function.
The "contrivance of Dirac's Delta function"? As we are talking about Dirac'sIf you have a mathematical function that has no width
and exists only at discrete points then it is zero-integrable,
with the exception of the contrivance of Dirac's Delta function.
Delta function does that not make it rather relevant?
Your problem is that you don't understand even the basics of what you are
trying to study. Dirac's delta function has unit AREA and tends toward zero
width. The fact that it is defined as an AREA _repeat AREA _ then it is
intergrable. If not, then sampling would not work.
Do you have any technical qualifications in this field? Any at all?
something a bit more than twice the bandwidth of the initial waveform, it
be exactly reconstructed.
Is this one of those discussions were facts are inconvenient?
Is this one of those discussions were facts are inconvenient?
Leigh
8 years ago
Post by Airy R. Bean
You behave like a 5 year old.....
That's two years older than the characteristics you display.You behave like a 5 year old.....
--
#!/bin/sh {who;} {last;} {pause;} {grep;} {touch;} {unzip;}
mount /dev/girl -t {wet;} {fsck;} {fsck;} {fsck;} {fsck;} echo
yes yes yes {yes;} umount {/dev/girl;zip;} rm -rf {wet.spot;}
{sleep;} finger: permission denied
#!/bin/sh {who;} {last;} {pause;} {grep;} {touch;} {unzip;}
mount /dev/girl -t {wet;} {fsck;} {fsck;} {fsck;} {fsck;} echo
yes yes yes {yes;} umount {/dev/girl;zip;} rm -rf {wet.spot;}
{sleep;} finger: permission denied
Chimera
8 years ago
Post by Airy R. Bean
1. The person masquerading as "Chimera" has latched onto
the attributes of the Delta Function, which were never in dispute.
However, taken with her infantile stance of name-calling, she is
best ignored for the irrelevance that she undoubtedly is.
Examples of her infantile stance may be seen below.
2. Whereas what you say is true, there is a problem with
real sampling taken as points in that it yields samples that are
zero-integrable
and therefore impossible to determine the frequency spectrum for
by conventional mathematical analysis.
3. The spectrum of real sampling changes dependant upon the
width of the sampling pulse, and we are only interested in the
value of the sampled waveform at the rising edge, and a spectrum that
is independent of the sampling pulse width.
4. So, to represent that rising edge only, we treat our real samples
as existing only at that edge
5. As such, those samples are isomorphic to the Unit Impulse but
because of their small size are zero-integrable.
6. Therefore, in order to achieve an analysis, we replace the unity
of one that is the characteristic of the real world with the unity
of infinity which is the amplitude of the Unit Impulse.
7. This is a contrivance for modelling only, and it is important
to stress that real sampling is NOT multiplying by a Unit Impulse,
for this raises so many valid mathematical objections.
Facts are inconvenient? Only to those who have swallowed the
religious lie that real sampling _IS_ multiplying by a comb of impulses
rather then _IS MODELLED_ by such.
1. If the attributes of the unit impulse were never in dispute,1. The person masquerading as "Chimera" has latched onto
the attributes of the Delta Function, which were never in dispute.
However, taken with her infantile stance of name-calling, she is
best ignored for the irrelevance that she undoubtedly is.
Examples of her infantile stance may be seen below.
2. Whereas what you say is true, there is a problem with
real sampling taken as points in that it yields samples that are
zero-integrable
and therefore impossible to determine the frequency spectrum for
by conventional mathematical analysis.
3. The spectrum of real sampling changes dependant upon the
width of the sampling pulse, and we are only interested in the
value of the sampled waveform at the rising edge, and a spectrum that
is independent of the sampling pulse width.
4. So, to represent that rising edge only, we treat our real samples
as existing only at that edge
5. As such, those samples are isomorphic to the Unit Impulse but
because of their small size are zero-integrable.
6. Therefore, in order to achieve an analysis, we replace the unity
of one that is the characteristic of the real world with the unity
of infinity which is the amplitude of the Unit Impulse.
7. This is a contrivance for modelling only, and it is important
to stress that real sampling is NOT multiplying by a Unit Impulse,
for this raises so many valid mathematical objections.
Facts are inconvenient? Only to those who have swallowed the
religious lie that real sampling _IS_ multiplying by a comb of impulses
rather then _IS MODELLED_ by such.
why did you dispute them _AND_ insist that it had unit amplitude?
2. The unit impulse only approaches zero width, it never actually
becomes zero. This concept is as old as Newton,
surely you have come across it before?
3. Which part of the rising edge would that be? Even with your
warped version of the unit pulse (before you stopped disputing its
attributes)
you should see that if it is only its edge that is significant then its
amplitude
and width would be irrelevant. What we are really interested in is the POWER
in the waveform being sampled so the width can not be zero. Zero width =
zero power.
4. You might treat the samples as existing only at the edge but those
who understand sampling know that it is invalid. See 3, above.
5. New word "isomorphic". Not applicable in this case but a new word for
you.
Maybe you can use it in Scrabble. If you will excuse the pun, don't stretch
it to infinite amplitude......
6. Whoaaaa "the unity of infinity". A good title for a love song maybe but,
in this context, nonsense.
7. Whoaa, you have suddenly come to the real world. A new experience for
you, it would appear.
Please stay awhile and have a look around. You will find there are people
here that understand DSP.
You have never actually done any DSP, I assume?
Never implemented a A/D converter so never analysed why you need a sample
and hold?
While you are in the real world I suggest you try doing so. A bit of reality
helps
everyone. Don't overdo it, it seems to have been awhile for you.
Chimera.
daestrom
8 years ago
Post by Airy R. Bean
If you have a mathematical function that has no width
and exists only at discrete points then it is zero-integrable,
with the exception of the contrivance of Dirac's Delta function.
Ah... Your problem is you think the pulse has zero width. It is *not*If you have a mathematical function that has no width
and exists only at discrete points then it is zero-integrable,
with the exception of the contrivance of Dirac's Delta function.
exactly zero. It can approach zero and get as close as you are physically
able to make it and/or want. But it *never* reaches zero. If it did, then
there would be no pulse at all.
The area under the pulse is what is important. If the pulse width is fixed
at any arbitrary size greater than zero, the pulse is definitely intergable.
daestrom
jim <"N0sp"@
8 years ago
Post by Chimera
Delta function does that not make it rather relevant?
Your problem is that you don't understand even the basics of what you are
trying to study. Dirac's delta function has unit AREA and tends toward zero
width. The fact that it is defined as an AREA _repeat AREA _ then it is
intergrable. If not, then sampling would not work.
No, this is completely incorrect. The dirac delta function is just a convenient
Post by Airy R. Bean
If you have a mathematical function that has no width
and exists only at discrete points then it is zero-integrable,
with the exception of the contrivance of Dirac's Delta function.
The "contrivance of Dirac's Delta function"? As we are talking about Dirac'sIf you have a mathematical function that has no width
and exists only at discrete points then it is zero-integrable,
with the exception of the contrivance of Dirac's Delta function.
Delta function does that not make it rather relevant?
Your problem is that you don't understand even the basics of what you are
trying to study. Dirac's delta function has unit AREA and tends toward zero
width. The fact that it is defined as an AREA _repeat AREA _ then it is
intergrable. If not, then sampling would not work.
construct that simply encompasses the notion that the spectrum of the sampling
process is flat. Similarly the notion of a bandlimited function is a convenient
idealization. In reality there are lots of working sampling processes that don't
meet these ideal conditions. In fact its fairly safe to say that you will never
encounter a sampling process that meets these conditions perfectly.
In fact, a sampling process doesn't even have to come close to the idealized
dirac pulse to work. For instance digital cameras work just fine.
-jim
-----= Posted via Newsfeeds.Com, Uncensored Usenet News =-----
http://www.newsfeeds.com - The #1 Newsgroup Service in the World!
-----== Over 100,000 Newsgroups - 19 Different Servers! =-----
Brian Reay
8 years ago
Post by jim <"N0sp"@
construct that simply encompasses the notion that the spectrum of the sampling
process is flat. Similarly the notion of a bandlimited function is a convenient
idealization. In reality there are lots of working sampling processes that don't
meet these ideal conditions. In fact its fairly safe to say that you will never
encounter a sampling process that meets these conditions perfectly.
In fact, a sampling process doesn't even have to come close to the idealized
dirac pulse to work. For instance digital cameras work just fine.
I don't think there is a disconnect between Chimera's version and the point
Post by Chimera
Delta function does that not make it rather relevant?
Your problem is that you don't understand even the basics of what you are
trying to study. Dirac's delta function has unit AREA and tends toward zero
width. The fact that it is defined as an AREA _repeat AREA _ then it is
intergrable. If not, then sampling would not work.
No, this is completely incorrect. The dirac delta function is just a convenient
Post by Airy R. Bean
If you have a mathematical function that has no width
and exists only at discrete points then it is zero-integrable,
with the exception of the contrivance of Dirac's Delta function.
The "contrivance of Dirac's Delta function"? As we are talking about Dirac'sIf you have a mathematical function that has no width
and exists only at discrete points then it is zero-integrable,
with the exception of the contrivance of Dirac's Delta function.
Delta function does that not make it rather relevant?
Your problem is that you don't understand even the basics of what you are
trying to study. Dirac's delta function has unit AREA and tends toward zero
width. The fact that it is defined as an AREA _repeat AREA _ then it is
intergrable. If not, then sampling would not work.
construct that simply encompasses the notion that the spectrum of the sampling
process is flat. Similarly the notion of a bandlimited function is a convenient
idealization. In reality there are lots of working sampling processes that don't
meet these ideal conditions. In fact its fairly safe to say that you will never
encounter a sampling process that meets these conditions perfectly.
In fact, a sampling process doesn't even have to come close to the idealized
dirac pulse to work. For instance digital cameras work just fine.
you make. The feature that is common is the idea that sampling takes a
finite time which is, in itself, and integration process. Think of a sample
and hold- it integrates the signal over the time the sample gate is open, it
doesn't take a sample in zero time.
As Chimera and daestrom point out, the area of the unit pulse is
significant.
--
73
Brian
G8OSN
www.g8osn.org.uk
www.amateurradiotraining.org.uk for FREE training material for all UK
amateur radio licences
www.phoenixradioclub.org.uk - a RADIO club specifically for those wishing
to learn more about amateur radio
73
Brian
G8OSN
www.g8osn.org.uk
www.amateurradiotraining.org.uk for FREE training material for all UK
amateur radio licences
www.phoenixradioclub.org.uk - a RADIO club specifically for those wishing
to learn more about amateur radio
Airy R. Bean
8 years ago
But it isn't my problem, nor anyone else's. It is a fact of the
action of sampling. We are interested in the amplitude of the
sampled function at the rising edge only.
If we consider the rising edge to be the point of sample, then
we become independent of the width of the sampling pulse in
whatever circuit you are using.
As such, we wish to analyse a single point. That we wish to analyse
through an integrable transform gives us a difficulty because such
points are zero-integrable. The solution is to model using the infinity
that is represented by the Unit Impulse's amplitude as our unity.
It is misleading to state that the area of the pulse is of interest, because
there is no part of the calculus that supports the instantaneous multiplying
of one
function by the area of another. This last ruse is one of the religious
icons of those who state that sampling _IS_ the effect of multiplying
the incoming waveform by a comb of Delta Functions rather than
stating that it is only _MODELLED_ by such. It is a religious icon
because it is a matter of blind faith and not a matter of the
underlying calculus. Like all religions, you need to contrive more
and more weird and ridiculous explanations to explain away your
initial assumption which is wrong.
action of sampling. We are interested in the amplitude of the
sampled function at the rising edge only.
If we consider the rising edge to be the point of sample, then
we become independent of the width of the sampling pulse in
whatever circuit you are using.
As such, we wish to analyse a single point. That we wish to analyse
through an integrable transform gives us a difficulty because such
points are zero-integrable. The solution is to model using the infinity
that is represented by the Unit Impulse's amplitude as our unity.
It is misleading to state that the area of the pulse is of interest, because
there is no part of the calculus that supports the instantaneous multiplying
of one
function by the area of another. This last ruse is one of the religious
icons of those who state that sampling _IS_ the effect of multiplying
the incoming waveform by a comb of Delta Functions rather than
stating that it is only _MODELLED_ by such. It is a religious icon
because it is a matter of blind faith and not a matter of the
underlying calculus. Like all religions, you need to contrive more
and more weird and ridiculous explanations to explain away your
initial assumption which is wrong.
Post by daestrom
exactly zero. It can approach zero and get as close as you are physically
able to make it and/or want. But it *never* reaches zero. If it did, then
there would be no pulse at all.
The area under the pulse is what is important. If the pulse width is fixed
at any arbitrary size greater than zero, the pulse is definitely intergable.
Post by Airy R. Bean
If you have a mathematical function that has no width
and exists only at discrete points then it is zero-integrable,
with the exception of the contrivance of Dirac's Delta function.
Ah... Your problem is you think the pulse has zero width. It is *not*If you have a mathematical function that has no width
and exists only at discrete points then it is zero-integrable,
with the exception of the contrivance of Dirac's Delta function.
exactly zero. It can approach zero and get as close as you are physically
able to make it and/or want. But it *never* reaches zero. If it did, then
there would be no pulse at all.
The area under the pulse is what is important. If the pulse width is fixed
at any arbitrary size greater than zero, the pulse is definitely intergable.
Airy R. Bean
8 years ago
Whoever is the lady masquerading as, "Chimera", she seems
to have become obsessed by the wrong end of the stick.
I have never disputed the facts below that she attributes to
the Delta function. I have held these to be true for years, but
it is their very truth that means that using a comb of Delta
Functions can only be an idealised model of sampling and never
the actuality of sampling.
Still, right from her very first appearance a couple of months ago,
"Chimera"'s motivation seems to have been to vent her spleen
at me rather than to introduce any technical enlightenment. The
google record speaks! Her aggressive jeering from the sidelines
makes her irrelevant and she is best ignored.
.....[All of jim's remarks snipped!].....
to have become obsessed by the wrong end of the stick.
I have never disputed the facts below that she attributes to
the Delta function. I have held these to be true for years, but
it is their very truth that means that using a comb of Delta
Functions can only be an idealised model of sampling and never
the actuality of sampling.
Still, right from her very first appearance a couple of months ago,
"Chimera"'s motivation seems to have been to vent her spleen
at me rather than to introduce any technical enlightenment. The
google record speaks! Her aggressive jeering from the sidelines
makes her irrelevant and she is best ignored.
Post by Chimera
Delta function does that not make it rather relevant?
Your problem is that you don't understand even the basics of what you are
trying to study. Dirac's delta function has unit AREA and tends toward zero
width. The fact that it is defined as an AREA _repeat AREA _ then it is
intergrable.
Post by Airy R. Bean
If you have a mathematical function that has no width
and exists only at discrete points then it is zero-integrable,
with the exception of the contrivance of Dirac's Delta function.
The "contrivance of Dirac's Delta function"? As we are talking about Dirac'sIf you have a mathematical function that has no width
and exists only at discrete points then it is zero-integrable,
with the exception of the contrivance of Dirac's Delta function.
Delta function does that not make it rather relevant?
Your problem is that you don't understand even the basics of what you are
trying to study. Dirac's delta function has unit AREA and tends toward zero
width. The fact that it is defined as an AREA _repeat AREA _ then it is
intergrable.
Airy R. Bean
8 years ago
Not so. The accepted analyses of sampling use
only the value of f(T) and not the integrated
sum over the interval f(T) - f(T+dt). There is no integration of the
input function f(t) over the sampling period
in the standard analyses.
Whatever the width of the sampling pulse in your circuit, the
value of the input function at the rising edge only is used.
only the value of f(T) and not the integrated
sum over the interval f(T) - f(T+dt). There is no integration of the
input function f(t) over the sampling period
in the standard analyses.
Whatever the width of the sampling pulse in your circuit, the
value of the input function at the rising edge only is used.
Post by Brian Reay
I don't think there is a disconnect between Chimera's version and the point
you make. The feature that is common is the idea that sampling takes a
finite time which is, in itself, and integration process. Think of a sample
and hold- it integrates the signal over the time the sample gate is open, it
doesn't take a sample in zero time.
I don't think there is a disconnect between Chimera's version and the point
you make. The feature that is common is the idea that sampling takes a
finite time which is, in itself, and integration process. Think of a sample
and hold- it integrates the signal over the time the sample gate is open, it
doesn't take a sample in zero time.
Chimera
8 years ago
Post by jim <"N0sp"@
construct that simply encompasses the notion that the spectrum of the sampling
process is flat. Similarly the notion of a bandlimited function is a convenient
idealization. In reality there are lots of working sampling processes that don't
meet these ideal conditions. In fact its fairly safe to say that you will never
encounter a sampling process that meets these conditions perfectly.
In fact, a sampling process doesn't even have to come close to the idealized
dirac pulse to work. For instance digital cameras work just fine.
Your link to the 'real world' is very apt and valid for the most part. But,
Post by Chimera
Delta function does that not make it rather relevant?
Your problem is that you don't understand even the basics of what you are
trying to study. Dirac's delta function has unit AREA and tends toward zero
width. The fact that it is defined as an AREA _repeat AREA _ then it is
intergrable. If not, then sampling would not work.
No, this is completely incorrect. The dirac delta function is just a convenient
Post by Airy R. Bean
If you have a mathematical function that has no width
and exists only at discrete points then it is zero-integrable,
with the exception of the contrivance of Dirac's Delta function.
The "contrivance of Dirac's Delta function"? As we are talking about Dirac'sIf you have a mathematical function that has no width
and exists only at discrete points then it is zero-integrable,
with the exception of the contrivance of Dirac's Delta function.
Delta function does that not make it rather relevant?
Your problem is that you don't understand even the basics of what you are
trying to study. Dirac's delta function has unit AREA and tends toward zero
width. The fact that it is defined as an AREA _repeat AREA _ then it is
intergrable. If not, then sampling would not work.
construct that simply encompasses the notion that the spectrum of the sampling
process is flat. Similarly the notion of a bandlimited function is a convenient
idealization. In reality there are lots of working sampling processes that don't
meet these ideal conditions. In fact its fairly safe to say that you will never
encounter a sampling process that meets these conditions perfectly.
In fact, a sampling process doesn't even have to come close to the idealized
dirac pulse to work. For instance digital cameras work just fine.
as Dr Reay has pointed out, sampling does not take place on zero time. If it
did, no energy would be transferred, which is clearly not tenable.
The _AREA_ of the unit pulse is relevant and, in the real world, equates to
the sample time.
Chimera
Chimera
8 years ago
Post by Airy R. Bean
Whoever is the lady masquerading as, "Chimera", she seems
to have become obsessed by the wrong end of the stick.
I have never disputed the facts below that she attributes to
the Delta function. I have held these to be true for years, but
it is their very truth that means that using a comb of Delta
Functions can only be an idealised model of sampling and never
the actuality of sampling.
Still, right from her very first appearance a couple of months ago,
"Chimera"'s motivation seems to have been to vent her spleen
at me rather than to introduce any technical enlightenment. The
google record speaks! Her aggressive jeering from the sidelines
makes her irrelevant and she is best ignored.
You have disputed the nature of the Delta function, you claimed theWhoever is the lady masquerading as, "Chimera", she seems
to have become obsessed by the wrong end of the stick.
I have never disputed the facts below that she attributes to
the Delta function. I have held these to be true for years, but
it is their very truth that means that using a comb of Delta
Functions can only be an idealised model of sampling and never
the actuality of sampling.
Still, right from her very first appearance a couple of months ago,
"Chimera"'s motivation seems to have been to vent her spleen
at me rather than to introduce any technical enlightenment. The
google record speaks! Her aggressive jeering from the sidelines
makes her irrelevant and she is best ignored.
amplitude was unity whereas it is the _AREA_ which is unity.
Have you ever actually had any formal education in maths or engineering? If
so, can I suggest you ask for a refund.
Chimera
Chimera
8 years ago
Post by Airy R. Bean
Not so. The accepted analyses of sampling use
only the value of f(T) and not the integrated
sum over the interval f(T) - f(T+dt). There is no integration of the
input function f(t) over the sampling period
in the standard analyses.
Whatever the width of the sampling pulse in your circuit, the
value of the input function at the rising edge only is used.
Accepted by you only, to those of us with real experience your analysis isNot so. The accepted analyses of sampling use
only the value of f(T) and not the integrated
sum over the interval f(T) - f(T+dt). There is no integration of the
input function f(t) over the sampling period
in the standard analyses.
Whatever the width of the sampling pulse in your circuit, the
value of the input function at the rising edge only is used.
laughable.
Your comment re the rising edge shows a lack of understanding that I have
never seen the like of.
If only the edge matters, why did Dirac specify the area as unity and not
some measure of the rise time of the unit impulse. It would then be the zero
rise time pulse not the unit pulse.
Chimera
Chimera
8 years ago
Post by Airy R. Bean
that
Post by jim <"N0sp"@
Dirac's
Post by Chimera
Post by Airy R. Bean
If you have a mathematical function that has no width
and exists only at discrete points then it is zero-integrable,
with the exception of the contrivance of Dirac's Delta function.
The "contrivance of Dirac's Delta function"? As we are talking aboutIf you have a mathematical function that has no width
and exists only at discrete points then it is zero-integrable,
with the exception of the contrivance of Dirac's Delta function.
Post by jim <"N0sp"@
are
Post by Chimera
Delta function does that not make it rather relevant?
Your problem is that you don't understand even the basics of what you
Delta function does that not make it rather relevant?
Your problem is that you don't understand even the basics of what you
Post by jim <"N0sp"@
zero
Post by Chimera
trying to study. Dirac's delta function has unit AREA and tends toward
trying to study. Dirac's delta function has unit AREA and tends toward
Post by jim <"N0sp"@
convenient
Post by Chimera
width. The fact that it is defined as an AREA _repeat AREA _ then it is
intergrable. If not, then sampling would not work.
No, this is completely incorrect. The dirac delta function is just awidth. The fact that it is defined as an AREA _repeat AREA _ then it is
intergrable. If not, then sampling would not work.
Post by jim <"N0sp"@
construct that simply encompasses the notion that the spectrum of the
samplingconstruct that simply encompasses the notion that the spectrum of the
Post by jim <"N0sp"@
process is flat. Similarly the notion of a bandlimited function is a
convenientprocess is flat. Similarly the notion of a bandlimited function is a
Post by jim <"N0sp"@
idealization. In reality there are lots of working sampling processes
idealization. In reality there are lots of working sampling processes
Post by Airy R. Bean
don't
willdon't
Post by jim <"N0sp"@
meet these ideal conditions. In fact its fairly safe to say that you
meet these ideal conditions. In fact its fairly safe to say that you
Post by Airy R. Bean
never
you make. The feature that is common is the idea that sampling takes a
finite time which is, in itself, and integration process. Think of a sample
and hold- it integrates the signal over the time the sample gate is open, it
doesn't take a sample in zero time.
As Chimera and daestrom point out, the area of the unit pulse is
significant.
Sanity at last.never
Post by jim <"N0sp"@
encounter a sampling process that meets these conditions perfectly.
In fact, a sampling process doesn't even have to come close to the
idealizedencounter a sampling process that meets these conditions perfectly.
In fact, a sampling process doesn't even have to come close to the
Post by jim <"N0sp"@
dirac pulse to work. For instance digital cameras work just fine.
I don't think there is a disconnect between Chimera's version and the pointdirac pulse to work. For instance digital cameras work just fine.
you make. The feature that is common is the idea that sampling takes a
finite time which is, in itself, and integration process. Think of a sample
and hold- it integrates the signal over the time the sample gate is open, it
doesn't take a sample in zero time.
As Chimera and daestrom point out, the area of the unit pulse is
significant.
Chimera
jim <"N0sp"@
8 years ago
Post by Airy R. Bean
Not so.
What's not so? Your post appears in response to mine, but you quote some one else.Not so.
Post by Airy R. Bean
The accepted analyses of sampling use
only the value of f(T) and not the integrated
sum over the interval f(T) - f(T+dt). There is no integration of the
input function f(t) over the sampling period
in the standard analyses.
Standard analysis of what? Is f(t) the notes Mozart scored? or is it the soundThe accepted analyses of sampling use
only the value of f(T) and not the integrated
sum over the interval f(T) - f(T+dt). There is no integration of the
input function f(t) over the sampling period
in the standard analyses.
waves coming out of the orchestra? or is it the current in the microphone? at what
point does f(t) become f(t)?
Post by Airy R. Bean
Whatever the width of the sampling pulse in your circuit, the
value of the input function at the rising edge only is used.
what circuit? who said anything about circuits.Whatever the width of the sampling pulse in your circuit, the
value of the input function at the rising edge only is used.
-jim
Post by Airy R. Bean
-----= Posted via Newsfeeds.Com, Uncensored Usenet News =-----
Post by Brian Reay
I don't think there is a disconnect between Chimera's version and the
pointI don't think there is a disconnect between Chimera's version and the
Post by Brian Reay
you make. The feature that is common is the idea that sampling takes a
finite time which is, in itself, and integration process. Think of a
sampleyou make. The feature that is common is the idea that sampling takes a
finite time which is, in itself, and integration process. Think of a
Post by Brian Reay
and hold- it integrates the signal over the time the sample gate is open,
itand hold- it integrates the signal over the time the sample gate is open,
Post by Brian Reay
doesn't take a sample in zero time.
doesn't take a sample in zero time.
http://www.newsfeeds.com - The #1 Newsgroup Service in the World!
-----== Over 100,000 Newsgroups - 19 Different Servers! =-----
Airy R. Bean
8 years ago
No - it's posted in response to Mr.Reay.
Post by jim <"N0sp"@
Post by Airy R. Bean
Not so.
What's not so? Your post appears in response to mine, but you quote some one else.Not so.
Post by Airy R. Bean
Post by Brian Reay
I don't think there is a disconnect between Chimera's version and the
pointI don't think there is a disconnect between Chimera's version and the
Post by Brian Reay
you make. The feature that is common is the idea that sampling takes a
finite time which is, in itself, and integration process. Think of a
sampleyou make. The feature that is common is the idea that sampling takes a
finite time which is, in itself, and integration process. Think of a
Post by Brian Reay
and hold- it integrates the signal over the time the sample gate is open,
itand hold- it integrates the signal over the time the sample gate is open,
Post by Brian Reay
doesn't take a sample in zero time.
doesn't take a sample in zero time.
Frank Turner-Smith G3VKI
8 years ago
Post by Airy R. Bean
But it isn't my problem, nor anyone else's. It is a fact of the
action of sampling. We are interested in the amplitude of the
sampled function at the rising edge only.
If we consider the rising edge to be the point of sample, then
we become independent of the width of the sampling pulse in
whatever circuit you are using.
OK, but if you sample the pulse during its rise time, how can you predictBut it isn't my problem, nor anyone else's. It is a fact of the
action of sampling. We are interested in the amplitude of the
sampled function at the rising edge only.
If we consider the rising edge to be the point of sample, then
we become independent of the width of the sampling pulse in
whatever circuit you are using.
its final amplitude?
--
;>)
73 de Frank Turner-Smith G3VKI - mine's a pint.
http://turner-smith.co.uk
;>)
73 de Frank Turner-Smith G3VKI - mine's a pint.
http://turner-smith.co.uk
jim <"N0sp"@
8 years ago
Post by robert bristow-johnson
Sane maybe, but not a very good grasp of the sampling process. By the reasoning
Post by Brian Reay
I don't think there is a disconnect between Chimera's version and the
pointI don't think there is a disconnect between Chimera's version and the
Post by Brian Reay
you make. The feature that is common is the idea that sampling takes a
finite time which is, in itself, and integration process. Think of a
sampleyou make. The feature that is common is the idea that sampling takes a
finite time which is, in itself, and integration process. Think of a
Post by Brian Reay
and hold- it integrates the signal over the time the sample gate is open,
itand hold- it integrates the signal over the time the sample gate is open,
Post by Brian Reay
doesn't take a sample in zero time.
As Chimera and daestrom point out, the area of the unit pulse is
significant.
Sanity at last.doesn't take a sample in zero time.
As Chimera and daestrom point out, the area of the unit pulse is
significant.
you guys are using the Weather Service is going about it all wrong for sampling
rainfall. Instead of recording the rainfall in the gauge once a day and then
emptying it. what they should be doing is just sticking the gauge out the window
for a second at the same time each day. Mr Bean would go even further and not even
allow them to retract their arm before noting the measurement, but instead insist
that they record the measurement as soon as the arm is fully extended.
There's no integration involved - the contents of the rain are just recorded once
a day. The sampling theorem tells you that there exists a continuos function that
can be derived that interpolates these samples. It doesn't tell you whether the
rain gauge is in a desert or tropical island, or if the gauge is in inches or
millimeters. Those things will affect what the continuous function looks like. A
crack in the bottom of the rain gauge or placing the rain gauge where the water
runs off a roof will also give you a different function f(t). You can't possibly
imagine that the dirac function is a mapping that ecompasses all these variable
and yields f(t) ~ that pure function "rainfall".
-jim
-----= Posted via Newsfeeds.Com, Uncensored Usenet News =-----
http://www.newsfeeds.com - The #1 Newsgroup Service in the World!
-----== Over 100,000 Newsgroups - 19 Different Servers! =-----
Chimera
8 years ago
Post by jim <"N0sp"@
you guys are using the Weather Service is going about it all wrong for sampling
rainfall. Instead of recording the rainfall in the gauge once a day and then
emptying it. what they should be doing is just sticking the gauge out the window
for a second at the same time each day. Mr Bean would go even further and not even
allow them to retract their arm before noting the measurement, but instead insist
that they record the measurement as soon as the arm is fully extended.
There's no integration involved - the contents of the rain are just recorded once
a day. The sampling theorem tells you that there exists a continuos function that
can be derived that interpolates these samples. It doesn't tell you whether the
rain gauge is in a desert or tropical island, or if the gauge is in inches or
millimeters. Those things will affect what the continuous function looks like. A
crack in the bottom of the rain gauge or placing the rain gauge where the water
runs off a roof will also give you a different function f(t). You can't possibly
imagine that the dirac function is a mapping that ecompasses all these variable
and yields f(t) ~ that pure function "rainfall".
For the rain gauge, this equates to measuring the rain fall for on day, the
Post by robert bristow-johnson
Sane maybe, but not a very good grasp of the sampling process. By the reasoning
Post by Brian Reay
I don't think there is a disconnect between Chimera's version and the
pointI don't think there is a disconnect between Chimera's version and the
Post by Brian Reay
you make. The feature that is common is the idea that sampling takes a
finite time which is, in itself, and integration process. Think of a
sampleyou make. The feature that is common is the idea that sampling takes a
finite time which is, in itself, and integration process. Think of a
Post by Brian Reay
and hold- it integrates the signal over the time the sample gate is open,
itand hold- it integrates the signal over the time the sample gate is open,
Post by Brian Reay
doesn't take a sample in zero time.
As Chimera and daestrom point out, the area of the unit pulse is
significant.
Sanity at last.doesn't take a sample in zero time.
As Chimera and daestrom point out, the area of the unit pulse is
significant.
you guys are using the Weather Service is going about it all wrong for sampling
rainfall. Instead of recording the rainfall in the gauge once a day and then
emptying it. what they should be doing is just sticking the gauge out the window
for a second at the same time each day. Mr Bean would go even further and not even
allow them to retract their arm before noting the measurement, but instead insist
that they record the measurement as soon as the arm is fully extended.
There's no integration involved - the contents of the rain are just recorded once
a day. The sampling theorem tells you that there exists a continuos function that
can be derived that interpolates these samples. It doesn't tell you whether the
rain gauge is in a desert or tropical island, or if the gauge is in inches or
millimeters. Those things will affect what the continuous function looks like. A
crack in the bottom of the rain gauge or placing the rain gauge where the water
runs off a roof will also give you a different function f(t). You can't possibly
imagine that the dirac function is a mapping that ecompasses all these variable
and yields f(t) ~ that pure function "rainfall".
sampling period. From that you can determine no more than how much it rained
on one day (the sample time, which equates to the width of the sample
pulse).
For the unit pulse sampling a waveform, a single pulse sampling the waveform
once, all you determine is the value of wave form being sampled over the
sample pulse width. You cannot determine anything about the nature of the
waveform at other times.
In the case of the rain gauge, the water collect is the rain that fell in
the sample period (assuming there are no error sources). In the sample pulse
case, it is the power of the sampled waveform averaged over the pulse width.
Also, no single sample process is immune from the error due to things link
leaky gauges etc. It is possible to account for some error sources but can
we get Airy to understand the basics first.
Sampling theory (Nyquist) tells use that we must sample waveform at twice
its frequency of repetition, if we are to reconstructed or, as is more
appropriate in this analogy, be able to predict a value at some future time.
Airy's problem hasn't extended that far yet, he still can't grasp the way a
single sample works. The width of the Dirac pulse is finite AND its area 1.
If it is repeated, like a comb as he refers to, you get a series of samples,
each sample being the width of the sampling pulse and repeated at the
samplying frequency.
Chimera
daestrom
8 years ago
Post by jim <"N0sp"@
you guys are using the Weather Service is going about it all wrong for sampling
rainfall. Instead of recording the rainfall in the gauge once a day and then
emptying it. what they should be doing is just sticking the gauge out the window
for a second at the same time each day.
Not so. The two methods you mention for rainfall are a *sampling*
Post by robert bristow-johnson
Sane maybe, but not a very good grasp of the sampling process. By the reasoning
Post by Brian Reay
I don't think there is a disconnect between Chimera's version and the
pointI don't think there is a disconnect between Chimera's version and the
Post by Brian Reay
you make. The feature that is common is the idea that sampling takes a
finite time which is, in itself, and integration process. Think of a
sampleyou make. The feature that is common is the idea that sampling takes a
finite time which is, in itself, and integration process. Think of a
Post by Brian Reay
and hold- it integrates the signal over the time the sample gate is open,
itand hold- it integrates the signal over the time the sample gate is open,
Post by Brian Reay
doesn't take a sample in zero time.
As Chimera and daestrom point out, the area of the unit pulse is
significant.
Sanity at last.doesn't take a sample in zero time.
As Chimera and daestrom point out, the area of the unit pulse is
significant.
you guys are using the Weather Service is going about it all wrong for sampling
rainfall. Instead of recording the rainfall in the gauge once a day and then
emptying it. what they should be doing is just sticking the gauge out the window
for a second at the same time each day.
technique, and a *measurement* technique. If you have the resources to
measure every item (in this case rate of rainfall over time), then 100%
measurement is the way to go. But if you don't have the resources to sample
continuously, you can sometimes get a very good approximation by sampling at
appropriate intervals and infering the continuous function based on the
sample points. To get an *accurate* reproduction you would need to sample
at least twice the frequency of interest. Considering that rain storms
typically come and go in the course of hours or faster, 'the Weather
Service' would have to sample more often than once a day.
And such a sample would be the *rate* of rainfall, not the total so far. To
find the total, one would have to *assume* the rate is changing between
samples by some known function f(t). Then one could integrate the total
rainfall with some degree of accuracy.
But since the weather is unpredictable, you may have to sample the rate of
rainfall quite often and then just *assume* the rate changes linearly
between samples.
Post by jim <"N0sp"@
Mr Bean would go even further and not even
allow them to retract their arm before noting the measurement, but instead insist
that they record the measurement as soon as the arm is fully extended.
There's no integration involved - the contents of the rain are just recorded once
a day. The sampling theorem tells you that there exists a continuos function that
can be derived that interpolates these samples. It doesn't tell you whether the
rain gauge is in a desert or tropical island, or if the gauge is in inches or
millimeters. Those things will affect what the continuous function looks like. A
crack in the bottom of the rain gauge or placing the rain gauge where the water
runs off a roof will also give you a different function f(t). You can't possibly
imagine that the dirac function is a mapping that ecompasses all these variable
and yields f(t) ~ that pure function "rainfall".
Because all those things imply that the rate of rainfall is a rather complexMr Bean would go even further and not even
allow them to retract their arm before noting the measurement, but instead insist
that they record the measurement as soon as the arm is fully extended.
There's no integration involved - the contents of the rain are just recorded once
a day. The sampling theorem tells you that there exists a continuos function that
can be derived that interpolates these samples. It doesn't tell you whether the
rain gauge is in a desert or tropical island, or if the gauge is in inches or
millimeters. Those things will affect what the continuous function looks like. A
crack in the bottom of the rain gauge or placing the rain gauge where the water
runs off a roof will also give you a different function f(t). You can't possibly
imagine that the dirac function is a mapping that ecompasses all these variable
and yields f(t) ~ that pure function "rainfall".
f(t), to get a reasonable accuracy, one would have to estimate the highest
frequency component and sample at least twice this rate. No simple matter.
But the beauty of such a rain gauge is it never needs emptying :-)
If you empty a conventional gauge once a day, how do you calculate the
average rainfall for a month? Easy, you have ~30 samples of rainfall with
each sample measuring inches-of-rain per day. You just have a sample width
that is very close to the sample period (minus a second or two to empty it
each day).
Some weather observers empty the gauge more often than once a day. The more
often one empties it, the more the situation approaches a digital sample of
the volume/time and you have a rain-rate sample. The 'gauge' is just a
long-time-constant 'hold' device in a sample and hold system.
daestrom
No comments:
Post a Comment