Big K - laying the ghost to rest

Although not posting here for some years, I have nevertheless been
a regular reader.

For some reason, two of the kindergarten class from uk.radio.amateur,
reay and cole, in order to draw attention to themsleves, decided to
annoy the denizens of this NG by raking over the embers from 10 years ago,
so perhaps it is appropriate to lay the ghost of Big K, for those
interested in the fundamental basis of sampling.

So...

Sampling with a period of  T is given by (after asciification) as ..

(1/T)sum (0, inf)(d(t-T) * f(t-T) )

... with * representing multiplication and not convolution as we
are still in the time domain.

However, (and this is where my protest came in having
previously fully revised Fourier, Laplace, Butterworth, Tchebyschev,
Elliptical, and PID, etc,   to degree standard thus giving me a full 
understanding of the
Diracian Delta and its characteristics), all the texts that I encountered,
and, indeed, much of the Interweb give it as ...

sum (0, inf)(d(t-T) * f(t-T) )

 ... which lacks the essential divisor of  T.


(In the recent diatribe from reay, he tried to claim that this division 
factor
of T is mentioned in all the texts which is simply untrue, so I suspect that 
in
his haste to want to blurt out an infantile insult that reay is confusing 
the
descriptions of sampling with the derivation of the Fourier Series)

What is the justification for this derivation?

It is because the real representation of sampling is not done with
Diracian Delta Funcions, but with Unit Steps, as follows ...

sum (0, inf)( f(t-T)  * ( U(t-2T)  - U(t-T))  )

... but this is very messy to deal with analytically.

So, as the Diracian Delta is a doddle to deal with, having
a frequency spectrum of unity (ie, every possibly cosine in
phase at t = 0), is there some way that the sampling expression
could be re-represented with Diracian Deltas?

The answer is a resounding, "Yes!"!

Consider the definition of the Diracian Delta, as it is presented to
electronics engineers (in my case, the second year at Essex Uni 1970 - 1971)
which is a pulse of unity area T volts high and 1/T seconds long, with
T tending towards zero, which in out asciification comes out as ..

T * (  U(t-2T) - U9t-T)  )

... and therefore our sampling mechanism is strongly related to
the Diracian Delta except for the multiplication factor of  T
and thus ...

sum (0, inf)( f(t-T)  * ( U(t-2T)  - U(t-T))  )

... can also be represented as ..


(1/T)sum (0, inf)(d(t-T) * f(t-T) )

... with T (or even 1/T) being the missing factor which
I had dubbed Big K.

Now, having resolved this issue, and not having any further direct use
for DSP, I retired from my studies knowing that my fundamental mathematical
understanding was on such a strong footing that I could easily move on from 
there
should the need arose.

However, ISTR that in Bristow's article about sampling and reconstruction 
(in
one of Bristow's rare manifestation as as a grown up?) that he had to 
re-introduce
the factor of T out-of-thin-air for reconstruction, so I'd like to suggest 
from
my analusis above that it is not necessary to bring in the deus-ex-machina 
of T at the
end because it should always have been there from the beginning?

EOE

-----ooooo-----

(Cross-posted to uk.radio.amateur for the benefit of cole who has demanded
such a explanation, although I doubt he will understand any of it, and will
respond, if he ever dares to show his face, with abuse and bluster)

"gareth" <no.spam@thank.you.invalid> wrote in message 
news:mcmu7v$3rh$1@dont-email.me...
> Although not posting here for some years, I have nevertheless been
> a regular reader.

Bugger! The perils of composing off-the-cuff where I should have
used (t-nT) and not (t-T), etc, etc.

"gareth" <no.spam@thank.you.invalid> wrote:
> Although not posting here for some years, I have nevertheless been
> a regular reader.
> 
> <snip unreferenced and unsourced wall of text>

Come along now, Gareth. This screed simply cannot be peer reviewed as
you've rather evasively refused to make any references whatsoever. I can't
waste my time with this hogwash, try harder man. 

-- 
STC // M0TEY // twitter.com/ukradioamateur

"Stephen Thomas Cole" <usenet@stephenthomascole.com> wrote in message 
news:mcn45k$q19$4@dont-email.me...
> "gareth" <no.spam@thank.you.invalid> wrote:
>> Although not posting here for some years, I have nevertheless been
>> a regular reader.
>>
>> <snip unreferenced and unsourced wall of text>
>
> Come along now, Gareth. This screed simply cannot be peer reviewed as
> you've rather evasively refused to make any references whatsoever. I can't
> waste my time with this hogwash, try harder man.

It remains that 100% of your postings consist of rather silly and infantile
personal remarks.

As amateur radio is a technical pursuit, and you yourself elected to
cross post to comp.dsp which is even more technical, why not make
your first technical post ever, since you first arrived to pollute Usenet
just over 2 years ago with your tirades of abuse?

I think that you lack any technical acumen and your bluster
is your attempt to cover up.

On 26.02.2015 11:58, gareth wrote:
> Although not posting here for some years, I have nevertheless been
> a regular reader.

Frindly reminder: You can't "lay a ghost to rest" when you resurrect it
yourself by initially posting about some 10-year-back event. And while I
cannot judge the technical side of your posting I can say that you're
making a fool of yourself by constantly replying to your foes with
"yadda yadda yadda only personal attacks yadda yadda". Just leave it be,
please.

Cheers,
Johannes

-- 
>> Wo hattest Du das Beben nochmal GENAU vorhergesagt?
> Zumindest nicht �ffentlich!
Ah, der neueste und bis heute genialste Streich unsere gro�en
Kosmologen: Die Geheim-Vorhersage.
 - Karl Kaos &#4294967295;ber R&#4294967295;diger Thomas in dsa <hidbv3$om2$1@speranza.aioe.org>

"Johannes Bauer" <dfnsonfsduifb@gmx.de> wrote in message 
news:mcnalg$5oo$1@news.albasani.net...
> On 26.02.2015 11:58, gareth wrote:
>> Although not posting here for some years, I have nevertheless been
>> a regular reader.
>
> Frindly reminder: You can't "lay a ghost to rest" when you resurrect it
> yourself by initially posting about some 10-year-back event.

It was cole and reay who resurrected it and not I.


> And while I
> cannot judge the technical side of your posting I can say that you're
> making a fool of yourself by constantly replying to your foes with
> "yadda yadda yadda only personal attacks yadda yadda". Just leave it be,
> please.

No-one who speaks up for decency and maturity in an international forum
makes a fool of himself.

May I suggest that you google for the topic of, "kill file" and act 
accordingly?

Stephen Thomas Cole <usenet@stephenthomascole.com> wrote:
> "gareth" <no.spam@thank.you.invalid> wrote:
>> Although not posting here for some years, I have nevertheless been
>> a regular reader.
>> 
>> <snip unreferenced and unsourced wall of text>
> 
> Come along now, Gareth. This screed simply cannot be peer reviewed as
> you've rather evasively refused to make any references whatsoever. I can't
> waste my time with this hogwash, try harder man. 


I see he has wasted another day bouncing off the walls of his self
constructed cell. 

As you say, his post is less than convincing, I gave up on it due to the
'revisionist' nature, those familiar with his crack pot theories will know
what I mean. 

His habit of claiming that he understands things 'to his satisfaction'
explains a lot, after all, success relies on satisfying others. 

Anyway, I've had a busy and productive day, time for some dinner, a chat
with my XYL, then turn on the soldering iron. 

I've check in later to see how the ball game is going, I can see this one
bouncing for sometime yet ;-)

"Brian Reay" <no.sp@m.com> wrote in message 
news:768834759446662030.833121no.sp-m.com@news.eternal-september.org...
> I see he has wasted another day bouncing off the walls of his self
> constructed cell.
> As you say, his post is less than convincing, I gave up on it due to the
> 'revisionist' nature, those familiar with his crack pot theories will know
> what I mean.
> His habit of claiming that he understands things 'to his satisfaction'
> explains a lot, after all, success relies on satisfying others.
> Anyway, I've had a busy and productive day, time for some dinner, a chat
> with my XYL, then turn on the soldering iron.
> I've check in later to see how the ball game is going, I can see this one
> bouncing for sometime yet ;-)

It continues to be, brian, that it is you who attempts to cause trouble by
stirring things up, despite that it is a label that you try to attach to 
others.

Shame on you.

Brian Reay <no.sp@m.com> wrote:
> Stephen Thomas Cole <usenet@stephenthomascole.com> wrote:
>> "gareth" <no.spam@thank.you.invalid> wrote:
>>> Although not posting here for some years, I have nevertheless been
>>> a regular reader.
>>> 
>>> <snip unreferenced and unsourced wall of text>
>> 
>> Come along now, Gareth. This screed simply cannot be peer reviewed as
>> you've rather evasively refused to make any references whatsoever. I can't
>> waste my time with this hogwash, try harder man. 
> 
> 
> I see he has wasted another day bouncing off the walls of his self
> constructed cell. 

Yes, he's been full of angst these last few days, I imagine that there's
been some upset for him, a benefits sanction, perhaps. 

> 
> As you say, his post is less than convincing, I gave up on it due to the
> 'revisionist' nature, those familiar with his crack pot theories will know
> what I mean. 
>

It's the standard Evans gobbledygook, clearly trying to dig himself out of
a hole but ending up buried deeper, as per. 

> His habit of claiming that he understands things 'to his satisfaction'
> explains a lot, after all, success relies on satisfying others. 
>

Indeed, his threshold for "satisfaction" is evidently far, far lower than
those of us with standards. 

> Anyway, I've had a busy and productive day, time for some dinner, a chat
> with my XYL, then turn on the soldering iron. 
>
> I've check in later to see how the ball game is going, I can see this one
> bouncing for sometime yet ;-)

He'll be howling at the moon for the rest of the night. He's gone off the
deep end over this nonsense, again. 

-- 
STC // M0TEY // twitter.com/ukradioamateur

"Stephen Thomas Cole" <usenet@stephenthomascole.com> wrote in message 
news:mcnnfb$atp$1@dont-email.me...
> Yes, he's been full of angst these last few days, I imagine that there's
> been some upset for him, a benefits sanction, perhaps.
> It's the standard Evans gobbledygook, clearly trying to dig himself out of
> a hole but ending up buried deeper, as per.
> Indeed, his threshold for "satisfaction" is evidently far, far lower than
> those of us with standards.
> He'll be howling at the moon for the rest of the night. He's gone off the
> deep end over this nonsense, again.


It remains that 100% of your postings consist of rather silly and infantile
personal remarks.

As amateur radio is a technical pursuit, and you yourself elected to
cross post to comp.dsp which is even more technical, why not make
your first technical post ever, since you first arrived to pollute Usenet
just over 2 years ago with your tirades of abuse?

I think that you lack any technical acumen and your bluster
is your attempt to cover up.