In article <FAEBJHPJNNGCAGDNGLNPOELDEIAA.gsellani@...>, gary
<gsellani@...> writes
>I stated what in error twice?

"the pixel should not have size"
followed by:
"imaging does not have a pre-filter".

Since you "know" that multiplication in the frequency domain is
equivalent to convolution in the time domain then you should be aware
that these amount to exactly the same, erroneous, statement. Imaging
DOES have a prefilter and indeed, by comparison with the full audio
analogy as opposed to the partial one you used, SHOULD have one, and as
a consequence the pixels MUST have, and SHOULD have, a finite size.

In fact, if you really want to make the full analogy to audio, the
pixels should have an infinite size with a sinc shaped point spread
function, which would thus appear as the ideal brick wall filter in
spatial frequency, meeting the Nyquist sampling requirement perfectly!

> I never brought up the pre-filter for imaging.
>You did.

Yes, I did, because you claimed "the pixel should not have size" - which
is completely wrong! The size IS the prefilter, which you conveniently
ignored in your audio comparison in order to support a false analogy!
Sampling broadband audio (or any signal) without a prefilter results in
just as much garbage as sampling images with infinitely small pixels!
The first sentence of your first post on the topic addressing the
analogy: "the sample time is infinitely small" is completely false
because it ignores the prefilter which acts as an aperture in the time
domain in EXACTLY the same way as the imaging pixel's finite width.
Presumably you know that ignoring the prefilter in any sampling system
is at your peril, but you just did and now you complain that I have
introduced it to correct your error - arrogant or what? Just ignore all
of the theory and practice and make it up as you go along, why don't
you?

> I try to stick with the theory, and you bring up side issues that
>simply cloud the discussion.

I have not brought up side issues, I have attempted to explain to you
where your analogy is wrong and departs significantly from sampling
theory and best practice! The departure is right in those first two
sentences, samples of which I have now quoted back to you on several
occasions - they are simply wrong! Ignoring my warnings doesn't make
them right!

If you make an analogy and ignore significant points in one aspect then
your conclusions in the other are almost certain to be wrong.
>
>Mash dacs? Why bring that into the discussion?
>
I didn't specify MASH because they are only one example of an
oversampling DAC, it would appear that you are unfamiliar with any
others though. I brought the general topic of oversampling DACS into
the discussion for the reasons set out clearly in the section of the
post you quoted, but I will try to explain the issue a little clearer
because I obviously assumed that you understood the topic better than
you apparently do.

Your conclusion was based on the frequency spectrum of the audio output
by the DAC being wrong because of the stepped output of the DAC. You
specifically stated:
"if you take the sample impulses and play them back on a DAC making
staircase waveforms, the high frequency response will be incorrect. The
nature of the staircase implies a sinc filter was used, so the playback
must incorporate an inverse sinc filter."

Again you ignore the effect of the bandlimiting reconstruction filter
which ensures that high frequency components of the staircase waveform
do not reach the amplifier. The correct filter to apply to remove the
frequency discrepencies of a staircase waveform is certainly NOT "an
inverse sinc", but a "brick-wall" type, indeed that is what should be
applied instead of the sinc filter in the first place!

If an inverse sinc (which is theoretically impossible, in any case,
although it can be approximated) was applied to the output of such a
staircase waveform the result would be a series of disconnected delta
functions, not a continuous waveform, and you would have even more high
frequency discrepancy than you started with!

Whilst the reconstruction filter was analogue in early audio systems, it
is implemented digitally (and much more accurately) in an oversampling
DAC.

To implement what you are making the analogy with you must filter at
finer resolution than the sample density - either, just as in early
audio systems, using an analogue filter or by oversampling the data and
implementing the filter digitally. Since a digital filter is the only
real option in digital imaging then the obvious corollary in the audio
field is an oversampling DAC. That is why they come into the discussion
- it isn't a side issue, it is fundamental to the digital implementation
of what you are drawing an analogy with!

>If you can't argue in a straightforward manner, I don't see the point of
>discussing the issue. Right? I rather teach a pig to sing.
>
I apologise for trying to explain the errors of your analysis, but I
believe that doing so is much more useful than simply responding that
you are comparing apples and atoms, but if that is what you want, fine:
GARY - YOUR ENTIRE ANALOGY IS WRONG!!
--
Kennedy
Yes, Socrates himself is particularly missed;
A lovely little thinker, but a bugger when he's pissed.
Python Philosophers
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