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Questions about equivalents of audio/video and digital/analog.

R

Randy Yates

[...]
Nyquist's theorem:
A theorem, developed by H. Nyquist, which states
that an analog signal waveform may be uniquely
reconstructed, without error, from samples taken at
equal time intervals. The sampling rate must be
equal to, or greater than, twice the highest
frequency component in the analog signal. Synonym
sampling theorem.
[...]
That is 100%, definitively incorrect.

What is not correct about it. What do you claim is
correct instead?

One thing that's incorrect and has been discussed many times here
before is that the inequality must be strict. That is, the wording
should have omitted "equal to".

Here's a example of a signal that wouldn't work with your definition:
an Fs/2 sine wave. The sampling rate is equal to twice the highest
frequency component, but since the sample points are precisely at the
zeros of the sine() function, you get zero output.
--
% Randy Yates % "So now it's getting late,
%% Fuquay-Varina, NC % and those who hesitate
%%% 919-577-9882 % got no one..."
%%%% <[email protected]> % 'Waterfall', *Face The Music*, ELO
http://home.earthlink.net/~yatescr
 
F

Floyd L. Davidson

Jim Kelley said:
Here are some valid standard defintions:

Actually, they are good definitions, but they are *not*
"valid standard definitions" for this discussion. You
are citing a dictionary of _common_ English, as spoken
by the general population. But we are discussing what
is called a "term of art".

Term of Art:
technical word: a word or phrase with a special
meaning, used in a specific field of knowledge

In other words, it may or may not be the same, when used
in the information or communications industry as it is
used by the general population of English speakers.

It does happen that in this case there is no significant
difference, and your definitions are useful
illustrations, but they are not very precise, while the
term of art definitions are *very* precise.
"quantize - to subdivide into small but measurable increments."
(Merriam Webster's Collegiate Dictionary, Tenth Edition)

Note that in the definition, there appears no mention of
assigning a value.

It says "into small but *measurable* increments". That
is assigning a value, no more and no less. (Indeed,
it would be worthless otherwise.)

Whatever, here is what Wordnet says,

quantize
v 1: telecommunications: approximate (a signal varying
continuously in amplitude) by one whose amplitude is
restricted to a prescribed set of discrete values [syn:
quantise]

2: apply quantum theory to; restrict the number of possible
values of (a quantity) or states of (a physical entity or
system) so that certain variables can assume only certain
discrete magnitudes that are integral multiples of a
common factor; "Quantize gravity" [syn: quantise]

They provide both a term of art definition and a common
usage definition. Both make if very clear that the
result is digital. They both use the word "discrete",
and *that* is indeed the key to defining "digital".
Assigning a value would then be
considered a part of a separate and distinct process of
converting to digital form, as in

Well, except that it is clearly an intrinsic part of
quantization you are right. Of course that also clearly
negates your point.

Indeed, if we do look at a "valid standard definition"
for the term of art,

quantization:

A process in which the continuous range of values
of an analog signal is sampled and divided into
nonoverlapping (but not necessarily equal)
subranges, and a discrete, unique value is assigned
to each subrange.

From Federal Standard 1037C.

We can see that it *clearly* does mean to make it digital.
That is the *only* purpose for quantization.
"digital - of, or relating to data in the form of numerical digits",

That is one of the several common English definitions.
It is rather poorly stated if one is thinking of the
term of art used in the communications/information
industries simply because it will confuse people (just as
you were above by the "measurable increment" as opposed
to stating a "value").

Not all things that are in the *form* of numerical
digits are obviously so. For example, it might be a
difference between flags.... round, square and
triangular. That would in fact be a digital signaling
system, and those are in fact "in the form of numerical
digits", but it might not be immediately obvious either.
and as opposed to

"analog - of, relating to, or being a mechanism in
which data is represented by continuously variable
physical quantities."

Again, that is close, but it is an imprecise common
usage definition. It does not make if clear that the
*value* of the data is continuous, and that merely being
represented using some physical characteristic that is
continuously varying is *not* what it means. It could
easily be misconstrued (and commonly is), for example,
to mean that because a binary digital system using
voltage to encode data does not have *instant* rise and
fall times, that it is in fact an analog system, which
it is not.
 
F

Floyd L. Davidson

Don Bowey said:
The Working Groups of ANSI accredited Committee T1. Telecommunications, used
the IEEE definitions. Occasionally there were questions, which were
amicably resolved.

Is there some reason you can never be specific about anything?

Why not provide us with those definitions?
 
F

Floyd L. Davidson

Richard Dobson said:
Floyd L. Davidson wrote:
..

My ISP removes headers quite aggressively after only a
short time, so I can no longer check what exactly this

Google archives it.
is all referencing (had everyone not spent quite so much
time hurling sarcastic "thanks" to each other, the
messages might still be there). Is this all still about
"quantized = digital", and *standard* definitions of
"digital"?

Yep. We have people who simply refuse to accept
standardized definitions for terms of art. There have
been several personal opinions on definitions, but not
one authoritative reference to anything that is not
precisely the same as the one that I originally cited.

The reason for that is quite clear, though I suppose not
everyone has understood it yet. That "standard"
definition truly is a standard definition. It has been
accepted virtually across the board by every standards
committee. There is no competing definition available,
and that is why nobody has been able to cite one.
And I guess someone will ask "how does one decide this
or that source is 'valid'? ". Wikipedia? Opportunities
for more fruitless bipolar arguments there, I fancy!

ANSI Standards are not a bad place to start. In this
case virtually all of the interested American standards
groups worked together to generate a single
comprehensive glossary of terms. That is of course what
I quoted to start with. Those who initially said it
wasn't valid are being a lot more careful now though,
because they probably add did try to find something
different, and discovered there simply isn't.
 
B

Bob Myers

Floyd L. Davidson said:
Here is the theorem:

Nyquist's theorem:
A theorem, developed by H. Nyquist, which states
that an analog signal waveform may be uniquely
reconstructed, without error, from samples taken at
equal time intervals. The sampling rate must be
equal to, or greater than, twice the highest
frequency component in the analog signal. Synonym
sampling theorem.

And that "explanation" of the Nyquist theorem itself
contains a glaring error. The Nyquist rate, as shown by
Nyquist himself, is NOT "equal to, or greater than,
twich the highest frequency component in the analog
signal." If you're at all familiar with what Nyquist
actually said, and why, you should easily be able to
see where the error in that lies.

Floyd, you also continue to cite my refusal to post or
point to an "alternate definition" as if it were some huge
victory for you. But as the old saying goes, "absence of
evidence is not evidence of absence." I choose not to
simply point to an opposing "definition" - although there
ARE certainl many such - for the reasons I have stated,
and which should again be obvious here. An argument
from authority pales to insignificance when up against
arguments based on evidence and reason - and when two
people attempt to argue with nothing but "authorities" to
cite, this becomes even more obvious. What would you
have us do, stack the "authoritative references" on either
side up and weigh them to determine the "truth"? That's
a very, very foolish position to take.

Bob M.
 
B

Bob Myers

Randy Yates said:
One thing that's incorrect and has been discussed many times here
before is that the inequality must be strict. That is, the wording
should have omitted "equal to".

That's one error. It's not the only one.

Bob M.
 
B

Bob Myers

Richard Dobson said:
Well, I seem to have spent my life doing that, as much as I am able. But
agreeing upon terminology, the core vocabulary of the subject, is by
definition a group exercise. Otherwise, people take a term and
arbitrarily make it mean what they want it to mean, which seems to be the
issue here.

Very true, but in agreeing upon terminology there are also some
"rules" to be followed. We prefer to agree upon terms which
are distinct and which have their own unique meaning or
flavor; if a word is completely equivalent to another word, then
it is a redundancy and should not be preferred. Further, we wish
the words we use to have some basic reason for being chosen -
i.e., the etymology of these words should give the reader or
listener some clue as to their meaning. For instance, what Hooke,
Leeuwenhoek, and others came up with in the 17th century wasn't
called a "microscope" simply because people liked the sound of
that word; it meant something. Similarly, the terms we are discussing
here ,"analog" and "digital," were specifically chosen for these
applications because of what the words already meant and implied.

Bob M.
 
B

Bob Myers

Floyd L. Davidson said:
Is there some reason you can never be specific about anything?

Why not provide us with those definitions?

Ummm...Floyd, I hate to point this out, but I believe they've
already been provided. You simply didn't recognize them without
someone hanging a big "these are the IEEE definitions" sign
on them.

Bob M.
 
B

Bob Myers

Term of Art:
technical word: a word or phrase with a special
meaning, used in a specific field of knowledge

What, you're not going to cite the source of that
definition? Then how could anyone POSSIBLY
consider it to be correct or "authoritative"?

Bob M.
 
F

Floyd L. Davidson

Randy Yates said:
[email protected] (Floyd L. Davidson) said:
[...]
Nyquist's theorem:
A theorem, developed by H. Nyquist, which states
that an analog signal waveform may be uniquely
reconstructed, without error, from samples taken at
equal time intervals. The sampling rate must be
equal to, or greater than, twice the highest
frequency component in the analog signal. Synonym
sampling theorem.
[...]
That is 100%, definitively incorrect.

Whoa, too much context is being trimmed here. Lets put some
back in to keep this straight about what was claimed:

"Right let me spell it out for you. That glossary
explained the Nyquist frequency. As part of that
definition it explicitly gave the requirement that
the Nyquist frequency be EQUAL to twice the highest
frequency being reproduced.

That is 100%, definitively incorrect."

But the above quote is for the Nyquist Theorem, and that
is not what was claimed to be incorrect. The statement
made was about the "Nyquist frequency", and as I pointed
out (and you snipped), the defintion for Nyquest rate
says *nothing like* what was claimed.

Here it is again:

Nyquist rate:
The reciprocal of the Nyquist interval, i.e., the
minimum theoretical sampling rate that fully
describes a given signal, i.e., enables its
faithful reconstruction from the samples.

It is absolutely correct.
One thing that's incorrect and has been discussed many times here
before is that the inequality must be strict. That is, the wording
should have omitted "equal to".

You are looking at the definition of the Theorem, not
the definition of the rate, and then saying the
definition of "Nyquist Rate" should not have the words
"equal to". It doesn't.

But the above is a statement of the theorem, and it
includes the theoretical case (which is totally
impractical) for the quantum size as it approaches 0
size. It is not wrong. (Granted that it is confusing,
and probably would be less so if it has used something
like channel bandwidth rather than frequency component.)
Here's a example of a signal that wouldn't work with your definition:
an Fs/2 sine wave. The sampling rate is equal to twice the highest

The sampling rate. But you are not arguing the
definition of the Nyquist Rate, which *never* says a
thing about "equal to". So you say one definition is
wrong, but your "proof" discusses an entirely different
definition (which happens not to be wrong at all).
frequency component, but since the sample points are precisely at the
zeros of the sine() function, you get zero output.

So why not apply the specific definition given, i.e.,
for Nyquist Rate rather than what you imagine is implied
from the Nyquist Theorem?

Opps, that turns out to be quite correct after all.

What definitions does the IEEE use?
 
F

Floyd L. Davidson

Bob Myers said:
Very true, but in agreeing upon terminology there are also some
"rules" to be followed.

The number one rule is that once a term is standardized,
*that* is the way it is used. Homespun definitions
might be fun for parlor games, but not in technical
discussions.
 
D

Don Bowey

Ummm...Floyd, I hate to point this out, but I believe they've
already been provided. You simply didn't recognize them without
someone hanging a big "these are the IEEE definitions" sign
on them.

Bob M.

I see Floyd continues to be an ass, in this and other ways. I don't read
his posts any longer, because, having questionable veracity, he is not
relevant.
 
F

Floyd L. Davidson

Bob Myers said:
And that "explanation" of the Nyquist theorem itself
contains a glaring error. The Nyquist rate, as shown by
Nyquist himself, is NOT "equal to, or greater than,
twich the highest frequency component in the analog
signal." If you're at all familiar with what Nyquist
actually said, and why, you should easily be able to
see where the error in that lies.

The standard definition of Nyquist Rate from the
glossary is not incorrect.

I don't believe you understand the theorem.
Incidentally, Nyquist didn't come up with the theorem,
hence you really don't want to look at what Nyquist
wrote much as at Shannon's mathematical proof of what
Nyquist proposed.
Floyd, you also continue to cite my refusal to post or
point to an "alternate definition" as if it were some huge
victory for you.

Every single time you claim the standard definition is
wrong you indict yourself. The only way out of the
corner you paint yourself into, claiming to be an expert
and all, is to cite where other experts agree with you.
But clearly none do.

It isn't just your claim that the standard definitions
are wrong that is bogus...
But as the old saying goes, "absence of
evidence is not evidence of absence."

But since we do have a great deal of evidence, all of it
saying only one thing, your claim that it is wrong does
require some form of evidence before it is credible.
I choose not to
simply point to an opposing "definition" - although there
ARE certainl many such - for the reasons I have stated,

Yeah, sure Bob! There are certainly any number of hokum
folks just like you that have their own definitions for
any number of things. Put on a tin foil hat and go for
it!

But you don't cite a credible opposing definition
because there are none.
and which should again be obvious here. An argument
from authority pales to insignificance when up against
arguments based on evidence and reason - and when two

You have provided no evidence at all. Your reasoning is
so flawed as to be a joke. And I hate to tell you, but
a *valid* arugment from authority is very very difficult
to overcome. When virtually every standards
organization in the country has agreed to a standard
definition, and accepted it for years, your homespun
hokum defs are nothing other than evidence that your
ability to reason is indeed questionable.
people attempt to argue with nothing but "authorities" to
cite, this becomes even more obvious. What would you

When people argue with no evidence, yes something is
obvious.
have us do, stack the "authoritative references" on either
side up and weigh them to determine the "truth"? That's
a very, very foolish position to take.

There is nothing in the stack on your side of the
question Bob. You have already taken a very very
foolish position.
 
F

Floyd L. Davidson

Bob Myers said:
Ummm...Floyd, I hate to point this out, but I believe they've
already been provided. You simply didn't recognize them without
someone hanging a big "these are the IEEE definitions" sign
on them.

That is correct. If you don't cite the source, it has very
little meaning.

Incidentally, the ANSI T1 committee was involved in the
process of developing the glossary that I've cited.
 
F

Floyd L. Davidson

Bob Myers said:
What, you're not going to cite the source of that
definition? Then how could anyone POSSIBLY
consider it to be correct or "authoritative"?

I didn't assume you were quite that trite, but I guess I
should have expected it from you.

http://encarta.msn.com/dictionary_/term%20of%20art.html

Other definitions exist:

term of art
: a term that has a specialized meaning in a
particular field or profession

http://www.merriam-webster.com/dictionary/term of art

What sort of hokum definition do you use?
 
F

Floyd L. Davidson

Don Bowey said:
I see Floyd continues to be an ass, in this and other ways. I don't read
his posts any longer, because, having questionable veracity, he is not
relevant.

It's just exceedingly difficult argue someone who has
facts and understands to topic, isn't it.
 
D

Don Pearce

Here is the definition it has of the *rate* (you incorrectly call it
the Nyquist "frequency"):

Nyquist rate:
The reciprocal of the Nyquist interval, i.e., the
minimum theoretical sampling rate that fully
describes a given signal, i.e., enables its
faithful reconstruction from the samples. Note: The
actual sampling rate required to reconstruct the
original signal will be somewhat higher than the
Nyquist rate, because of quantization errors
introduced by the sampling process.

Here is the theorem:

Nyquist's theorem:
A theorem, developed by H. Nyquist, which states
that an analog signal waveform may be uniquely
reconstructed, without error, from samples taken at
equal time intervals. The sampling rate must be
equal to, or greater than, twice the highest
frequency component in the analog signal. Synonym
sampling theorem.

It appears that you are somewhat confused as to what is
being defined. The definition for the Nyquist rate says
absolutely nothing about being equal to anything.
Instead it says it is the minimum rate that will "fully
describe" the signal.


What is not correct about it. What do you claim is
correct instead?

Explain *your* definition. (Oh, and do so for all values
of sampling rate as the size of the quantum steps approach
zero.)

Whatever, I can't tell what you are disagreeing with. You
read one definition and claim it is something else, you don't
say what you think is wrong with it or what would be right.

Maybe you disagree with the way the words are spelled,
with the use of the term "analog" or you just can't
understand what it says...


You are the howler.

You probably should look up Shannon's "Communication in
the Presence of Noise" from 1949.


It appears to me that the definition they gave is
precisely correct, and again *you* are abjectly
clueless.

I guessed you would think it was correct. You can't sample at a rate
equal to twice the frequency you are sampling. The wanted signal has
collided with its image and you can't disambiguate them. Thank you for
showing us that you are clueless.

d
 
D

Don Pearce

So demonstrate where there is another!

No need. You claim your definitions to be correct because they appear
to be borne out by a list you claim to be definitive. The list has
been shown to be errored, so your authority has vanished. Deal with
it.

d
 
R

Richard Dobson

Floyd L. Davidson wrote:
...
...
Indeed, if we do look at a "valid standard definition"
for the term of art,

quantization:

A process in which the continuous range of values
of an analog signal is sampled and divided into
nonoverlapping (but not necessarily equal)
subranges, and a discrete, unique value is assigned
to each subrange.

From Federal Standard 1037C.

We can see that it *clearly* does mean to make it digital.
That is the *only* purpose for quantization.


This only addresses values, it does not address time. So how would you
classify this signal:

the output of a standard 1V/oct (voltage control) music keyboard - a
monophonic (= non-overlapping) series of stepped voltages corresponding
precisely to the 12-tone equal-termperament subdivisions of the octave.
This control signal is typically applied to the frequency control input
of an analogue voltage-controlled oscillator (VCO; think MiniMoog), in
order to synthesise tones at the specified frequency. Thus, values are
quantized. There is no time quantization (no clock) - the notes can be
played at any time, and changed at any speed (presumably within the
limits of the human player).

I would call this an analogue signal; it meets exactly the definition
above, it is only you who extrapolates from it the notion of "digital".
And manifestly, making a digital signal is ~not~ the only purpose for
quantization!

And if the Federal Standard had meant to make it mean "digital" surely,
given its importance, they would have said so.

Richard Dobson
 
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