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Sci.Electronics.Basics -> Questions about equivalents of audio/video and digital/analog.

There are 304 messages in this thread.
You are currently looking at messages 260 to 280.






Author: Richard Dobson
Date: 15:38 25-08-07

Floyd L. Davidson wrote:
..
>>
>>Users may insert a simple control (may be called "Key
>>Follow" but is basically just an analogue level control)
>>that can reduce/expand the size of the steps so that 24
>
>
> So there are not precisely 12 voltages per octave, but
> rather there are now ever many you choose, and the
> adjustment is continuously variable.
>
> You described one device before, and now describe
> a different device...
>
> How do you expect a valid answer if you purposely
> distort the question with false information?
>

Good grief man, it's the SAME DEVICE! The same cable, the same modules,
the same everything. All that changes is that the user tweaks a pot.

So I suppose we have to define "device" now as well as everything else.

I gave you a picture, a micrograph, of a system that ~can~ produce a
signal of precisely stepped voltages. You promptly pronounce that as
"digital". Then I zoom out, give you a broader picture of the same
system, and all of a sudden we discover sginals that can morph
seamlessly between stepped and non-stepped - between "digital" and
"analogue". Perhaps that simply doesn't arise in your universe.

Away now for a week, so you will have to figure the rest out by yourself!

Richard Dobson






Author: Floyd L. Davidson
Date: 19:38 25-08-07


Richard Dobson <richarddobson@blueyonder.co.uk> wrote:
>Floyd L. Davidson wrote:
>..
>>>
>>>Users may insert a simple control (may be called "Key
>>>Follow" but is basically just an analogue level control)
>>>that can reduce/expand the size of the steps so that 24
>> So there are not precisely 12 voltages per octave, but
>> rather there are now ever many you choose, and the
>> adjustment is continuously variable.
>> You described one device before, and now describe
>> a different device...
>> How do you expect a valid answer if you purposely
>> distort the question with false information?
>>
>
>Good grief man, it's the SAME DEVICE! The same cable,
>the same modules, the same everything. All that changes
>is that the user tweaks a pot.

You didn't accurately describe the device the first
time. Which is *exactly* why my answer was conditional
on there being *precisely* 12 voltages per octave. Then
you admit that there are not, that it can be any of an
infinite number of voltages because it is actually
continuously variable.

You just aren't ready to be honest at all, are you.

>So I suppose we have to define "device" now as well as everything else.

Somebody else uses that game...

>I gave you a picture, a micrograph, of a system that
>~can~ produce a signal of precisely stepped
>voltages. You promptly pronounce that as "digital". Then

No, I did not. I said *if* what you described was
accurate. It wasn't, and the difference negates
everything.

Why not be honest?

>I zoom out, give you a broader picture of the same
>system, and all of a sudden we discover sginals that can
>morph seamlessly between stepped and non-stepped -

A, yes... a "continuous" set of values... which
clearly makes it analog. If it had actually been just
12 levels, as you initially said, it would be digital.

But you just had to be dishonest.

>between "digital" and "analogue". Perhaps that simply
>doesn't arise in your universe.

How anyone could miss the distinction is beyond me. But
worse yet, it is *obvious* that you have not missed that
distinction, and instead are merely trying to make a
point with deceitful and abject dishonesty.

>Away now for a week, so you will have to figure the rest out by yourself!

How hard did you think it would be to figure you out?

--
Floyd L. Davidson <http://www.apaflo.com/floyd_davidson>;
Ukpeagvik (Barrow, Alaska) floyd@apaflo.com

Author: Richard Dobson
Date: 20:47 25-08-07

Floyd L. Davidson wrote:
.
>
> You didn't accurately describe the device the first
> time. Which is *exactly* why my answer was conditional
> on there being *precisely* 12 voltages per octave. Then
> you admit that there are not, that it can be any of an
> infinite number of voltages because it is actually
> continuously variable.
>
When it is used as I described, in its "standard" arrangement, it ~is~
exactly quantised to 12 voltages per octave. Just like the frets on a
guitar. At other times, it may be quantized in some different way, or
all smoothed out. Same hardware, same cable, same interface. Only you
claimed this describes a digital signal.

Perhaps you were too quick to jump to conclusions, and not ask necessary
clarifying questions?
..
> A, yes... a "continuous" set of values... which
> clearly makes it analog. If it had actually been just
> 12 levels, as you initially said, it would be digital.
>
..

So we have at last reached a consensus, that that a signal can be
quantized, just as I have described, and nevertheless be analogue.
"Quantized" of itself is not a sufficient condition for a signal to be
classed as digital. You would require further information to make that
determination. As you have yourself now clearly indicated. The term
"digital" can at last be reserved for where it is truly appropriate.
"Quantized" is a subset, an aspect of, "digital", but it is
manifestly
not the same as "digital".

QED. Isn't music wonderful, that it can demonstrate such things!

Richard Dobson

Author: Floyd L. Davidson
Date: 21:19 25-08-07

Richard Dobson <richarddobson@blueyonder.co.uk> wrote:
>Floyd L. Davidson wrote:
>.
>> You didn't accurately describe the device the first
>> time. Which is *exactly* why my answer was conditional
>> on there being *precisely* 12 voltages per octave. Then
>> you admit that there are not, that it can be any of an
>> infinite number of voltages because it is actually
>> continuously variable.
>>
> When it is used as I described, in its "standard"
>arrangement, it ~is~ exactly quantised to 12 voltages

If it is quantized, it is digital. (I cannot see how
what you are describing is quantized though.)

All you have done is adjusted the range of an analog
signal to have 12 steps over a given voltage range.
That has nothing at all to do with quantization.

>per octave. Just like the frets on a guitar. At other
>times, it may be quantized in some different way, or all
>smoothed out. Same hardware, same cable, same
>interface. Only you claimed this describes a digital
>signal.

I claimed that if you quantize something to a set of
only 12 voltages, that it is digitized. That is a true
fact. If you adjust the range of an analog signal to
have 12 steps, that is not quantizing it and it is not
digital.

>Perhaps you were too quick to jump to conclusions, and
>not ask necessary clarifying questions?

Why do you thing I put the "if" in my response?
Obviously I know you aren't likely to be honest or
clueful either one.

>> A, yes... a "continuous" set of values... which
>> clearly makes it analog. If it had actually been just
>> 12 levels, as you initially said, it would be digital.
>>
>..
>
>So we have at last reached a consensus, that that a
>signal can be quantized, just as I have described, and
>nevertheless be analogue.

If the signal is quantized, it is digital. That is a
fact, by the very definition of quantized.

> "Quantized" of itself is not a sufficient condition
>for a signal to be classed as digital. You would require

It absolutely is.

>further information to make that determination. As you
>have yourself now clearly indicated. The term "digital"
>can at last be reserved for where it is truly
>appropriate. "Quantized" is a subset, an aspect of,
>"digital", but it is manifestly not the same as
>"digital".

Look up any standard definition you like for "quantized",
and every one of them will indicate changing a
continuous range of values to a discrete value from a
finite set.

That of course defines digital too, as you find if you
look at *any* standard definition of the term.

Of course if you make up your own definitions, it can
mean anything you like. I won't know what it is, and
neither will anyone else. You won't be able to
communicate, and will be reduced to posting even more
nonsense.

--
Floyd L. Davidson <http://www.apaflo.com/floyd_davidson>;
Ukpeagvik (Barrow, Alaska) floyd@apaflo.com

Author: Jerry Avins
Date: 21:28 26-08-07

Floyd L. Davidson wrote:

...

> It isn't "telephone system thinking", it's Information
> Theory. That applies to a great deal more than high
> fidelity audio.

So Information Theory tells us that a quantized signal is digital?
Consider the output of the limiters in an FM IF driving a Foster-Seely
discriminator. It has two states -- saturated and zero -- before the
tank that smooths the edges. I guess Information theory says that FM
radio is digital (maybe unless you use an Avins-Seely ratio detector,
but even those work better with at least one limiter).

Jerry
--
Engineering is the art of making what you want from things you can get.
¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯
¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯

Author: Jerry Avins
Date: 22:20 26-08-07

Randy Yates wrote:
> "Bob Myers" <nospamplease@address.invalid> writes:
>
>> "Floyd L. Davidson" <floyd@apaflo.com> wrote in message
>> news:87abshyoo2.fld@apaflo.com...
>>
>>> Lets be clear... The definitions I cited are standard.
>>> I posted 5 or 6 varied references to the same definitions.
>> And everyone knows, ""standards" are holy.
>
> Not that I necessarily agree or disagree with Floyd's original point,
> but citing a written reference holds more water than a post from an
> individual on a usenet newsgroup, in my opinion.

Floyd maintains that any signal whose values are restricted to a finite
set -- IOW, "quantized" -- is digital. I cited a two-level analog signal
and I can demonstrate a digital signal with a relatively large
continuous range of values. His definitions are simply too restrictive
to accommodate those, and he seems to be having a fit.

Jerry
--
Engineering is the art of making what you want from things you can get.
¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯
¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯

Author: Randy Yates
Date: 22:41 26-08-07

Jerry Avins <jya@ieee.org> writes:

> Randy Yates wrote:
>> "Bob Myers" <nospamplease@address.invalid> writes:
>>
>>> "Floyd L. Davidson" <floyd@apaflo.com> wrote in message
>>> news:87abshyoo2.fld@apaflo.com...
>>>
>>>> Lets be clear... The definitions I cited are standard.
>>>> I posted 5 or 6 varied references to the same definitions.
>>> And everyone knows, ""standards" are holy.
>> Not that I necessarily agree or disagree with Floyd's original point,
>> but citing a written reference holds more water than a post from an
>> individual on a usenet newsgroup, in my opinion.
>
> Floyd maintains that any signal whose values are restricted to a
> finite set -- IOW, "quantized" -- is digital. I cited a two-level
> analog signal and I can demonstrate a digital signal with a relatively
> large continuous range of values. His definitions are simply too
> restrictive to accommodate those, and he seems to be having a fit.

I've decided that it's not fruitful to continue this discussion since
the knowledge I work with admits anough understanding to get a lot of
real work done. These sorts of discussions take too much time and
produce little or no fruit.

My ability to do work does not depend on others' judgement of the
correctness of my definitions.
--
% Randy Yates % "She has an IQ of 1001, she has a jumpsuit
%% Fuquay-Varina, NC % on, and she's also a telephone."
%%% 919-577-9882 %
%%%% <yates@ieee.org> % 'Yours Truly, 2095', *Time*, ELO
http://home.earthlink.net/~yatescr

Author: Floyd L. Davidson
Date: 22:57 26-08-07

Jerry Avins <jya@ieee.org> wrote:
>Floyd L. Davidson wrote:
>
> ...
>
>> It isn't "telephone system thinking", it's Information
>> Theory. That applies to a great deal more than high
>> fidelity audio.
>
>So Information Theory tells us that a quantized signal
>is digital? Consider the output of the limiters in an FM
>IF driving a Foster-Seely discriminator. It has two
>states -- saturated and zero -- before the tank that
>smooths the edges. I guess Information theory says that
>FM radio is digital (maybe unless you use an Avins-Seely
>ratio detector, but even those work better with at least
>one limiter).

You aren't making a lick of sense Jerry. That suggests
you don't have even a foggy notion of what you are
talking about.

Tell us exactly what information is encoded in those
"saturated and zero" states?

--
Floyd L. Davidson <http://www.apaflo.com/floyd_davidson>;
Ukpeagvik (Barrow, Alaska) floyd@apaflo.com

Author: Jerry Avins
Date: 00:45 27-08-07

Floyd L. Davidson wrote:
> Jerry Avins <jya@ieee.org> wrote:
>> Floyd L. Davidson wrote:
>>
>> ...
>>
>>> It isn't "telephone system thinking", it's Information
>>> Theory. That applies to a great deal more than high
>>> fidelity audio.
>> So Information Theory tells us that a quantized signal
>> is digital? Consider the output of the limiters in an FM
>> IF driving a Foster-Seely discriminator. It has two
>> states -- saturated and zero -- before the tank that
>> smooths the edges. I guess Information theory says that
>> FM radio is digital (maybe unless you use an Avins-Seely
>> ratio detector, but even those work better with at least
>> one limiter).
>
> You aren't making a lick of sense Jerry. That suggests
> you don't have even a foggy notion of what you are
> talking about.
>
> Tell us exactly what information is encoded in those
> "saturated and zero" states?

Very little; the information is in the zero crossings. The signal is
quantized in amplitude. Is it digital or not? If not, does your
definition hold?

Jerry
--
Engineering is the art of making what you want from things you can get.
¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯
¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯

Author: Floyd L. Davidson
Date: 01:16 27-08-07

Jerry Avins <jya@ieee.org> wrote:
>
>Floyd maintains that any signal whose values are
>restricted to a finite set -- IOW, "quantized" -- is
>digital. I cited a two-level analog signal and I can
>demonstrate a digital signal with a relatively large
>continuous range of values. His definitions are simply
>too restrictive to accommodate those, and he seems to be
>having a fit.

I'll admit to a really great fit of laughter at that one!

You are so thoroughly confused that it is hilarious.

The recognized standard definitions say that a quantized
signal is digital. You can indeed have a two-level
analog signal, but the fact is that the *possible*
values are infinite (all values between your two listed
ones, for example). You cannot possibly have a digital
signal with a continuous range of values (large or
small, relative or otherwise).

I've cited multiple credible sources that agree with
what I say. You can't cite even one. There are none.

--
Floyd L. Davidson <http://www.apaflo.com/floyd_davidson>;
Ukpeagvik (Barrow, Alaska) floyd@apaflo.com

Author: Floyd L. Davidson
Date: 01:37 27-08-07

Jerry Avins <jya@ieee.org> wrote:
>Floyd L. Davidson wrote:
>> Jerry Avins <jya@ieee.org> wrote:
>>> So Information Theory tells us that a quantized signal
>>> is digital? Consider the output of the limiters in an FM
>>> IF driving a Foster-Seely discriminator. It has two
>>> states -- saturated and zero -- before the tank that
>>> smooths the edges. I guess Information theory says that
>>> FM radio is digital (maybe unless you use an Avins-Seely
>>> ratio detector, but even those work better with at least
>>> one limiter).
>> You aren't making a lick of sense Jerry. That suggests
>> you don't have even a foggy notion of what you are
>> talking about.
>> Tell us exactly what information is encoded in those
>> "saturated and zero" states?
>
>Very little; the information is in the zero
>crossings.

The voltage amplitude has nothing to do with whether
the signal is digital or analog. It can be anything,
with any characteristics you'd like to imagine.
That is because it carries no information.

>The signal is quantized in amplitude.

First, it is not. It varies between two voltages, and
does so continuously (and apparently too quickly for a
slow person to follow, eh?). But since the variations
contain no information and therefore do not represent
symbols of any kind, the amplitude does not determine
whether the signal is digital or analog.

>Is it
>digital or not? If not, does your definition hold?

We can't tell Jerry. You have not stated anything that
describes the symbols set. The information is carried
by some other characteristic of that signal (e.g., phase
or frequency). Not knowing if it carries only discrete
values from a finite set, or if the symbols are
continuously variable, we just don't know what it is.

This is *very* basic...

--
Floyd L. Davidson <http://www.apaflo.com/floyd_davidson>;
Ukpeagvik (Barrow, Alaska) floyd@apaflo.com

Author: Floyd L. Davidson
Date: 02:57 27-08-07

glen herrmannsfeldt <gah@ugcs.caltech.edu> wrote:
>Jerry Avins wrote:
>
>(snip)
>
>> So Information Theory tells us that a quantized signal
>> is digital? Consider the output of the limiters in an
>> FM IF driving a Foster-Seely discriminator. It has two
>> states -- saturated and zero -- before the tank that
>> smooths the edges. I guess Information theory says
>> that FM radio is digital (maybe unless you use an
>> Avins-Seely ratio detector, but even those work better
>> with at least one limiter).
>
>This sounds like what I previously tried to describe as quantized
>but not sampled. The signal has two states, but the transition
>can happen at any time.

Jerry's signal does not have two states. Voltage
amplitude is *not* what determines signal "state"
(value) with an FM signal.



--
Floyd L. Davidson <http://www.apaflo.com/floyd_davidson>;
Ukpeagvik (Barrow, Alaska) floyd@apaflo.com

Author: glen herrmannsfeldt
Date: 03:32 27-08-07

Jerry Avins wrote:

(snip)

> So Information Theory tells us that a quantized signal is digital?
> Consider the output of the limiters in an FM IF driving a Foster-Seely
> discriminator. It has two states -- saturated and zero -- before the
> tank that smooths the edges. I guess Information theory says that FM
> radio is digital (maybe unless you use an Avins-Seely ratio detector,
> but even those work better with at least one limiter).

This sounds like what I previously tried to describe as quantized
but not sampled. The signal has two states, but the transition
can happen at any time.

-- glen


Author: Arny Krueger
Date: 08:24 27-08-07

"glen herrmannsfeldt" <gah@ugcs.caltech.edu> wrote in
message news:7eWdnQDrYun48k_bnZ2dnUVZ_ovinZ2d@comcast.com
> Jerry Avins wrote:
>
> (snip)
>
>> So Information Theory tells us that a quantized signal
>> is digital? Consider the output of the limiters in an FM
>> IF driving a Foster-Seely discriminator. It has two
>> states -- saturated and zero -- before the tank that
>> smooths the edges. I guess Information theory says that
>> FM radio is digital (maybe unless you use an Avins-Seely
>> ratio detector, but even those work better with at least
>> one limiter).
>
> This sounds like what I previously tried to describe as
> quantized but not sampled. The signal has two states,
> but the transition can happen at any time.

The signal might be thought of as being quantized in the aplitude domain,
but it is clearly not quantized in the time domain. For a signal to be
quantized, it has to be fully quantized, that is quantized in both the time
domain and the amplitude domain.




Author: Jim Kelley
Date: 13:27 27-08-07



Floyd L. Davidson wrote:
> Actually, they are good definitions, but they are *not*
> "valid standard definitions" for this discussion.

They are valid for any discussion in which I care to use them. But
thanks for your input.

jk


Author: Floyd L. Davidson
Date: 14:35 27-08-07

Jim Kelley <jwkelley@uci.edu> wrote:
>Floyd L. Davidson wrote:
>> Actually, they are good definitions, but they are *not*
>> "valid standard definitions" for this discussion.
>
>They are valid for any discussion in which I care to use
>them. But thanks for your input.

That is true. You can use any definition for any word
you like, in Alice's Wonderland.

And you won't be understood by anyone else, which seems to
be the point of many who post this sort of drivel.

--
Floyd L. Davidson <http://www.apaflo.com/floyd_davidson>;
Ukpeagvik (Barrow, Alaska) floyd@apaflo.com

Author: Jim Kelley
Date: 15:12 27-08-07



Floyd L. Davidson wrote:
> And you won't be understood by anyone else, which seems to
> be the point of many who post this sort of drivel.

Perhaps true insofar as the word might not be understood by someone
who also does not know how to use a dictionary. Admitedly, I had not
accounted for that possibility. 8-|

jk


Author: Floyd L. Davidson
Date: 15:49 27-08-07

Jim Kelley <jwkelley@uci.edu> wrote:
>Floyd L. Davidson wrote:
>> And you won't be understood by anyone else, which seems to
>> be the point of many who post this sort of drivel.
>
>Perhaps true insofar as the word might not be understood
>by someone who also does not know how to use a
>dictionary.

You, for example.

>Admitedly, I had not accounted for that
>possibility. 8-|

That was fairly obvious, and still is.

You are implying that any dictionary definition (hence
not your unique Alice in Wonderland definition) is
correct in any context. That is not the way a
dictionary is properly used.

"Digital", for example, has at least three different
definitions. You want to be able to pull any one of
them out of a hat, and say that it means what it
means... But that is back to Alice in Wonderland.

The word "Digital" is a Term of Art, and your common
language dictionary definition is not valid in a
technical discussion.

--
Floyd L. Davidson <http://www.apaflo.com/floyd_davidson>;
Ukpeagvik (Barrow, Alaska) floyd@apaflo.com

Author: Jim Kelley
Date: 16:15 27-08-07



Floyd L. Davidson wrote:
> You are implying that any dictionary definition (hence
> not your unique Alice in Wonderland definition) is
> correct in any context.

I'm not implying that at all. I'm simply saying that the terms and
definitions I used are correct in the context in which I used them.

jk




Author: Floyd L. Davidson
Date: 16:53 27-08-07

Randy Yates <yates@ieee.org> wrote:
>Jerry Avins <jya@ieee.org> writes:
>> Randy Yates wrote:
>>> "Bob Myers" <nospamplease@address.invalid> writes:
>>>> "Floyd L. Davidson" <floyd@apaflo.com> wrote:
>>>>> Lets be clear... The definitions I cited are standard.
>>>>> I posted 5 or 6 varied references to the same definitions.
>>>>
>>>> And everyone knows, ""standards" are holy.
>>>
>>> Not that I necessarily agree or disagree with Floyd's original point,
>>> but citing a written reference holds more water than a post from an
>>> individual on a usenet newsgroup, in my opinion.
>>
>> Floyd maintains that any signal whose values are restricted to a
>> finite set -- IOW, "quantized" -- is digital. I cited a two-level
>> analog signal and I can demonstrate a digital signal with a relatively
>> large continuous range of values. His definitions are simply too
>> restrictive to accommodate those, and he seems to be having a fit.
>
>I've decided that it's not fruitful to continue this discussion since
>the knowledge I work with admits anough understanding to get a lot of
>real work done. These sorts of discussions take too much time and
>produce little or no fruit.
>
>My ability to do work does not depend on others' judgement of the
>correctness of my definitions.

So you figure that posting invalid definitions to Usenet
or proving that you cannot understand standard
definitions won't be a problem for you?

It's amazing though, just who finds what with web
searches. Anyone who reads what you've had to say
here... well it could easily affect your work!

Whatever, an article with out of hand invalid statements
quoted from the two people who clearly post from an IEEE
host is a really good place to throw out something that
I've asked them for repeatedly, and they have weaseled
around the question in odd ways: IEEE definitions of
"digital" and "analog". I think it was Randy Yates who
claimed they had been posted but did admit that nobody
had ever cited IEEE as a source.

Well, it appears that the person who posted it was me.
IEEE apparently uses the standard definitions which I
have posted from other sources.

However, here is a very interesting discussion from an
IEEE dictionary:

An analog signal implies /continuity/,
as contrasted to a digital signal that
is concerned with /discrete/ states.
Often the means of carrying information
is the distinguishing feature between
analog and digital. The information
content of an analog signal is conveyed
by the value or magnitude of some
characteristics of the signal such as
phase, amplitude, frequency of the
voltage, the amplitude or duration of a
pulse, and so on. To extract the
information, it is necessary to compare
the value or magnitude of the signal to
a standard. The information content of
a digital signal is concerned with
discrete states of the signal, such as
the presence or absence of a voltage, a
contrast in the open or closed position,
or a hole or no hole in certain
positions on a card. The digital signal
is given meaning by assigning numerical
values or other information to the
various possible combinations of the
discrete states of the signal."

"The New IEEE Standard Dictionary of Electrical and
Electronic Terms", 5th ed., IEEE Std. 100-1992,
IEEE Press, New York, 1992.

I'm quoting it from Roger L. Freeman's "Telecommunications
System Engineering", 3rd ed., 1996.

For one, it clearly shows the FM-signal-through-a-limiter
example given by Jerry very clearly to be exactly as my
analysis indicated, and not at all what Jerry said.
Also they clearly state that the values assigned to a
digital symbol need not be "numerical" as someone argued
repeatedly in earlier posts.

Another example of credible references that support each
and every point that I've made. And it again highlights
that none of those saying it isn't so can find *anything*
credible to support their statements. (And that of course
is why it is not "fruitful" to argue with me. I don't buy
rotten fruit.)

--
Floyd L. Davidson <http://www.apaflo.com/floyd_davidson>;
Ukpeagvik (Barrow, Alaska) floyd@apaflo.com

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