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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 160 to 180.






Author: Floyd L. Davidson
Date: 02:30 21-08-07


Don Bowey <dbowey@comcast.net> wrote:
>On 8/20/07 10:19 PM, in article 87odh1ea6x.fld@apaflo.com, "Floyd L.
>Davidson" <floyd@apaflo.com> wrote:
>
>> Don Bowey <dbowey@comcast.net> wrote:
>>> On 8/20/07 8:14 PM, in article 874pitfujh.fld@apaflo.com, "Floyd L.
>>> Davidson" <floyd@apaflo.com> wrote:
>>>>>>
>>>>>> Of course if you then run that digital PAM signal through
virtually
>>>>>> any analog channel, it no longer has a limited set of values...
>>>>>
>>>>> Including a two foot piece of cable, or two inches with a small
cap.
>>>>
>>>> Nope. It would take a fair sized cap.
>>>>
>>>> Keep in mind that that is *exactly* what a V.90 modem puts on a
>>>> regular twisted pair telephone cable, and it works just fine for
>>>> a couple miles at least, sometimes even much farther.
>>>>
>>>> And that signal is digital, and is processed as a digital signal
>>>> by the receiving modem.
>>>
>>> Digital data CSUs and T1 transmitter line signals are digital and look
>>> similar to distorted square waves. An all 1's signal looks like a
distorted
>>> sinewave .
>>
>> Your point is? (Besides the poor description? They
>> don't look like distorted square waves. The look like
>> only slightly distorted sine waves!)
>
>Have you looked at a DSX-1 envelope lately?

Yes. I've got the specs right here! :-) Literally, I have
had a graph on my web site for several years now that I drew up
to illustrate something I wrote once upon a time

http://www.apaflo.com/floyd_davidson/t1pulse.jpg


>>> Using the same V.90 example....... It will work as well if two v.90 modems
>>> are connected back-to-back by a short pair of wires.
>>
>> It won't. They can't talk to each other that way except
>> using v.34 protocols.
>>
>> Regardless, what is your point? I said that v.90 works
>> fine for a couple of *miles*, minimum, so what
>> significance would there be to working "back-to-back by
>> a short pair of wires"?
>
>My point is...... You are making too much of your point that "Of course if
>you then run that digital PAM signal through virtually any analog channel,
>it no longer has a limited set of values."

Yeah, your are probably right on that one. I should
have left the "virtually any" out, and just said "an
analog channel". It depends greatly on the
characteristics of the channel, and it happens that a
wireline is a pretty "good" channel, while many
amplifiers would not be so good.

Sorry if I'm getting a bit cranky here, the abject
silliness being displayed by a couple of people is
annoying.

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

Author: Steve Underwood
Date: 04:44 21-08-07

glen herrmannsfeldt wrote:
> Dave Platt wrote:
>
> (snip)
>
>> Some of the TV networks are speeding up syndicated reruns by using
>> this sort of technique. They appear to be using the "chop out audio
>> samples" method to speed up the dialog (without pitch-shifting it) and
>> dropping out complete frames of the video. This works fairly well
>> when watching scenes with little action, but causes an odd
>> stuttering-jerk effect when the camera pans or somebody walks across
>> the screen.
>
> I have a VCR that will play back at 1.5X without pitch shifting.
> At higher playback speeds at only gives you part of the sound.
> Maybe two second pieces with gaps depending on the speed.
>
> The 1.5X playback is just a little too fast to watch a show
> comfortably.

A lot of relatively simple variable speed constant pitch playback
techniques - e.g. various TDHS derivatives, like PICOLA or PSOLA - work
well up to x1.5 or so. They start to sound nasty beyond about x2. That
isn't too important, as speech that fast isn't awfully useful.

I find for the majority of TV, x1.5 is far too slow to be comfortable. :-)

Steve

Author: glen herrmannsfeldt
Date: 05:20 21-08-07

Dave Platt wrote:

(snip)

> Some of the TV networks are speeding up syndicated reruns by using
> this sort of technique. They appear to be using the "chop out audio
> samples" method to speed up the dialog (without pitch-shifting it) and
> dropping out complete frames of the video. This works fairly well
> when watching scenes with little action, but causes an odd
> stuttering-jerk effect when the camera pans or somebody walks across
> the screen.

I have a VCR that will play back at 1.5X without pitch shifting.
At higher playback speeds at only gives you part of the sound.
Maybe two second pieces with gaps depending on the speed.

The 1.5X playback is just a little too fast to watch a show
comfortably.

-- glen


Author: Floyd L. Davidson
Date: 10:19 21-08-07

Don Bowey <dbowey@comcast.net> wrote:
>On 8/20/07 10:31 PM, in article 87bqd1e9n8.fld@apaflo.com, "Floyd L.
>Davidson" <floyd@apaflo.com> wrote:
>
>> There simply are no such things as "analog repeaters"
>> on local telephone loops.
>
>Since when?

Oh, perhaps 1950, maybe a few as late as 1960 or so...

Do you know of any telco that actually uses them today?

>If a loop is long enough, and there is no pair-gain facility available, it
>gets an "E" type repeater. If that isn't an analog repeater nothing is.

Of course I suppose it is possible they are still being
used where *you* live. But I don't know of any telco in
all of Alaska that has used an E repeater in the last 30-40
years. In particular, in the last 10-20 years that would
be totally unacceptable.

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

Author: Bob Myers
Date: 11:37 21-08-07


"Floyd L. Davidson" <floyd@apaflo.com> wrote in message
news:87veb9hjev.fld@apaflo.com...

>>
>>"Analog" != "continuous," even though most commonly
>>"analog" signals are also continuous in nature.
>
> Analog signals are by *definition* continous.

Nonsense. You don't believe it is possible to sample
an "analog" signal and have it remain analog?

> You have misunderstood what that means though. The
> analog value of a signal is continuous,

Well, THAT certainly makes it clearer....

Since you seem to be so hung up on definitions, Floyd,
try this one on for size:

Continuous: unchanged or uninterrupted: continuing
without changing, stopping, or being interrupted in space
or time.

Note that this does not say anything at all about the range
of possible values being "continuous" (which is what you
seem to be trying to say in the above).

Bob M.





Author: Bob Myers
Date: 11:40 21-08-07


"glen herrmannsfeldt" <gah@ugcs.caltech.edu> wrote in message
news:sPidnS0J6f5rzVfbnZ2dnUVZ_tuonZ2d@comcast.com...
> There needs to be a way to describe sampled but not quantized
> signals. They are not continuous in time, but the function
> can take on any value at each sample point.

Such signals are simply referred to as "sampled."
Whether the data they carry is encoded in "digital"
or "analog" form is a separate question.

The value that any symbol has (to use the proper
communications or information theory term) is
ALWAYS limited in accuracy/resolution, regardless
of the encoding system used. There is no such thing
as an information encoding system or communications
channel which provides "infinite" accuracy/resolution,
therefore to say that a signal can take on "any"
value becomes to a large extent meaningless.

Bob M.




Author: Bob Myers
Date: 11:43 21-08-07


"Floyd L. Davidson" <floyd@apaflo.com> wrote in message
news:87mywlki1d.fld@apaflo.com...

>>>>>
>>>>>If you quantize the magnitude, it is digital. That is
>>>>>by definition.
>>No, you haven't. You merely have a signal at a set of discrete levels.
>
> Sheesh! That *is*, by definition a digital signal.

Really? Suppose I show you an oscilloscope screen which
is displaying a single line of video, which happens to be
carrying an 8-level gray-scale pattern. It clearly shows
a set of discrete levels. Further, since this video happened
to be created by a D/A converter with only three bits at
the input (our video generator was built on the cheap!), those
are the ONLY levels this signal may exhibit. Is this a
"digital" signal?

> Bullshit son. Look it up. I've provided you with
> quotes from an authoritative reference, twice now. You
> don't have to take my word for it, that *is* the agreed
> technical definition of the term.

Ah, Floyd - argument from authority again, huh?

Bob M.



Author: Bob Myers
Date: 11:53 21-08-07


"Floyd L. Davidson" <floyd@apaflo.com> wrote in message
news:87ir79hghp.fld@apaflo.com...
> It wasn't analog until you ran it through an analog amplifier.

More nonsense.

Again, the ONLY definitions of "analog" and "digital"
which make any sense treat these as distinctions in
the form of information encoding being used. If I
run EITHER a "digital" or "analog" signal through an
amplifier, what comes out can still be interpreted (the
information recovered from the signal) ONLY if the
encoding intent is understood and the proper decoding
applied.

A serial stream of digital data still makes sense, whether
the amplitude assigned to the "1" or "true" state is
0.1V, 1V, 10V, or 100 kV. But it makes sense
ONLY when interpreted AS a serial stream of bits.

Similarly, an analog representation of, say, video makes
sense only if interpreted AS "analog". No matter how
"digital-ish" it might look, if you try to interpret THIS
signal as a "digital" stream, you'll get gibberish.

Floyd, you would be well advised to stop treating your
"definitions" as though they were somehow handed
down by God, and instead try to employ arguments
that are actually based in something sensible.

> The NTIA is an authority, and MilStd specifications are
> also authoritative. That is the reason I cited them.
> And the *fact* is that you have not and cannot cite any
> authoritative standards body that does not agree with
> them.

Neither of these - and for that matter, NO standards body
- is an Infallible Source of Absolute Truth, and no standard
should be looked at as a substitute for good ol' basic
theory and experimentation. This is the fundamental flaw
with any argument "from authority": wrong is wrong, no matter
who writes it down on a piece of paper. God knows I've
spent way more than enough time in my career working
with various standards organizations (in fact, I am currently
chairing one fairly well-known such group), including both
"industry" and "government" efforts, and I can tell you from
long and painful experience that simply because something
appears in a standards document does not make it correct.
With the right people paying close attention, these documents
can often turn out pretty darn good - but they should NEVER
EVER be used as a substitute for some actual thought and
understanding of the subject matter at hand.

Bob M.



Author: Arny Krueger
Date: 11:54 21-08-07


"Bob Myers" <nospamplease@address.invalid> wrote in message
news:faf16o$96g$1@usenet01.boi.hp.com...
>
> "Floyd L. Davidson" <floyd@apaflo.com> wrote in message
> news:87mywlki1d.fld@apaflo.com...
>
>>>>>>
>>>>>>If you quantize the magnitude, it is digital. That is
>>>>>>by definition.
>>>No, you haven't. You merely have a signal at a set of discrete levels.
>>
>> Sheesh! That *is*, by definition a digital signal.
>
> Really? Suppose I show you an oscilloscope screen which
> is displaying a single line of video, which happens to be
> carrying an 8-level gray-scale pattern. It clearly shows
> a set of discrete levels.

Well it shows what was once a set of discrete levels. Since it is now in the
analog domain, there will be rise time, overshoot, tilt, simple inaccuracy,
and etc. .

> Further, since this video happened
> to be created by a D/A converter with only three bits at
> the input (our video generator was built on the cheap!), those
> are the ONLY levels this signal may exhibit. Is this a
> "digital" signal?

It's an analog signal that represents something that was once quantized.

>> Bullshit son. Look it up. I've provided you with
>> quotes from an authoritative reference, twice now. You
>> don't have to take my word for it, that *is* the agreed
>> technical definition of the term.

The definitions are fine, it is the misapplication of them that sticks.



Author: Bob Myers
Date: 11:55 21-08-07


"Floyd L. Davidson" <floyd@apaflo.com> wrote in message
news:87ir79khtk.fld@apaflo.com...
>>The signal can be reconverted to an
>>analogue one later by a D to A.
>
> It's best to call that a quasi-analog signal...

Why? What does that mean, EXACTLY, that
isn't already conveyed (and conveyed more accurately)
by other, more appropriate terms? What additional
information does this "quasi-analog" nonsense bring
to the party?

Bob M.



Author: Don Bowey
Date: 11:59 21-08-07

On 8/21/07 7:19 AM, in article 87ps1hc6nf.fld@apaflo.com, "Floyd L.
Davidson" <floyd@apaflo.com> wrote:

> Don Bowey <dbowey@comcast.net> wrote:
>> On 8/20/07 10:31 PM, in article 87bqd1e9n8.fld@apaflo.com, "Floyd L.
>> Davidson" <floyd@apaflo.com> wrote:
>>
>>> There simply are no such things as "analog repeaters"
>>> on local telephone loops.
>>
>> Since when?
>
> Oh, perhaps 1950, maybe a few as late as 1960 or so...
>
> Do you know of any telco that actually uses them today?
>
>> If a loop is long enough, and there is no pair-gain facility available, it
>> gets an "E" type repeater. If that isn't an analog repeater nothing
is.
>
> Of course I suppose it is possible they are still being
> used where *you* live. But I don't know of any telco in
> all of Alaska that has used an E repeater in the last 30-40
> years. In particular, in the last 10-20 years that would
> be totally unacceptable.

I didn't leave my telco job until the end of 94. At which times they were
still in use, but there was talk of using gain within the switching
machines. It wouldn't surprise me if that is being done now, being a simple
process. In any case, there are loops that require gain to meet minimum
requirements. Also, we had a tariff that provided additional gain (for a
price) where feasible.

My concerns were not just for where "I lived." I was on the Transmission
Engineering staff, and we had 14 states with which to be concerned.



Author: Bob Myers
Date: 12:02 21-08-07


"Floyd L. Davidson" <floyd@apaflo.com> wrote in message
news:876439hg3o.fld@apaflo.com...
> You don't appear to understand that the limited set of values makes
> it digital, by definition. PERIOD.

More argument from authority. Yawn.

Bob M.



Author: Bob Myers
Date: 12:05 21-08-07


"Floyd L. Davidson" <floyd@apaflo.com> wrote in message
news:87abslhg6j.fld@apaflo.com...

>>Wouldn't this make the output of a D/A converter digital by definition?
>
> It is in fact! It's a digital PAM signal. Indeed, v.90 modems
> make use of it.

That's funny, so do the analog inputs of a PC monitor.
Ya just gotta wonder - how do they KNOW? :-)

> However, just as you can convert an analog signal to digital, you
> can indeed convert digital to analog. One method is to produce a
> digital PAM signal and run it through an analog channel.

Floyd, help me out here - is a length of coax an "analog
channel" or a "digital channel"? Mine don't seem to be
labelled....

Bob M.



Author: Bob Myers
Date: 12:11 21-08-07


"Floyd L. Davidson" <floyd@apaflo.com> wrote in message
news:87bqd1kgxl.fld@apaflo.com...
> That is, since you seem unable to grasp or investigate
> it, the web site of the National Telecommunications and
> Information Administration, a part of the US Federal
> Department of Commerce, in Boulder Colorado. Which is
> to say they are next door to and under that same
> management as the NIST (the National Institute of
> Standards and Technology), and NOAA (National Oceanic
> and Atmospheric Administration) which you may also have
> heard of...
>
> Or, to put it another way, you will not find anywhere in
> the world a valid definition that disagrees with that
> one. If yours is not in agreement, you are *wrong*.

And here, kids, we see the entire heart and soul of
Floyd's argument. "My definitions are correct, because
they come from a source that I considered to be correct.
Any that aren't in agreement with these definition are
wrong, since they aren't what I consider correct."

Could it possibly GET any more circular than that?

By the way, NIST is just up the road from me: I've
contributed to (and corrected) several standards that
NIST personnel were developing. None of those people,
by the way, showed any evidence of halos or made any
claims of infallibility.

But by Gawd, Floyd will trust them implicitly, because,
after all, they're the GUMMINT!!!!!!

> Logically you are walking the plank. Such technical
> definitions have nothing to do with logic.

At least in your case, this is obvious.

> It is an
> arbitrary decision that it means this or it means that.
> If we all agree on the arbitrary decision then we have a
> standard, and we can use it knowing that others will
> understand what it means.

Hardly arbitrary. Floyd, have you ever done ANY
standards work at all? Erroneous definitions in such
standards tend to stand until someone walks in to the
committee meetings, notices the problem, and makes
a compelling *logical* argument as to what the problem
is and how to correct it. Then it gets cleaned up in
the next revision. This does NOT mean that the older
revision was correct up until the point of change, you
know...

Bob M.



Author: Bob Myers
Date: 12:37 21-08-07


"Floyd L. Davidson" <floyd@apaflo.com> wrote in message
news:873aydkfr4.fld@apaflo.com...

>
> What you need to get straight is that it is not *my*
> definition. It is the *standard* technical definition
> recognized by virtually *every* standards organization.

Really? Then I shouldn't be able to find any standards
organizations which use a conflicting definition, right?

> That is a logical fallacy on your part. An "argument
> from authority" has great weight if it is valid. To
> be valid it must pass three tests:
>
> 1) The authority cited must actually be an authority.
> 2) All authorities must agree on the topic.
> 3) The authority cannot be misquoted, taken out of
> context, or be joking.

But ANY argument from authority always takes a back
seat to an argument from evidence and reason, since
those arguments directly undermine item (1) above.
Prior to the very late 19th century, all "authorities"
could be quoted as saying that it was impossible to
create a heavier-than-air flying machine. They were
all wrong. There is a nearly-endless supply of simlar
examples.

> Clearly citing the NTIA and MilStd definition is indeed
> a *very* strong appeal to authority, and no mere opinion
> can even come close to invalidating it.

Well, it's very strong, I suppose, if you're impressed by
something simply being an NTIA or MIL standard;
if you've actually seen such things being put together,
you tend to lose a lot of reverence for them, and
certainly would never consider them to be infallible.
Standards also have a tendency to enshrine common
but erroneous thoughts, simply because they ARE
common and no one stops to question them before
they get put into the standard, simply BECAUSE
"everyone knows this" or "everyone says it."
Arguments from authority have a nasty habit of
breeeding more "authority," through cycles of
repeated reference to incorrect notions.

> You know one way to be absolutely positive that your
> logic is not good is to do a reality check and find that
> the answer you have is wrong. It this case that is very
> easy to do, which is why *standard* definitions are
> quoted from authoritative sources. If you disagree,
> then clearly you *don't* have the logic right!

You sound exactly as one who would be arguing, in
early 1904, against investing in those crazy Wright
brothers, since it's clear RIGHT HERE IN THIS
TEXT that a flying machine is impossible! Anyone
who says or even, God forbid, demonstrates otherwise
clearly MUST be wrong. (This is the Reality Must
Always Change to Conform To Established Thought
position.)

>>However, if you like, I can also point to several
>>references which support the definition that Don and I (and
>
> So cite even one such valid reference! (You *cannot*,
> because there are none.)
>
> (And recognize that if you think you have one, then
> there is one of two things clearly true: Either 1) you
> do not understand that the other definition is not
> actually different, or 2) your reference is not a valid
> one.)

Once again: "MY references are right, because they
agree with me - YOURS simply MUST be wrong, because
they don't!" What a wonderfully circular form of
argumentation you have there!

> You are not a valid reference. You don't even come
> close to being equal to the NTIA.

Floyd, who do you think makes up the NTIA or
any other standards body? Gods who have come
down from Olympus?

Bob M.



Author: Bob Myers
Date: 12:46 21-08-07


"Floyd L. Davidson" <floyd@apaflo.com> wrote in message
news:87tzqtj09u.fld@apaflo.com...
> You can repeat that all you like, but you are wrong
> every time you do.
>
> By *definition* it is a digital signal.
>
> 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.

Funny, I don't see the word "digital" in there. Perhaps
you could point it out? No one is arguing that
"quantized" does not mean the above - but you seem
to be arguing that "quantized" is precisely equivalent
to "digital," while none of the definitions you provide
say that.

> If you do not stay with standard definitions it is
> impossible to discuss anything rationally.

Yes, you have made that quite evident.


>>> 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.

Yes, you said that again; you repeat it as though it
were a mantra that would somehow make your particular
odd misunderstandings correct. Again, please show me
the word "digital" IN THIS DEFINITION.


> No matter how dense you want to be about it, that
> government "expert" happens to be right. And you cannot
> find *any* expert that will disagree.

No one that you will accept as an "expert," at least,
since apparently "by definition," an "expert" is someone
who agrees with your position, and no one who disagrees
could possibly be an "expert." Or can you please tell
us some OTHER criteria that you would use to judge
"expertise," so that we can search for "experts" that
you would find authoritative?

> That is the
> *standard* definition, and virtually *everyone* agrees
> that it is correct.

Since there are numerous respondants in this thread
who apparently do NOT agree with your claim that
this is the "standard definition," that statement is
prima facie incorrect.

Bob M.



Author: Don Bowey
Date: 12:47 21-08-07

On 8/20/07 11:30 PM, in article 87y7g5cscy.fld@apaflo.com, "Floyd L.
Davidson" <floyd@apaflo.com> wrote:

> Don Bowey <dbowey@comcast.net> wrote:
>> On 8/20/07 10:19 PM, in article 87odh1ea6x.fld@apaflo.com, "Floyd L.
>> Davidson" <floyd@apaflo.com> wrote:
>>
>>> Don Bowey <dbowey@comcast.net> wrote:
>>>> On 8/20/07 8:14 PM, in article 874pitfujh.fld@apaflo.com, "Floyd
L.
>>>> Davidson" <floyd@apaflo.com> wrote:
>>>>>>>
>>>>>>> Of course if you then run that digital PAM signal through
virtually
>>>>>>> any analog channel, it no longer has a limited set of
values...
>>>>>>
>>>>>> Including a two foot piece of cable, or two inches with a small
cap.
>>>>>
>>>>> Nope. It would take a fair sized cap.
>>>>>
>>>>> Keep in mind that that is *exactly* what a V.90 modem puts on a
>>>>> regular twisted pair telephone cable, and it works just fine for
>>>>> a couple miles at least, sometimes even much farther.
>>>>>
>>>>> And that signal is digital, and is processed as a digital signal
>>>>> by the receiving modem.
>>>>
>>>> Digital data CSUs and T1 transmitter line signals are digital and look
>>>> similar to distorted square waves. An all 1's signal looks like a
>>>> distorted
>>>> sinewave .
>>>
>>> Your point is? (Besides the poor description? They
>>> don't look like distorted square waves. The look like
>>> only slightly distorted sine waves!)
>>
>> Have you looked at a DSX-1 envelope lately?
>
> Yes. I've got the specs right here! :-) Literally, I have
> had a graph on my web site for several years now that I drew up
> to illustrate something I wrote once upon a time
>
> http://www.apaflo.com/floyd_davidson/t1pulse.jpg

(snip)

The pulse for which you provided the link, is not DSX-1, because it will not
fit within the DSX-1 envelope.

I posted the DSX-1 template, and a representative pulse within it (MS Word),
on a.b.s.e. The pulse shown was from equipment that generated the pulse
using an analog method. As you can see from the envelope, other pulses,
specifically, those generated digitally, could be much more "square" if
given enough processing time.

Numeric points for plotting the template to a spreadsheet are available if
anyone wants them, but I will be away until next Saturday.


Author: Bob Myers
Date: 12:48 21-08-07


"Floyd L. Davidson" <floyd@apaflo.com> wrote in message
news:87ps1hizm7.fld@apaflo.com...
> (Again, that is
> the nature of arbitrary definitions, this time of what
> "encode" and "modulate" mean.)

Definitions are arbitrary only to those who don't
truly understand them.

Bob M.



Author: Bob Myers
Date: 12:50 21-08-07


"Floyd L. Davidson" <floyd@apaflo.com> wrote in message
news:87hcmtiyzf.fld@apaflo.com...
>
> Your opinion of standard definitions is worthless.
>

...because it disagree's with Floyd's opinion, and
Floyd has somehow been granted Infallibility by the
Gods of Technology.

Or does that only apply when you are wearing the
big white hat and formally speaking ex cathedra?

Bob M.



Author: Bob Myers
Date: 12:51 21-08-07


"Floyd L. Davidson" <floyd@apaflo.com> wrote in message
news:87d4xhiysv.fld@apaflo.com...

> Again, not really true. Quantized is necessarily
> digitized.

Why? And please, for a change, try to cite a REASON,
not merely a definition. After all, if you have the level
of understanding of this topic that you implicitly claim,
you should easily be able to do that.

Bob M.



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Transformers
TTL
USB

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