On Going Digital
 By Frogman

 (note: Of intrest to some, this article, except for this note and some
        minor typographical changes has been written on a TI-92 in the
        text editor.  I transfered it to my 'miggy with Amiga92 and a
        parallel cable I built.  I just opened the raw variable, found
        that it contained ASCII and some other nasty control chars and
        cleaned it up into this.)

   Some time ago I purchased a microcassette recorder.  I've used it to 
record many things, including some of the DefCon 6.0 presentations (I 
should have gotten the CDC's BO release on tape!) and my thoughts on 
certain subjects.  One of them is my initial thoughts on going 
digital.  In my own words:

 And so it begins.  Heh, Frogman gets personal with an elctromagnetic 
device.  Who would have thought the day would come?  Digital 
technology and all it's wonders is no match for an analog recording, 
except for the fact that one's friggin' permenant and the other erodes 
away in the dusts of time.  Immortality, that's what it's all about.  
Overrated media-hype.  The digital immortality, still f***ing analog.  
In my 90's world, my way of thinking, everything is simplification.  
What do you do to simplify analog?  What is analog?  High, low.  The 
difference between is called analog.  When the difference no longer 
matters, 'cept that there is a difference, that is digital.  Both do 
erode in the way of time.  The only question is, how fast?  The fact 
that there is a difference is still discernable.  The fact of how 
much, that get's fuzzy.  That is the difference.  Like I said, 
immortality is f***ing overrated.  Who ever wants to be immortal has 
go something wrong in their head.  Who wants to be the same person for 
centuries,nothing changing over time?  Nobody else change over time?  
Who wants to be the same person they were six billion years ago?  
That's immortality.  Immortality won't last you about three years and 
go away.  Immortality is f***ing forever.  People want to live 
forever, they will see their friends, their family, everyone they 
either knew, hear of, cared about, thought about, considered dating, 
considered f***ing, whatever.  When they are gone you'll still be 
around six billion years from now.  Watching ---------- world.  ------
----- friggin' planet.  Like I said, overrated media-hype.

 <end of that rant>

   Well, for the time being we can ignore the immortality aspects and 
such.  They stem from a philosophy class I was taking at the time.  
What I want to focus on is the deal about analog vs. digital and their 
self refrencing traits.  As I said, digital is a subset of analog, 
where all that matters is the fact of a difference in states.  
Converting from analog to digital is not all that hard, simply 
identify a regular period to meaure from, mark high and low points, 
and thats about it.

   The conversion of digital to analog is tougher, because of the 
missing information.  To start, we need a new way to get from analog 
to digital that describes the wave.  One way to do this is to increase 
the period to identify not just highs and lows, but the rise and fall 
values in between.  But digital doesn't allow for anything but two 
values, right?  Well, we can combine those two values into patterns to 
represent bigger numbers, like we do in base 10, or decimal.  The old 
standard of digital to analog conversion in the home market was 8 bit.  
The analog signal was abstracted into a list of numbers representing 
the value of the wave at a point in a given period.  Well, by 
narrowing the time between two gaps, we can get a good approximation of 
the wave, even to the point that we end up going past the abilities of 
out 8 bit value set.  In that set we are abstracting the wave in to 
values of 0 to 255 or from -127 to 128.  The problem with this is that 
small sublties in the wave are lost if they are between two values 
available,  The way to correct this is to base the conversions on a 
larger set, such as 16 bits.  This gives us a range of 0 to 65536 or 
-32767 to 32768.  This gives a much clearer and accurate abstraction of 
the wave.  If memory serves, this is about on par with the average 
quality that the human ear identifies.

   Now, with a much clearer way of going from analog to digital, going 
in reverse is quite simple, just convince some DAC (digital to analog 
converter or circuit) to smooth out a few rough edges, and we have our 
original waves general look back.

   The problem I identified with analog and digital (before heading into 
the immortality rant) are clear, when you consider the proposals I 
have just made about conversions.  The analog wave is being 
approximated and abstaracted into a string of numbers, which can be 
stored and coppied in an exact form, since they are working in a 
bounded set, ie. the range allocated by how many bits you use.  The 
waves exact properties are lost in the conversion, but the only known 
ways to reproduce analog waves is by approximation.

   So, having found that digital is a subset of analog, and that the 
subset can be used to represent values larger than the individual 
digits in the set, we can guess the whole "digital is better" mindset 
really isn't true.  Digital is what we have to do.  That sounds alomst 
ominous, but digital is the only way to maintain exact copies of our 
analog world, only suffering a loss of data in the inital conversion.

   Now that some chunks of theory and analysis are out on the table, if 
you've read this far, you may be wondering where this is leading.  There 
are many applications for this whole topic, but in this issue I want 
to focus on audio, specifically analog to digital and vice versa, 
especially in the case of data transmission, such as modems. =]  This 
all brings me around to the coupler Axon built.

   Why don't people use couplers more often, you may wonder?  Well, 
acoustic couplers convert signal to signal, just like a hardwired modem.
But they have more conversions, and therefore more room for data loss.  
A modem converts the digital signal from a souce such as an RS-232, 
RS-442, PCMCIA, ISA, PCI, or what ever interface goes from the computer 
to the modem.  It is digital all the way.  From the modem down the phone 
line to the next modem is an analog connection, which a basic analog signal 
is sent that the other modem can pull the digital highs and lows out of.  
From there it gets sent to the other computer throught the whathaveyou 
interface digitally.  Nice, one conversion to and from analog.

   But what about the acoustic coupler?  We start at the modem this time,
and the initial digital to analog conversion.  From there it goes through
the coupler, which blasts the analog signal from a speaker.  That speaker 
approximates the analog electrical signal, and turns it into moving 
air.  The air in turn moves the microphone of the handset the
acoustic coupler is attached to.  The microphone apporoximates the air
movement into an electrical signal, and sends it merrily on its way
through the phone line,as in the strait modem to modem example.  What this
shows is two more analog to analog approximations to the data signal in
top of what is there to start with.  Those approximations can be royally
screwed if the speaker on your coupler sucks, the microphone in the handset 
sucks, or the air movement in between is interefed with, which sucks.

   And what you have learned today, I hope is that approximation is 
necessary, to a degree.  Too much approximation ruins the abstraction 
of the analog data, and ruins this whole point of using digital tools 
to reduce data loss.