Analog Digital 2 (24 mins)

So here's how the deal is going to work
Official computer science terminology.

Alright, so, I've got this signal. And
for, to make it digital, what I want to do

is I want to take the signal in like
[inaudible], the, the digital equivalent

of a microphone. I'm going to take in
sound signal. And what I want to do is

reduce it basically to a series of
numbers. So then it looks the RGB data

that we applied with so that once I've got
those numbers, I could put them on a file

or send them on a network or whatever so
that process is called digitization.

Taking in analog reducing it to numbers so
I'm going to show you how that works. So

the way digitization is done. Is I, I,
I've got this signal, I've drawn sort of

big, and I want to match, so this, the
signal is analog. Let, let's say this is

really in the air and that is really
perfectly what the signal looks like and

so I want to try and capture that signal.
So, the way that this is done with

digitization is called sampling. And what
am I going to do is I'm going to run a

little system which is going to measure
what the height of the curve is very

quickly overtime And so I'm going to use
as my example the audio CD format. So the

audio CD format, digitizers, sounds and is
samples 4400 per second. So I've drawn the

samples for the coarsely on the curve here
but in reality for sounds you can actually

hear the samples will be very tightly
spaced against the curve so it's going to

come up pretty good. Alright so here's
what sampling does. Let's say this is

going to be my first sample here. The way
it's going to have a notional kind of zero

line going Down the middle here All right?
So that will be, that's going to be sort

of the base line and the way these sounds
work is I, I've always talked about them

going above the zero line but actually
have the time on there below. So, we

record it as a series of both positive and
negative numbers. So, the way that samples

go work, let's say I start recording right
here, this is going to be my first sample.

So what I'm going to do is I'm going to
look at like well, how high is t his above

the zero line and I'm going to measure it.
And I'm just going to have some scale

where let's say, way up here for really
loud noise will be the way audio CDs work

will be about 32,000 would be the max and
so, in that scale. Maybe this is kind of a

not very loud sound so I'm just going to
measure on that scale. We're just, where

is that number. So, let's say, that one
turns out to be a 1003. So I'm going to

record that number. Okay, that was a
three, that's my first sample. So then,

144,000 of a second later, the curve, now,
this is very, this example, the curve is

way moving much farther than it would for,
for real sound here just to show. So let's

say for this next sample I gauge the
height of that like that's about 1720, so

I'm going to record that number. That's
going to be my second sample. Now here's

my third sample, oh, 1939 and my next
sample, you know, 2,102 and so on. So, I

just keep sampling this thing overtime.
Now, here's can be a bunch the positive

numbers but actually down here can be a
bunch of negative numbers, that's fine.

The result is I take signal in and I just
reduce it to this like [inaudible] of

numbers. So there are, this is not a
perfect process but it does work very

well. There's two sources of problems.
Once source is let's that I was getting

this very first sample and I've said well
let's call that a 1003. What if really

that signal, it was like a little bit
higher than a 1003 but it wasn't quite so

far as a 1004. But in my system I'm stuck
picking one of those two numbers. It's

either a 1003 or 1004 in my system and so
there has maybe been a tiny error there as

I kind of put it in the nearest bucket and
Audio CD ... A little bit of detail but I

mentioned, so they use numbers between
roughly between -32,000 and +32,000. And

the reason is, that's the, that's the
range of numbers you can store in two

bytes. So, the, the byte and its 8-bits
comes back here And so it turns out, on an

audio CD, example, one sample started two
bytes And so that, that kind of give us

how many different buckets and h ow many,
you know, how many distinct numbers we can

have. Alright So that's a small
[inaudible] I should just mention. So,

audio CDs, I think by most accounts, sound
fantastic like, you know, whatever, the

"error" I was mentioning here is like,
well, it's pretty small. The other source

of error which also for audio CD's is not
a problem is like when one of the signal

had some big excursion like it went way up
and then when it came down before my next

sample came in. I've, I could miss
something and it turns out for audio CD's

just for the range of sound, a sound that
did on audio CD would be outside of human

hearing. So, for the most part of that,
that's not really a problem. All right, so

those are the two sources of Tactically
imperfection but in reality this works

really well for [sound] aright so what AI
have done is I've taken in the signal and

now what I have is just like, there's a
lot of number and you can put those them

in to file or draw them on a CD or
whatever. So I think that this leads to

the natural question of okay well, How
does playback work? Well, I don't see why

to look at those numbers to be like, yeah.
No of course you wanted -- Alright sop

here's going to work. Just give me so the
reverse process. So, this is called

digital to audio conversion and there's a
piece of hardware that a chip that

specialized to just do this. What the
digital audio conversion is going to do is

it's going to take in the numbers and I
swear, the phrase that comes in mind to

this is connect the dots. So, what this
thing wants to do is to make actually a

pattern of electricity that exactly
follows the original signal and then,

that, that electricity then we can feed to
speaker and the speaker will make it back

in the sound. So, what the, what the
digital audio converter going to do is it

going to look at the first number, a 1003.
And so, it puts a dot, and like dot far

above line. Like okay, a 1003, got it. And
then let's look at the next sample, oh,

1720, all right. S, let's kind of put a
dot that height and then it, it's going to

come, basically draw a line so like, okay,
I'll connect those first two. And then it

takes the next sample and the next one and
the next one and you can see so we get

these dots and other, I drew actually
these straight lines between those

samples. As you could see, even though the
original was in some sense curved. The

straight lines put together, it does
basically capture the shape of the sound.

And as I was saying, for audio CDs because
really the sample are so close together

the straight lines were, worked very well.
So I [inaudible] so the effect of going

through these numbers is, is able to
recreate the original signal so this goes

to your direction. Taken a bunch of
numbers, recreate the signal beautifully

and the we could put that in the speaker
and now you're hearing one of the original

prerecorded sound was. So. That's how it
works. And also I just sort of mention the

chip that does that The DTA converter. I
see that sometimes in marketing materials

for like stereos or MP3 players you know,
extra awesome DTA converter so you may

actually, just a proof I'm not making this
up you actually, you may see that like a

box or something that's nearby. Alright,
those are two directions. The sampling to

recorded it and DTA conversion to play
back so I think the natural question here

would be. Why? Why go to all this trouble
like, it wasn't my little telephone

diagram was actually simpler, right? I
just have the microphone; I hook that to

the wire to the speaker. So what is the
advantage of putting stuff and then we

would say technically taking the data and
putting it in the digital domain. It used

to be was in the sound domain and then it
was on the electricity domain but now I've

put in the digital domain of just numbers
and we're going to see there's actually a

lot of advantages to having the data just
be in the digital domain. So, I'll talk

about those. All right, so the first thing
I want to think about is errors. It's

going to be one big advantage for digital
And so I, when I described that I've

recorded this thing as numbers, 1003, 1720
or whatever. You know, all take is covered

earlier. So, really, when I say numbers
that means in a computer it could be just

the [inaudible] one. It's just that, you
know, the 1720, there is just a pattern of

zeros and ones to represent that. It, it
does take two bytes to do it but it does

work. So, an audio CD At the end of the
day, what's recorded on an audio CD is

really the pattern of zeros and ones that
makes up the series of numbers that then

would feed in to the DDA converter makes
the music. So, if you, you got a

microscope and actually on the D, it
really is really picks and valleys, Like

there's a physicality of the ones in the
zeros u, you can actually see. Well, here

in the microscope we can see. Alright, so,
I want to think about. Let's think about

the C, audio CD playback. So, the way it
works is there's a laser that's in the end

of the CD and it's trying to kind of pull
off the patterns of ones and zeros so they

can remake the sample numbers so that you
can make the music. So, what is that going

to look like? And we talked about this a
little bit before in my networking section

and I would say, well, it's going to look
kind of like this. The pattern, the laser

is looking at the CD and let's say, the
first number it sees is a one, you know,

I'll say that it's a one And then the next
thing it sees is a zero. And then there's

a couple one and then a zero. So, it's
reading the ones and zeros off the CD.

That's what it looks like in the abstract.
Is that really what it's going to look

like coming off the CD? It I hook it in a
oscilloscope off to the laser and look as

the electricity coming out, is or going to
look like that with perfect 90 degree

corners, right? Now, there's going to be
noise. Right? All the little wires and

magnets and layers and CD like probably
jiggling a little bit while it seemly.

Here's what it's going to look like. It's
going to look like that. You've got the

ones and the zeros in there just as we
have for the analog scheme. There is noise

crowding up on top of our signal that's
wha t we actually get. We get back signal

with noise. All right now, this is a, this
is a little bit of a punchline moment

here. Suppose you're the CD player and
you're like, oh, no. My signal up the CD,

[laugh]. It's got all this noise, [laugh]
But look. Do you have any problem picking

the ones and zeros out of there? No.
Right? You can have a lot noise on that

signal but the 1s and 0s you start pick
them out and alright and so the effect on

the noise on the digital signal, it's
nothing. Right, I can see 10111 so that

means I can have the CD also [inaudible]
noise on it and I playback, it doesn't

come back like pretty close. The playback,
it's perfect. Right it's just like the

signal came out ideally. So that's why or
this is what is it. That's why digital

sound is better. Right? And I'm going to
have to kind of string together all these

steps but I can take the signal I care
about, encoded the zeros and ones, so

basically it's come to [inaudible] and it
gives me a lot of noise resistance. It's

not perfect, right? If you, if you draw a
hole in the CD you know, there could be a

mess up big enough on the CD to really to
really mess things up. But it can stand a

lot. In particular, it's much better than
analog but with analog, that hiss was just

mixed right in with the sound that I
wanted to hear. So this is the big jump up

in, yeah, lots of things digital. So
there, now you know. That, that's how it

works Alright, So, noise reduction or, you
know, noise elimination really is one big

example. I'll just mention for
completeness so the way CDs work,

obviously for the 0s and 1s is its greatly
resistant to little of specs or dust

whatever that cause noise. It is also the
case that the CD actually stores multiple

in a sense, multiple copies of the music.
It's a little bit like packets on the

network. Remember we talked about packets
and resend. The CD actually has multiple

copies and the copies are marked with
checksums which I talked about in the

networking section And the CD can actually
notice if there's like a little tiny h ole

or something but one part of the music
didn't come out right, it can go to a, I'm

over some final behavior, but basically it
can go to a fall back copy And so, it can,

it can swap that one in and just keep
playing. And so that is another, a higher

level of air resistance. It's called air,
air detection and correction that CDs have

and actually DVDs do as well. So that's
how it, yeah, I can see you know, when

someone else's DVDs you could figure out
like how big of a hole can you drill,

[laugh], in a, in a DVD and still have it
play. I'll place for a big but You can

stand a little bit of just missing data
and has another copy. That cannot, you

know so also that works, that works
because it's digital that we can have this

logic in these if statements to kind of
check someone copy and having if statement

that says oh, I'm going to go get the
other copy in some places so yeah anyway

that would work. Alright Let me show you
another thing that you can do with

digital. Alright so supposed the numbers
That I had coming off of my audio CD were

these. So 12,000, 12002, 12006, 12007 this
is actually pretty realistic that the, the

sampling is so fast on the audio CD that
the signal appears to just change very

slowly for sounds that actually you know
that you can hear. Alright so that's, so

what you notice about those numbers is
that they are pretty near to each other.

Right? Like even though the base number
12,000 is big, the change from one sample

to the next is like, is not very big,
right it's under ten. In fact, it's just

sort of five. So, I'm going to propose a
scheme, a compression scheme that we could

use so that we could record the audio data
and have it take a, take a plus base. So,

here's a scheme I'm going to propose. What
if. At the start of the audio data I just

put whatever the first number is so I
record that first sample. And then after

that, I don't record any more samples.
What I do, is I just record the difference

of each sample to the next. So, in this
case, I would end up with 12,000 and I

would say plus two because the next sample
is 12,002 and I would say plus four

because the difference between the third
sample and the second was going up by

four. And so you know + one + three - five
+ one I just gotta put these all numbers.

So now you just have to convince yourself
playback can still work so as long as

playback knows about my scheme. Like it's
playback after to know the sample numbers,

So, playback would say, alright, this is
next crazy this new called delta scheme

because you're just recording the deltas.
So, playback, you know, alright so 12,000

is the first sample and the we'll just
have to do the arithmetic to recreate the

sample. So, you could just work, it could
just, you know, undo it to work out the

samples where 12,002, 12,006, 12,007 and
then using those samples, feed those into

the DGA converter to like really recreate
the sample. Okay, so, what's the advantage

of this? What's better about +two, +four,
+one, +three than 12,000 to 12,006,

12,007. I mean it's sort of gets back to
bytes. What this comes down to is those

numbers are smaller, a lot smaller and the
reality is I could record them using to

your bytes. Right? If you just think about
the amount of space on the CD, the amount

of little bits and values or whatever, if
I use the scheme and, and then I'm

[inaudible] a little bit of complexity.
But basically, I could take that sound and

I can record it may be using just half
this much space because I'm just being KG

about making the number of small in those
cases so that maybe I could just use one

byte whereas previously I had to use two
bytes for each sample And I know that's in

complexity. So, that is compression. Right
we talked out in all media, sound and

images all of these sort of things, they
are typically stored in some compressed

format and this is an example where
instead of just storing the numbers in the

total like straight ahead obvious way,
we're going to have some scheme that takes

advantage of the fact and this is true for
the images as well that the numbers don't

intended as jump around rando mly. But if
I would get one pixel in an image and it

got certain red green blue values And then
suppose you look at the picture right next

to it. Super, super close probably the red
green blue values to that second pixel

they're probably really similar, really
close to the red green blue values for the

first pixel And so maybe you could take
advantage of that, have that some delta

encoding scheme where for each pixel maybe
you didn't record what the number was.

Maybe you recorded what the difference of
that pixel was versus the pixel to its

left and so then suddenly the numbers tend
to get a lot smaller. So that's just an

example or essentially compression is
comes up light so this is my kind of

zoomed in kind of simple example of how
that might work. Now this example, this

compression is called loss less Because
I've, I've changed the data around to take

up less space but I haven't given up any
fidelity at all. If you run through my

delta scheme here, the samples, they come
back exactly right. Right, I haven't, I

haven't given up any. I just add a
complexity to take a plus space. So just

an example so PNG I talked about that as I
think a little bit as a image format so

PNG is also laws less. It takes a bunch of
pixels. It arranges them to take up last

space but the image is not corrupted
anyway. It comes back professionally. So

laws less for mats I think are a little
bit a little bit more rare. The more

common approach to compression is called
lossy compression and so lossy compression

is going to take in the data. And it's
going to cost it, it's going to rearrange

it so it takes up a lot less space. But.
It's not going to repeat on playback. It's

not going to reproduce the data exactly.
It's just going to be sort of

qualitatively very close. So, so, you
pretty much can't tell. So JPEG, That's

the [inaudible] Lord knows we've been
using. A lot of, JPEG is actually lossy

and I, I'll demonstrate this a little bit.
So, you can give it an image with the

pixels just perfect and it takes up
certain amount of space. You encode it as

JPEG and it will take up a lot less space,
maybe ten actually less space but it will

make certain shortcuts how the red and
greens and blues are recorded. So, when

you look at it, it looks very good, but if
you put it under a microscope, you could

see where it had kind of fudged a little
bit to, to save space. So I can do a, a

simple example of a lossy compression,
sticking with my audio sample example here

would be what if. I think I have this oh
yeah, what if we just threw out every

other number? We just said, well whatever
we've got 44000 of these a second. Let's

just only record 22 thousand. And then on
playback they're going to have to know

that so we're going to record this number
and this number and this number and then

on playback, what could play back do?
Playback is going to have all these

missing numbers right so it'll get this
number and get this number then playback

is going to have to sort of fudge this
middle number. What could playback do

there? You could just guess, right? You
could say well, let's guess that it's

halfway in between. We're going to just
guess 12,003. Well maybe in reality it was

12,002. Let's point your sound pretty
good. All right But so, this is a little

bit lossy. We're fudging the data a little
bit, right? So in the next one would be

12,010, 12,006 so again maybe it would
guess 12,008 even though in reality, the

sample was 12,007. Now this is a big
savings, right? So you, this have the

space, my delta scheme also more or less
have the space maybe in a little bit

better. So you compile these techniques on
where your data was originally quite

large. It, it could take up a lot less
space and when you play it back, so I'll

do my JPEG example, it really does look
very good. But if you got out of the

microscope and look, you could see with
certain little, fudge is the word I want

to use but it was probably a better term.
Little adjustments have been made.

[laugh]. So it takes up my space. Okay, so
the, the two, you know, so any media data

that you played with. So, JPEG for images,
MP3 for sound a nd all the video formats

make heavy, heavy use of lossy
compression, Especially video data. If you

just had all the samples and you just
recorded them in the raw. It's an enormous

amount of data. Fortunately the data like
I said with the pixels and like the pixel

right next to it. It is, the pixel is said
to be have a, have a lot of redundancy in

it but actually, there are these patterns
in the data that you can take advantage of

to compress it quite a lot and have it
still look very good. So, JPEG does this

for images. Mp3. Which is like, it sounds
like the definition of being in college. I

guess not anymore. That's just being alive
anyway so MP3 is very, is aggressively

lossy. It's starts with a lot of data and
it has all these tricks to throw out and

cut corners a little bit to get it down to
be pretty small. As I mention before MP3

data works out about one megabyte, about a
million bytes per minute at your corporate

high quality audio. I should mention MP3
was the result. That format is a result of

a lot of research that they had Test
subjects and they would play sounds with

different compression schemes and really
home in on for the human ear and brain

what are kind of [inaudible] and omissions
that can be heard and what are omissions

that cannot be heard and there was, and a
lot of creativity and research went it to

having MP3 worked pretty well. And that
was like I don't know what to maybe

fifteen years ago or something? So in fact
there have been any advance since then.

Where they have gotten, the formats have
gotten. Even better when they take up less

space in MP3 but also make their trade
offs in more cover release so they even

sound better than MP3. Alrighty, So, that
is, so lossy compression is just like a

part, part of life.