Analog Digital 1 (22 mins)

Okay. So, today what I wanna talk about in
this section is analog versus digital.

And, I think of those words, like, you
know they sorta come up; I think they're

sorta like the word entropy, like, no
one's... It's hard to know exactly what

they mean. So I really liked today's
lecture of the section because I can show

you how those things really work, and in a
way, I think, it is something that every

day of your life from here on now, you'll
know something about how audio or all

these thing, they're just very ubiquitous,
how they work. So, let me get the, one of

the screen down here [sound]. So, I'm
going to start off. A really, really

question I want to address is a, what is
analog versus digital? And digital is how

things work in a computer so that, that's
where I want to get, so I'll start off

with a, analog. So the world is basically
analog, and what does that mean? Well. The

simplest case and the running example I'm
gonna use today is sound. So, What does

sound look like, how does sound work? You
know the sound of my voice or music or

something. So, sound is actually just
pressure waves in the air, just little

minute increases or decreases in pressure.
And inevitably it's described as traveling

up through the air like if you threw a
pebble in a pond and you sort of saw the

waves traveling out. So here is my, my
made up example of what a sound wave might

look like. It turns out many of the sounds
that are used in day to day life do have

this kind of repetitive pattern. And so
that'll, that'll come up. So oh here's a,

here's a slightly better example. So how
does a violin work? [laugh] No expenses

been spared on this artwork. Yeah
question. Oh, I'm sorry, yeah, I, I

haven't put this on the web page yet. I
will after class. But there is a. Please.

Sorry. So, a violin you know, a violin is
a musical instrument you can play it. But,

how does that work? Well the way the
violin works is that there is these

strings and they are attached to this
hollow wooden body And as the bow is drawn

across the strings. You know, they're
metal and they're under tension. And they,

they vibrate as some, at, at a repeating,
at sort of a repeating frequency. And

really the gist of it is that it; it
vibrates the wood of the violin. And so

the wood will flex out a little bit and
flex in a little bit. And so, it's sort of

like a drum where you can kind of think of
it as kind of bumping up and down. And

what that does is it creates little
pressure waves in the air. And so, those

travel out in all directions And event.
So, so, there's the signal in the violin.

I'm drawing it like this little wave. You
know what's going on? Half a millimeter up

and a half a millimeter down And then that
translates into the air where it's going

out as these little pressure waves. And
the thing about analog is that the shapes

are the same. So that on the violin if it
kind of a little down a [inaudible] you

know where, and we could have sounds with
different sharpness's and different

frequencies and a, that, that is
reproduced in the air basically. So it's

travelling out in the air and eventually
gets to your, you know, your [inaudible].

And you're listening and in your ear
there's the little eardrum, right, which

is very much like a, a drum head and the
air pushes against it and so it pushes it

in a little bit, out a little bit. So
that. I mean partly it's just my low

quality explanation of how violin sound
works. But also that's very, analog. That

you have something on the violin but
[inaudible] it would, then it translates

to some sort of other medium in the air,
but you sorta keep the shape, it travels

in the air for a while and starts to get
to your ear drum, and again in the ear

drum the shape is preserved. That is the
fundamental quality of analog processes;

you're sorta jumping from step to step but
keeping the shape. So to show you how this

works, we'll do some demos and experiments
and stuff. I'm gonna use a device called

an oscilloscope. A sure sign that your,
that nerds are near is if there's an

oscilloscope. Oscilloscopes are, are
really neat in my, you know, in my

opinion. Really neat device and it, it
very much gets this idea of analog. What

an oscilloscope does is it takes in
electricity on a pair of wires. And it

just looks at the wires, and it observes
the, the signal of voltage kinda going up

or down over time. It looks at that
signal. And it reproduces it on screen so

you can't, something which is very
abstract right I, I gesture my hands and I

say well there's the sand coming out of
the violin but it's all just hand waving.

This [inaudible] scope makes it real it
takes a signal out of the wire and it

draws it makes us visualize, I think we're
very visual creatures and so [inaudible]

kind of amazing you know very handy. This
things had been around for actually a long

time since I think the 1930's and the one
I'm going to use today When I switch this

screen here. [cough] [sound] This is
actually a, a digital oscilloscope hooked

up to my computer just cause it makes it
easy to display stuff. But it is at the

end of the day an oscilloscope. So this is
the oscilloscope out-scope, output right

now what its showing is nothing. Oh
actually I'm sorry let me switch back and

explain a little bit more how this works.
So the way the oscilloscope works is it

grabs the signal off the wire and it, it
draws it. And, the way the [inaudible]

works is that it leaves the signal up
there for maybe a tenth of a second. It

freezes it. And then it grabs another
signal off your hearing. And it puts that

one up. So, it doesn't quite track what's
on the wire in real time. There's maybe a

half second delay because that's the way
this one works. So what I've got for my

demo here is I've got this. And as will
become obvious, I'm no musician. But I, I

have this synthesizer hooked up. And so
the synthesizer is hooked up to the

speakers, so I can make sounds and kind of
play around with them, but it's also

hooked up to the [inaudible] scope. So
what it is what it's like two of the five

senses. Right? So, you can hear it, but
you can also see it. And so then we can

talk about what is a wave, what is a
signal? Alrighty [inaudible]. This is

where they complicated demo. This is where
I guess I need to appeal to the demo gods

for my complicated set up here. Let's
slide this over so I can actually reach

it. Alright y, so let's try this. So my
first claim, or I'll just start, try

making a sound here. Here we go. So this
is a, a, a [inaudible] math class, this is

a sine wave. And a sign wave, right this
sort of perfect mathematical wave has this

kind of boring, perfect bell like sound.
And so, that's the. That is the

electricity coming off the synthesizer
which is driving the speakers and it's

also making that thing. So let me try, so
what I wanna do just first off is just

talk about what are the properties of a
signal like that. I'm sometimes I'll use

the word signal, that's kind of the term
for this sort of. Data that I want to play

around with. Or I might use the word wave,
er [inaudible] but really what I'm talking

about here is signals. So, the, I'm going
to talk about some of the qualities that

signals have the first quality I'll talk
about is er, frequency. So this one, this

is kind of a low note. And so, remember
what I said, with the oscilloscope is that

it grabs a wave and then it shows it to
you again maybe a hundredth of a second

later or whatever, maybe a tenth of a
second later. So those variations in

pressure, that's actually maybe a hundred
per second, something like that, and we're

just seeing it very zoomed in, so the
width of the screen in this case I think

is a. A hundredth of a second across and
so really that's very, you know very

quickly and so most a human speeds things
like that, they tend to be in the range er

50 cycles per second up to maybe 20,000
cycles per second. Alright, so the first

quality I want to talk about, I just used
the phrase cycles per second but I never

explained it, is frequency. So if I go up.
So something where there is more and I'm

gonna, we are gonna say, this is more
cycles per seconds. How many ups and downs

do we pack into what did I say this was a
100th of a second. So when there's more in

there. [sound]. That's what you think of
as higher, when you have a note which is

higher or lower or whatever. Also this is
higher so it's kinda like, this is kinda

irritating. Okay, sorry, we'll
[inaudible]. [laugh]. All the dogs are

gonna like leave the building. So that's
what frequency is. You have just a greater

number of cycles per second. And there's
actually. I'm gonna go a... Well, let's

talk about music a little bit. So when you
go up one octave, so that's C to this one,

to this one. What you think of is kind of
a natural sounds repercussion, that's

exactly a doubling. So, if I look at the
number of cycles there and I go up an

octave, it's exactly, exactly a factor of
two. We can go up, into the dog range but

I won't. Alright, that is one quality of
signal of sound. Another [inaudible] which

is kinda obvious is Official vocabulary
word is amplitude, so. In a very analogue

sense, the height that, that is going up
and down corresponds to how the, how big

the pressure wave is. Right, how hard is
the speaker, the synthesizer pushing on

the air? So if I were to just turn it
down. It just like, goes down. So that's

what, that's what loud and soft is. Loud
is just, [inaudible], just like you know,

going out a little harder. So this leaves
me with the most kind of baffling quality

which is called tamber. And that just
refers to the shape of the wave, the

little curly cues, whatever. And the sine
wave is like there's no timbre. It's just

like the most vanilla sound possible. So,
I'm gonna switch the synthesizer. To do

like, cheesy, pan flute sound [sound] and
what you see, I don't think you'd tell,

that's the same cycles per second I was
doing before. It's actually the same

frequency, it's the same note, but it has
this flute timbre on it, all the little

curly cues and stuff on it. And what is
amazing is how the brain, that's what your

brain is getting. Those little curly cues,
and bumps and waggles and God knows what,

and your brain takes that in and what it
hears is. [sound] flute [laugh] but when

it hears this one it's like. >> Oh yeah,
sign waves. >> And, and what. >> That's

all a little basic to me... >> Well
certainly when we look at it visually just

as pixels it sort of. Yeah. I have new
found respect for the ear, and the brain.

I really the brain, obviously the brain,
The brain helps out there. Alright, So

what do we have there Frequency,
amplitude, timber. That's just like

classic, classic stuff to know about,
about these sorts of signals. Alright, so

what I want to talk about Is Another
question about how sound works and I'll go

back to my [inaudible] here, which is
there is just one air. Like in this room,

there is one body of air and all the
sounds in here, basically me talking and

you all clickety clacketing like [laugh]
[inaudible] paying attention or whatever.

It's all sharing the one air. And so the
question I want to get out is well how is

it, what happens if multiple sounds are
going on in the air at the same time.

Alright, if there's, someone's talking,
and then there's a low note, and a high

note and you can [inaudible], oh, maybe
they just sort of obliterate each other.

But, that's not true, really [inaudible]
you can hear, obviously, you can here

multiple things at the same time. And so I
wanna get a little bit is like, how does

that work? How do multiple sounds fit into
the one air? And so I'm gonna do that by

playing multiple notes at one time.
Alright, so I'm going to start off with.

Okay yes, we've seen this enough times, my
low note, the, the sign wave, so what

would happen if I played that one, and
let's say this one at the same time. And

I'll tell. I'll, I'll, I'll tell you, and
then we'll look at it. The answer is

addition. The pressure waves add on top of
each other. So, there might be one place

where one wave is kind of high and other
is also kind of high, so they add together

and they make it like even higher, and
there might be other places where one wave

is kind of high and other is kind of low,
so it is just rhythmetic. How do they add

toge ther, they make composite wave that
has both sounds in it. And, um... So it

just happens which bring out very neatly
and visually so I'll start with the low

one. And then here's the high one. [sound]
And I'll just do it at the same time.

[sound] Oh well, that doesn't come out
quite perfect there. Let me, let me try

one even a little higher. [sound] So
there's my low one. [sound] There's my

high one. If I do it at the same time or
if you can kinda see. There're sort of the

low one is in there but the just map on
top of it is this high one. Okay I like

everyone would just close your eyes for a
second. Just humor me. So now just isolate

you can here just listen to the high note.
Right You can recognize there is a height

note there or if you want you can also
here that there's the low note. Alright

you can open your eyes. So looking back
[sound] your brain is just getting the

signal. And this is the amazing part. Your
brain gets that, and it can parse out

[sound] The two sounds that are going into
to it. This again gets. I'm impressed with

the brain how it can like pull that stuff
apart. Allrighty, So I'll show you there's

a If you wanted to sort of prove, or show
for yourself that it's just addition you

can actually do it with graph paper. Where
you, you could sort of graph this note,

which is this one. And then you could
graph the note that's just one octave

higher. So this one and then this one,
Just, just 2X. And then with the graph

paper, you could sorta add up the
components. So where they're both high

make it high. And where they're both low,
make it low. And it and what you'll find

is that you get. The sort of a, this is
the classical one octave apart shape and

so only guys optional exercise that you
could, you could, you could sort of show

that I'm not just making this up.
Alrighty, So let me show you a couple

other a couple other interesting fact
about this summing together of sounds

There's sort of an eerie relationship
between mathematics and sounds, and in

particular sounds that sound good and
sounds th at don't sound good and this is

er, I guess the ancient Greeks were
captivated by this and it is kind of

magical. So, what you think of as a chord
in music, what sounds good is when the

peaks and valleys of two different sounds
that you're going to add together, they

kind of match up. So, for example, it's
kind of obvious that if I take this note.

And then I exactly double the frequency,
exactly double, then the peaks and the

valleys are gonna match up perfectly. And
so in fact, those sound pretty good

together So that's really, that's what a
chord is, is when mathematically it kind

of divides evenly so the things match up.
So we can look at the other side, well so

wait, what sounds bad? And the way to get
it to sound bad is to have one sound be,

let's say, at 100 cycles per second. So
that, you know, that's the spacing of the

piece of valleys. And have another sound
which is maybe 100, 100 one cycles per

second. Just a little bit off. And what
you'll find is then the peaks and the

valleys, they almost never coincide. The
thing is just staggered and it makes kind

of a mess. And what's neat about that. Is
that there's something in your brain. So

here like [sound] there's a chord where
they match up pretty well. Then I'm gonna

add on one. [sound]. Well like it doesn't
match. That's discard And what's amazing

is how like, it's not just bothering
everyone. It's like "I'm not happy" and

then if I just go up, I just go up a
little bit so it matches, then like "aah,

that sounds good". [laugh] So that's math,
chord and discord. Alright, so let me show

you. I want to talk about that. You know,
we [inaudible] that. So that's just a

signal, waves, things like that. So let me
bring this over to technology. And

eventually I want to get at basically
like, how a CD player works. Or the CD

player, I guess that an antique. So we'll
also talk about how mp3's work. So for

starters, I got, if I'm gonna talk about
Analog versus digital. I, I personally

want to talk about analog briefly. We
talked about this a little bit with my

viol in example. So, I'll talk about
there's the, the original telephone

system, the Alexander Grahambel model.
[cough] and I talked about analog a little

bit before so this very much follows that
pattern. The way the original phone system

work is, you know, we've got the person on
the left there and they speak, so they

make pressure waves in the air and it hits
a microphone. And. I'm not going into too

much detail what a microphone does but
basically it has little magnet arranged

next to a diaphragm that can be pushed by
the air and so as the air moves the little

diaphragm back and forth it makes a little
tiny electrical current. And so the result

is. Right, that's analog. It means when
the air cone is pushed a little bit one

way it's gonna make the electricity go a
little bit one way. When the air cone goes

the other way the electricity's gonna go a
little bit the other way. And so we end up

with this perfect. Essentially what the
microphone does is, is it's an analog

translator. It translates from wave in air
pressure over to little pattern of

electricity in the wires. And that's like,
that's the classic analog step. Alright,

so a telephone that takes the electricity
by having transformed the signal into

electricity, well now it can go on the
wires. And so it goes down the wires, now

in reality, the signal is so weak, so
there's gonna be some amplification of the

electricity, transistors, we talked about
before. So it goes down the wires, and

eventually gets to the other end where it
gets to a speaker. A speaker is just the

reverse of a microphone. So the speaker
takes in the electricity, and it has an

arrangement of magnets and cones,
whatever. So that then the electricity

pushes the cone out or in a little bit.
And so it basically recreates the pressure

wave and so then, then the sound comes
out. So this is the original design of the

telephone system, and what's funny, is
that. Not you guys obviously but you know,

your parents, people actually have phones
in their houses. The last mile of the

phone system, It st ill works this way.
Like once the standard was kinda set and

you know, everybody had all these zillions
of phones out there, it was hard just to

have something switch day, oh so
[inaudible] works differently, it's

sometimes called a network effect, but
yes, there's this tremendous inertia,

where the phone, even though the Central
Office of the phone company now works

completely differently, the end part is
still compatible like the way it's always

been. Alright, so that is your classic
analog structure which is mostly so we can

make fun of it a little bit. Alright, So
what I want to talk about is noise, hiss.

Like how is it that analog doesn't sound
so great. So, I want you to image this

signal: This is, you know, I call someone
up and I have this beautiful bell like

signing voice and I just sing this like
perfect sign wave. And I just, I just want

it to be enjoyed by the person at the
other end of the phone. So what I'm going

to do... Well, so, let, let's say I sing
that into the microphone, and it's

perfect... What comes out at the other
end? Right, it goes down the wire, it goes

through the microphone, down the wires,
and then it [inaudible] and then it comes

down the speakers in the other end. And
the answer is it doesn't come out looking

like that. What happens is really there's
a little bit of what we are going to call

noise. A little bit of error. And I'm
gonna. This isn't real; this is just me

drawing a model of air. But you can think
of the air as sort of like fuzz around

where the signal was supposed to be. And
the sources of error are many right? Well

maybe the microphone the paper cone was a
little rigid I mean it didn't quite flex

perfectly for my beautiful singing. And
then the magnet has certain electrical

properties that kinda shape the, the
pattern electricity it can make. And then

the wire has certain qualities where it's.
Most of the signals go through but it. The

shape of it kind of gets distorted by the
wire. All electrical components do distort

the shape a little bit as the signal goes
thro ugh there. And so what I get out of

the other side you can, you can think of
it as like well the signal, you can see

the signal. But there's this, and then the
term is noise. There's this noise kind of

added on top of it. And I'll tell you,
noise has a distinctive sound. You have

all heard noise. Noise is the hiss. It's
that, [sound], kinda like. So think of

analog technologies you've used, right? So
if you ever had, does anyone here have,

like, cassette tapes? Maybe you got'em
from your grandparents or something,

Anyway, when you play back cassette tapes,
mostly, the music would be there. But if

you turn it up loud enough, or if there
was a quiet station, or if there was a

quiet section, then you'd hear this, like,
[sound]. And that is exactly, it's the

noise from the tape and the magnets All
these sort of various layers that the

analog was going through. There's this
noise added on top. So er, phones actually

have this cuz phones are this, sort of,
comically old technology for that last

while, And so, that, or anyway, that's why
Skype sounds so much better than actually,

actually using a phone. Okay, so that's,
that's a problem other examples. I guess

VHS tapes. Those are analog. So in that
case, the hiss sort of shows up as,

[inaudible], pure hiss, pure noise in
video is that snow look where the pixels

are just kind of randomly flashing between
black and white and color and stuff. Okay,

so that's, whatever, analog. You can do
pretty well but it's not gonna. Oh, AM

radio. See, all, I need to think of a
technology you guys actually use that's

analog. So [inaudible] product for the
future Am radio has a significant amount

of hiss.