W01_L02_P01 - The FFT for Radar

so today we're going to talk about
something very important, just to just

illustrate to you how this is going to
change your life. And it's a problem that

actually a lot of people are not aware of.
I like to bring awareness to class. And

we're going to use math to help us out. So
I'm going to draw you a nice picture, and

try to motivate. What we're doing today.
Yes those are mountains. . And over here

it comes down to the nice shoreline. This
water, okay? And in this water, this is

the Lake Washington, Lake Whale, have you
heard of it? It's an endangered species,

very hard to find. And our, our objective
is to see to try to save these things. You

know because here's what happens, you know
what the U.S. Navy does? I don't know if

you've seen this on the news about every
few months. four or fifth page. Below the

fold, where you can't find it. maybe
vessels go out from Premberton. You know

these submarines and they got these
powerful SONAR's and they blow up whales

out in the water. Right?'Cuz a SONAR's
basically going through them and it's like

if I were take an ultrasound on you and
crank it up and then put it right here

you'd... Poof. Blow something up inside.
And that's what happens to the whales.

Okay? So this is why these are endangered
in Lake Washington. I'm not sure if

there's submarines there. But there are
the Navy runs exercises there. And we'd

like to identify where they are. So here's
what we're going to do. We're going to set

this up as sort of a radar problem. I
could have drawn a plane, that's what I

draw in the notes, but. We're going to
make more relevant. here's what I want to

do. Here's the idea behind sonar and
behind radar. In some sense we're going to

get a little lecture on this, so what I'm
going to do is I'm going to have. I'm a

scientist over here on the shore. And I
got this device that I attached to a

fishing pole. In and out here and what I'm
going to do with this its both a sender

and a receiver. And what I'm going to do
is I'm going to send out stuff. And

frequency. Omega not. And i t's going
everywhere. And what I'm going to look

for, is, stuff that bounces back. Right?
So, the idea behind radar, sonar, or any

of this stuff. Is that, it's going to come
over here, hit this whale. And bounce back

in all kinds of directions, okay? And so
what's going to come back towards this

detector is some field. that'll make a
not. And so I look, send it out, send my

signal out, wait till it comes back. The
time I send out to the time I receive I

can kind of get a distance estimate, so
forth. There's a lot of signal processing

that goes on here. We're just going to
talk about very rudimentary parts of this.

But the idea is I know my signal. Sending
it out and I know what's coming back.

Okay. So this allows me maybe to do some
detection. All right, so I could do the

same thing by the way, if I did do the
airplane example. You know, there's radars

that are up here and I have this
super-fast jet and I hope you all

appreciate that awesome little stick
drawing I have of the super-fast jet in my

notes. Okay? same thing happens here. I
send out a signal at some frequency. And

it bounces back. Okay so here's the idea.
Suppose you're in the that jet, and you

don't want people to know you're there. I
don't know why you would want that. Maybe

you want to be stealthy and then maybe
call the plane something like a stealth

plane or something. So the whole point is,
you don't want this thing to receive that

signal back. So, you might make, your
airplane out of a special material that

have absorbed omega knots. Nothing bounces
back. There's nothing there, right? All

right, so things like that. Or you try to
might, try to just figure out how can I

just reduce the scatter as much as
possible. So you might design your jet so

that, that would not happen. Or,
alternatively, you can you know fly one of

these big places up here. Have you seen
these? Awacs planes. You guys know these?

You guys read these? When I was a little
boy, I loved airplane books. And I, I

didn't like that jet so much, because it
looks dumb. This one I lik ed.

That one was dumb. What this does, you
know what this does? How about if I just

blast the entire space here with
omeganaut? I mean, this guy is going to

go, oh. I, okay I know this thing here is
flying like way up here. But I can't see

this anymore, because I just drowned out
the signal. Okay? Alright. So these are

the kinds of things you think about in
radar detection. How to detect, how to not

be detected, okay. So it's a signal
processing problem and in particular, for

many of these applications if I want a
good clean detection, I'm trying to send

out a signal and bring stuff back. Well
here's, here's part of the problem,

careless people. Look at these people here
texting. They're sending out all kinds of

frequencies. Polluting the airways. If you
could see beyond your little limited view

of the electro-magnetic spectrum, you'd
see pollution everywhere. Because we have

cell phone signals, we have wi-fi, we have
satellite dish networks dropping things

down. We have a lot of noise in this
thing, right. So if you were to look at

the electro-magnetic spectrum, there's
stuff everywhere. Okay? So it makes it

very noisy, to be detecting this stuff,
okay? So part of what we want to

understand, is how do I, extract out this
noise? Right? I mean, blast it with noise.

And I got to take this noise away somehow.
But the one thing I do know is I am

looking for a very specific frequency. If
I just simply take a measurement here of,

say, what's out there, I'm going to get.
These people's little tweets.'Kay? Anybody

tweet? Don't raise your hand if you do,
because I'm [INAUDIBLE], anybody tweet?

Cuz I'm going to totally make fun of you
if you do. okay? So whenever I ask do you

tweet, just say no. Cuz otherwise I will
bring you up front maybe even make fun of

you. Okay? Lol Okay? All right, so, so
anyway, you do this and you have all this

spectrum. What do we want to do? This is
the problem we kind of, want to look at

today, all right? Does everybody feel
super motivated? Yeah, like we're going to

save the world in Lake W ales. All at the
same time. I told you this was going to

change your life, this class, right? Just
in case you didn't believe me this is only

day two, this thing you know day 30 we'll
be like saving the universe not just, not

just this Earth. Okay, so what I want to
do is now to pull up Mat lab and we're

going to start playing around with this
idea. of how to think about signals. How

to filter them. And that is one of the
standard things you do in signal

processing. So a lot of this, again, falls
under the of what we call data analysis.

You have signal, you have data. Don't, if,
if you want to think about it this way.

Remember, I'm going to give. In all these
contexts, I'm going to give you an

example. Like, this is an example that
comes either sonar or radar. But you

should never think of it as sonar radar.
You just think of it as. This is a data

analysis problem. I'm trying to extract
the real data I want out of noisy data,

okay? Your application is very different.
Never confuse it that this is really about

radars. It's never about radars or it's
never about specifics of that sort. we're

going to do a lot of image processing in
the class, this is not an image processing

class. It's really easy to illustrate the
ideas within image processing, because I

can just show you. But this is just data
and you can take these techniques and

apply them to anything, okay? So that was,
that's. I want you to have that in your

mind, as we move through the quarter.