So lets get started. 
Any course that is concerned with the 
fundamentals of electric engineering has 
to be concerned with information and 
that's what we're going to talk about 
today to get started. 
So terms that are really going to be 
important to us are Signals and Systems. 
So the first thing I'm going to do is to 
define a signal, turns out this 
definition is very simple. 
You already know what a signal is, it 
turns out and we'll get, get through that 
very quickly. 
What's going to be more important are the 
various kinds of signals. 
Now when electrical engineers think about 
signals, the different ways in which we 
think about and categorize them. 
And then I'm finally going to link 
information to signals, and it turns out 
this link may be a bit tighter than you 
think. 
I would say some provocative things, I 
hope. 
Finally we'll talk about systems, which 
are. 
The way you operate on signals. 
And we're going to put systems together 
to create what is known as the 
fundamental model of communication. 
This model is very, very important. 
We're going to return to it throughout 
this course. 
Think of all this, not only will. 
In the process of understanding it, when 
we understand how real communication 
systems work, we will also, when we put 
the various components together, we'll be 
able to apply the things that we learned 
in this course. 
So, what's a signal? So, the definition 
of a signal is quite easy. 
It's a function. 
So, anything you've learned about 
functions in calculus, you've already 
learned about signals. 
They're exactly the same thing, there's 
no difference. 
So I can plot a signal. 
So lets say we have a signal as a 
function of t, which I, take to be time. 
And I'm going to call my signal s of t, 
and, there it is. 
That's a signal. 
That's all there is to it. 
I don't, there's nothing more complicated 
about a signal than it's just a function. 
And, before we get too far, I want to 
talk about electrical signals. 
And there's some interesting aspects of 
electric signals that have proven to be 
very important in the information age. 
As you know, electrical signals are 
voltages and currents, and 
electromagnetic waves. 
but what's very important to appreciate 
is that they carry two different 
quantities. 
First of all, they carry power You would 
plug into the socket in the wall, that's 
an electrical signal, that's carrying 
power, which powers your computer, your 
refrigerator in the home, the laser 
printer in the office, all kinds of 
things. 
Very important. 
There's also signals that convey 
information. 
For example a wireless signal. 
What you use with your cell phone to call 
one person. 
It's carrying information. 
It's carrying what you're saying. 
Now it turns out we're not going to talk 
much about power in this course. 
it's not our major concern. 
What is our concern, of course, is 
information. 
But you cannot design an information 
system without having some consideration 
about the power. 
How much power am I using, does it use, 
to send, to call somebody over my cell 
phone? How efficiently am I expending 
that power? These are going to be issues 
that are very important to the design of 
modern information systems, so we've 
gotta talk about power a little bit. 
But we won't certainly focus on it. 
it will come up. 
So, the various categories of signals 
that we think about. 
Well, there's two broad categories, 
Analog and Digital. 
A analog signal is a function of a 
continuous variable. 
So here's my good old s of t again. 
And it's a function of time and certain 
times continuous variable, and we can 
plot it, looks soemthing like that, very 
crudely The sinusoid, the sine wave is 
governed by 3 parameters versus the 
amplitude. 
Which determines how big the signal is. 
The frequency at zero, determines how 
often the peaks occur. 
If I were to whistle, [SOUND], that turns 
out to be an acoustic sine wave, at 
least, approximately. 
The frequency of my whistle, the pitch of 
my whistle. 
Corresponds with the frequency f 0. 
Phase has to do with how the sine wave 
begins at the origin. 
So here we have a very good analog signal 
as a sine wave as an explicit formula 
controlled by three different parameters. 
Now the next analog signal I want to talk 
about though, is a little different, and 
it's different in a very interesting way. 
So here's a plot of a segment of speech. 
That's me saying the vowel e, and what I 
want to point out is that there's no 
format. 
The sine wave has a formula. 
There is no explicit analytic formula for 
speech. 
However, we are going to want to operate 
on signals to understand the structure of 
signals, whether there is a formula or 
not. 
The structure of the signal with a 
formula, like I said, is covered by 3 
parameters. 
Here, we're going to have to think about, 
what, and for the speech signal, what the 
structure of it is. 
It kind of looks like a sine wave. 
But I think you can see that the 
succeedant peak values don't look the 
same. 
The peaks of these wave forms don't look 
the same. 
And wherever the peaks of every other, 
thing, tend to look the same. 
This is even more apparent at the bottom, 
where there's the big guys, very negative 
peaks, and then the ones that are 
smaller, that's negative. 
And they kind of interlace with each 
other. 
Well, that's a very tedious way to try to 
get at the structure of this signal. 
We're going to have to develop much more 
interesting ways and much more 
informative ways to under, appreciate the 
structure of a signal. 
But we will have signals that don't have 
any signal, formula. 
We'll have Signals that do have formulas. 
And we had to develop methods by which we 
can appreciate the structuring process, 
the signals. 
Whether or not there is a formula. 
It's going to be very interesting for us. 
So, the next kind of signal is a digital 
signal. 
An additional signal is a function of the 
integers. 
It's a function of the discrete valued 
independent variable, which we're just 
going to take to be the integers. 
So here's an example of a digital signal, 
and it's a sequence of numbers. 
So I intend for these numbers to be read 
from left to right and here's a plot of 
it. 
Just for fun, so this goes across like 
that and that corresponds to these 
sequence of values that we see across 
here. 
So from left to right to top to bottom 
you see the values of my Digital signal, 
So, I don't know about you, but I don't 
see much structure there. 
I don't quite see what's so interesting 
about this signal. 
I do want to point out, before we get too 
far along, about how I plotted it. 
This is what's known as a stem plot And 
every value is drawn by, with a little 
line, with a little bubble at the top to 
indicate the value. 
So this indicates this function only 
exists at the integers. 
The value at 29 1/2 doesn't exist. 
It's not even defined. 
This is a function only advantage. 
That's what a digital signal is. 
So, what is this thing? Well, it turns 
out, this is another digital signal. 
This is text and, and you may say that's 
a signal. 
Well, it turns out, if you take position 
of the character along the line. 
The value, of the signal, is a member of 
the alphabet. 
So, s of 1, is capital T. 
Well that's a digital signal, it's a 
function of the integers. 
What's even more interesting about this 
example, is that these 2 are the same 
thing. 
So I typed this text into my computer, 
inside the computer what the computer did 
was turn those symbols, the type 
characters into numbers. 
So a capital T is 84, a lower case h is a 
104 etc. 
So. 
They're exactly the same. 
So I think you'll agree that the text 
version, you can understand the 
structure, you know it's English text. 
For example, it's not something random. 
It actually makes sense. 
Whereas you look at a sequence of 
numbers, It's not quite apparent. 
And certainly if you plot it, it's even 
less apparent. 
What the structure is. 
The structure's signal may depend on how 
it's presented, kind of interesting thing 
to think about. 
So, let's talk about some other kinds of 
signals. 
another way of categorizing and I want to 
talk first about images. 
So the speech signal we already talked 
about is a function of time. 
Images are functions of space. 
So, they're a function of X and Y. 
So, I can give you an example of a black 
and white image. 
Here's a picture of a woman. 
And you say, why are you showing a 
picture of a. 
A beautiful woman. 
Well it turns out this image has been 
used in the image processing field for 
decades as a test image. 
And here's why. 
This one image contains a curve, contains 
some straight lines, contains a border, 
contains a highly complicated area. 
Something we call texture. 
Contains a smooth surface with a gradient 
of shading and it certainly contains a 
face, a very important thing. 
So, if you're trying to develop an image 
algorithm or image processing procedure. 
You want an image to test out how well it 
works. 
Well, you may discover that your 
procedure works very well on straight 
lines and curves, but doesn't work too 
well on texture. 
And so you want an image to test it with. 
Rather than having a textured image and a 
straight line image, etc., it's a bit 
more convenient to just have one image 
you can run through and see how well it 
works on that. 
That's why electrical engineers develop 
such test images so this one has been 
used for decades because it has all the 
right things in it that you need to test 
out images. 
But this is a function. 
Well I'm going to plot it. 
So here it is as a function. 
And so, here is the x and y. 
And, this is what's known as a heat map. 
This is a way of applying what's called 
2, what we call dimensional signals, so 
you can readily see what's, big and 
what's small. 
So big values are indicated in red, and 
big in the image turns out corresponds to 
white, so in terms of that corresponds to 
that little area right there. 
Blue values are small and that 
corresponds to black. 
So the gray scale values in between are 
somewhere In between. 
This is called a heat map, because the 
big values are hot, they're red. 
The small values are cold, they're black. 
So, this is just a very convenient way, 
of looking, at a plot, of such a signal. 
However, here we have the same situation 
we just had and with the digital signal. 
Looking at the image, the plot of the 
function, I have a hard time appreciating 
what it really is. 
It's a lot easier for me as a human to 
look at the image as opposed to a plot of 
it. 
Again this is how the computer sees it. 
There's absolutely no difference between 
the 2 and we're going to develop more 
insight into the presentation of 
information as we go through the course. 
Now another kind of signal that's 
interesting. 
This video, because you know video is a 
sequence of images occurring in time so 
that makes it a, function of three 
variables. 
So space and time, so the jargon is that 
an image is a 2D signal because it 
depends on two variables. 
This is a 3D signal. 
Cause it depends on three variables. 
and this is common terminology. 
So, again I one dimensional signal, for 
example was for speech, that we say 
earlier. 
'kay. 
But it can be a little bit more 
complicated than that. 
Because, if it's color video. 
Actually is 3, 3 D signals rolled up into 
one. 
Consider it as a signal, signal so our 
color video actually consists of a red, a 
green, and a blue signal each of which is 
a function of space and time. 
So this is a multivalued signal. 
So this image up here is in color, as an 
image. 
Not as a plot but as an image. 
And it's still considered a 2D image. 
So again, the dimension of a signal has 
to do with the number of variables upon 
which it depends, not how many values it 
may have. 
So this 2D image here Is red, green and 
blue components, each of which is a 2D 
signal. 
Now let's bring in information. 
Where's the information? So obviously 
something controversial here. 
That information does not exist without a 
signal. 
To represent it. 
So, lets think about this for a second. 
I've already shown you that text, is a 
signal. 
So, all books, contain signals from 1 
viewpoint. 
Certainly there's more to it than just 
that, it's the structure of that signal, 
that conveys Information. 
You may say, well information exists 
without there being a signal. 
For example, a memory that I have in my 
head. 
Well, it turns out that memory is 
mediated and brought to fore, in your 
brain, by electrical signals. 
And we'll talk about that a little bit. 
So It makes, there is no such thing 
information just existing in and of 
itself without there being a signal to 
represent it. 
So, signals and information are linked 
together in very important ways. 
Not all signals can be, contain 
information, but information doesn't 
exist without there being a signal. 
So, we talk about information being 
encoded in a signal by modifying its 
structure. 
That's why I was talking earlier about 
the structure of a signal, cause that's 
where the information is. 
It varies the structure of the signal, 
that's how you think about it. 
So. 
What we're going to do is look at this 
sine wave, so if I take this signal, 
which we've already talked about as 3 
parameters, highlighted in blue here, if 
I change the amplitude of that signal in 
such a way that the amplitude varies 
according to the speech signal that I'm 
producing now, that turns out to be 
What's called amplitude modulation, and 
that underlies AM radio. 
If I change the frequency, according to 
what I say, that gives you frequency 
modulation, or FM radio. 
There is something called phased 
modulation, but it turns out it's not 
used very often, because it's been shown 
that frequency modulation has better 
technical characteristics than phase 
modulation, but anyway, this, that's why 
I wanted to find out what the structure 
of the components of a sine wave were, so 
that I can change those. 
Components according to the information I 
want to encode in. 
So, what does the system do? What does 
the system that operates on signals to 
produce a modified signal so the system 
might do the encoding of the information, 
and it also. 
It can do the extraction. 
It can also use a thing that extracts 
information and the way we indicate, 
systems is with a what's called a block 
diagram kind of thing. 
So here is the idea. 
The input of my system is x. 
It's always in most. 
Drawings comes in from the left side of 
this block, box that denotes the system. 
And the output is y, usually comes out 
from the right. 
And so the arrow indicates the inputs, 
and the arrow coming out, indicates the 
output. 
So what this system does, is it Operates 
on the signal x, does something, who 
knows what, and produced an output y. 
So we could go down the mathematical path 
to talk about functions that are 
functions of functions So, that, that 
turns out to be overly com-, complicated. 
We won't need to go down that path. 
We'll just appre-, just learn and talk 
about systems as things that take, as an 
input, a signal, and produce another 
signal. 
So here's that Fundamental Model of 
Communication that I keep, was saying 
earlier is so important. 
It's a sequence of systems. 
I've labeled important signals. 
The source The idea is there is a source 
that has a message signal. 
And the goal of communication system is 
to get that signal over to its 
destination, which technically is called 
the sink. 
I do not know where the term sine comes 
from. 
Its just the terminologies used. 
We'll just go withe flow and use the 
terminology. 
The, the idea of three occasions to get 
something that contains information from 
one place to another. 
Now it turns out, and the easy if it 
wasn't for this funky, cloud-like thing 
in the middle, the channel. 
That's another system, but I've drawn it 
like this because this basically refers 
to phenomena we have no control over. 
And let me guarantee you at the channel 
nothing good happens to a signal in a 
channel.What comes in, is not what comes 
out at all. 
An in fact the channel can do Things the 
signals that you may not know in great 
detail. 
So trying to send the message in directly 
through this channel is a big mistake, in 
most cases, it won't get through. 
So here's what we're going to do. 
We're going to take our message signal 
in, and put it into a transmitter. 
And what the transmitter does, is, 
creates a signal, which is better suited, 
to go through the channel, then the 
message m would be. 
This is called engineering design. 
This is what electrical engineers, and 
communication engineers do. 
Try to get signals through the channel. 
So this is termed the modulated message. 
That's where the transmitted signal is. 
Transmitter is a box which takes the 
message m as input and produces x as an 
output, that goes through the channel. 
Where nothing good happens, and produces 
the received signal r, which is, trust 
me, it's a corrupted modulated message. 
it's going to do all kinds of things, and 
nothing good happens in a channel. 
The receiver's job, is to try to figure 
out What that message was that was being 
transmitted, despite the fact that it's 
been corrected, so I put this hat on top 
of the, symbol here, because it means 
that it's not exactly equal to m, so it's 
an approximation. 
So and half basically equals the message 
M plus some error. 
And one of the things you wanted to do 
when you design communication systems is 
try to fight the channel so you can 
minimize that error. 
And it's this. 
Message in hat that goes into the sink. 
Goes to the destination. 
That's what you get. 
It's known as the demodulated message. 
So, here are all the labeled pieces of 
our fundamental model. 
We are going to talk about this again and 
again. 
We're going to worry about how 
transmitters are designed. 
How receivers are designed. 
Turns out. 
You cannot design these without designing 
them together. 
and we will talk about that as we go 
through the course. 
So this is the fundamental model. 
You now know what a signal is, you know 
what a system is generically, and now 
we're ready to get serious and talk about 
things to get.