Linear Time Invariant Systems
Linear Functions
Function: something that takes in an input number x and
produces an output number y
x
f(x)
y
A linear function has the form y = ax
y
a
x
Note: y = ax+b is not linear (unless b=0).
Properties of Linear Funct
Effects of the Channel
Possible effects of the channel
The channel may cause the received signal y(n) to differ
from the transmitted signal x(n) in several ways.
1. Attenuation (decrease in amplitude)
2. Delay
3. Offset
4. Blurring of transitions
5. Noise
The Discrete Time Channel
Communication System
x(t)
Source
Receiver
information received
physical waveform
y(t)
physical waveform
Channel
Dest
information to send
Transmitter
Continuous Time Channel
x(n)
Source
sent bits
Bits to
Discrete-time
Waveform
x(t
Representing Bit
Waveforms
Equivalent Waveform Representations
Verbal
Encoding of the bit sequence 1,0,1,0,0,0,1 at 4 samples per bit
x(n)
1
Graph
0
List, table or
vector of
values
Sum of unit
step functions
4
8
12
16
20
24
28
n
n = [ 0 1 2 3 4 5 6 7 8 9
Continuous vs Discrete
Time Waveforms
Recap
Representing Bit Sequences as Waveforms
light intensity
A bit sequence can be encoded by changing the value of the physical
variable over time.
ON
b0=1
b1=0
b2=1
b3=0
b4=0
b5=0
b6=1
b7=0
bit time
OFF
time
Each
Now that we know about discrete time waveforms,
we can use this to start describing the bit waveforms
that we're going to use in our communication system.
So if you remember, when we introduced the idea of the bit waveform
we did that in continuous time.
Discrete Time Bit
Waveforms
Bit Sequences to Bit Waveforms
Continuous time
1
b0=1
b1=0
b2=1
b3=0
b4=0
b5=0
b6=1
b7=0
b6=1
b7=0
0
bit time
time
Discrete time
1
0
b0=1
b1=0
b2=1
b3=0
4 samples per bit
b4=0
b5=0
Bit Rate, Sampling Frequency, SPB
The bit tim
Today, what we'll be talking about is continuous
versus discrete time waveforms, and this is an important aspect
when we start talking about the way that we're
going to model the waveforms that we're sending through our communication
channel.
So let's tak
Let's talk about different ways that we can represent or describe
a bit waveform.
In this table, I show you four equivalent ways
of describing exactly the same bit waveform.
In this first one, the verbal representation,
it's very good for human to human c
So what I've said is that we can code information using bits,
and what I'd like to do in this part is talk
about two specific ways in which we can do that.
So just to review then, a bit is the basic unit of information
that we're going to use in our commu
Basic Communication System
Recap
Sent
bits
more
bits
Received
bits
Topics 1-7
Error
Correction
Waveforms
to Bits
Channel
Dest
Bits to
Waveforms
Topic 11
Source
Error
Correcting
Coding
sent
waveform
received
waveform
Noise
Topics
8-10
Basic Communication S
So now, let's take a look at the basic parts that make up the communication
system that we'll be talking about in this class.
So just to review, in this class we're going
to be talking about a general communication
chain from a single source to a single r
Lab Overview
Objective
The objective of the lab session is to help students understand the key concepts
of communication theory through building a real communication system.
Transmitter
One
Position
Transmitted
Information
Receiver
Communication System
An
Hi.
I'm Professor Bert Shi of the Department of Electronic
and Computer Engineering at the Hong Kong
University of Science and Technology.
I'm sure many of you have one of this - a smartphone.
And through this one device we can do a myriad of different t
Course Overview
How to transmit information wirelessly?
How to transmit information wirelessly?
Part 1 of 3: Point-to-point
- link from phone to
base station
Part 3 of 3: Network
- links between base stations
Part 2 of 3: Sharing a channel
- allowing mult