1. Introduction to Linear Systems
M. J. Roberts - All Rights Reserved.
Adapted by C.-T. Truong

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What is “Linear Systems”
 Something mathematic???
 Integral, differential, transforms, series
 A lot of problems to solve 
=> Student’s point-of-view!
 It is a practical tool to deal with Signals and Systems
 E.g., analyze signals and systems
 Computer-aided
=> Engineer’s point-of-view!!!
=> Before going into its mathematic details, today we study it
“visually” ^^

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Signals and Systems
 A signal is any physical phenomenon which
conveys information
 Systems respond to signals and produce new
signals
 Excitation signals are applied at system
inputs and response signals are produced at
system outputs

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A Communication System as a
System Example
 A communication system has an information
signal plus noise signals
 This is an example of a system that consists
of an interconnection of smaller systems

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Signal Types

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Conversions Between Signal Types
Sampling
Quantizing
Encoding

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Analog vs Digital
Analog
Digital
Time
Continuous Discrete
SignalValue
DiscreteContinuous

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Message Encoded in ASCII

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Noisy Message Encoded in ASCII
Progressively
noisier
signals

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Bit Recovery Using Filtering

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Image Filtering to Aid Perception
Original X-Ray Image Filtered X-Ray Image
Image
Processing
System

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Sound Recording System

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Recorded Sound as a Signal Example
 “s” “i” “gn” “al”

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“Transforms”
 What?
 To convert a signal into another (math) domain
 Time domain into frequency domain
 Why?
 Though it looks complex, it makes things much easier
 E.g., convolution => multiplication
 Which?
 Different transforms have different features
 Selection of a transform depends on certain application
 Our focus will be on Fourier transform

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Future Topics
 Signals and Systems in mathematic forms
 Linear Time-Invariant System
 Fourier series / Fourier transform
 Analysis of Signals and Systems using Fourier
transform
 Other transforms / representations
 Z-transform, Laplace transform, State space
 Applications

16. Our Research related to Linear Syst.
 Computer Communications Lab
 Applications over IP networks
 IPTV (e.g. Hikari-TV)
 Internet Streaming (e.g. Youtube, AppleTV)
 E-Health
 Networking
 Signal Processing
 Image/Video processing
 Multimedia Standards
 ISO/IEC MPEG, ITU-T IPTV
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Advanced IPTV (unicast & simulcast)

18. Adaptive Streaming over Internet
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19. e-Health System
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Related Standards
Content analysis
& annotation Networks
Decision
engine
Conten
t Adaptation
methods
Context-awareness
MPEG-7
MPEG-21
MPEG-21
Content-awareness
IETF protocols
(RTP, HTTP)
MPEG-2 TS
MPEG DASH
MPEG-1
MPEG-2
MPEG-4
JPEG
ITU-T
MPEG-21
ITU-T
OITF
DVB
Not standardized
Not standardized
Not standardized