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

12/11/20 2
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” ^^

12/11/20 3
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

12/11/20 4
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

12/11/20 6
Conversions Between Signal Types
Sampling
Quantizing
Encoding

12/11/20 7
Analog vs Digital
Analog
Digital
Time
Continuous Discrete
SignalValue
DiscreteContinuous

12/11/20 9
Noisy Message Encoded in ASCII
Progressively
noisier
signals

12/11/20 10
Bit Recovery Using Filtering

12/11/20 11
Image Filtering to Aid Perception
Original X-Ray Image Filtered X-Ray Image
Image
Processing
System

12/11/20 13
Recorded Sound as a Signal Example
 “s” “i” “gn” “al”

12/11/20 14
“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

12/11/20 15
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

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
12/11/20 16

12/11/20 17 17
Advanced IPTV (unicast & simulcast)

Adaptive Streaming over Internet
12/11/20 18

20
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

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Lecture01

2. 12/11/20 2 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” ^^

3. 12/11/20 3 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

4. 12/11/20 4 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

5. 12/11/20 5 Signal Types

6. 12/11/20 6 Conversions Between Signal Types Sampling Quantizing Encoding

7. 12/11/20 7 Analog vs Digital Analog Digital Time Continuous Discrete SignalValue DiscreteContinuous

8. 12/11/20 8 Message Encoded in ASCII

9. 12/11/20 9 Noisy Message Encoded in ASCII Progressively noisier signals

10. 12/11/20 10 Bit Recovery Using Filtering

11. 12/11/20 11 Image Filtering to Aid Perception Original X-Ray Image Filtered X-Ray Image Image Processing System

12. 12/11/20 12 Sound Recording System

13. 12/11/20 13 Recorded Sound as a Signal Example  “s” “i” “gn” “al”

14. 12/11/20 14 “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

15. 12/11/20 15 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 12/11/20 16

17. 12/11/20 17 17 Advanced IPTV (unicast & simulcast)

18. Adaptive Streaming over Internet 12/11/20 18

19. e-Health System 12/11/20 19

20. 20 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

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