# Signals and Systems

```Signals &amp; Systems
Spring 2009
UET TAXILA
1
Today's lecture
− The course
− Course contents
− Recommended books
− Course structure
− Assessments breakdown
− Before we start…
− Introduction to signals and systems
2
The Course
− Core course
− First course in Telecommunication Engineering
− A strong foundation for advanced courses
and research
− What the course is about
 Analysis and processing of information
 System design for required processing
− Mathematical &amp; theoretical
 Calculus, Linear Algebra, Differential
− Expectations
− Extensive and tough
3
Course contents
− Introduction to Signals and Systems
− Sinusoids
− Spectrum Representation
− Analysis of Periodic Waveforms
− Sampling and Aliasing
− Filters
− Convolution
− Frequency response
− Fourier Series and Transforms
− Continuous-time &amp; Discrete-time Systems
4
Books
Signal Processing First  Text book
by
James H. McClellan, Ronald W. Schafer,
Mark A. Yoder
Signals &amp; Systems (Second Edition)  Reference
book
by
Alan V. Oppenheim, Alan S. Willsky,
S. Hamid Nawab
5
Assessments
Quizzes
Assignments
Sessionals
Matlab
Final Exam
10%
2%
36%
2%
50%
6
Signal
− What is a signal
− A description of how one parameter is
related to another parameter
− Examples
 The voltage varies with time
v
t
7
Signal
 The Speech Signal
 The ECG Signal
8
Signal
 The image
9
Signal
 The image
10
Signal
− It is the variation pattern that conveys the
information, in a signal
− Signal may exist in many forms like acoustic, image,
video, electrical, heat &amp; light signal
11
System
− An entity that responds to a signal
input
system
output
− Examples
 Circuit
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System
 The camera
Image
 The Speech Recognition System
Identified
13
System
 The audio CD-player
− Block Diagram representation of a system
 Visual representation of a system
Input Signal
system
Output Signal
 Shows inter-relations of many signals involved
in the implementation of a complex system
− Look at everything around and try to identify
the signals and systems !!
14
Mathematical Representation
− A signal can be represented as a function of one or
more independent variables
− Examples
t
vt   sin t 
0  t  2
st 
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Mathematical Representation
 The image is a function of two spatial variables
sx, y 
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Continuous-time signals
− A value of signal exists at every instant of time
t
Independent variable
t
Independent variable
17
Discrete-time signals
− The value of signal exists only at equally
spaced discrete points in time
t
Independent variable
t
Independent variable
18
Discrete-time signals
− Why to discretize
− How to discretize
 How closely spaced are the samples
− Distinction between discrete &amp; digital signals
− How to denote discrete signals
− Is the image a discrete or continuous signal
 The image is generally considered to be a
continuous variable
 Sampling can however be used to obtain a
discrete, two dimensional signal (sampled
image)
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Notation
− A continuous-time signal is represented by
enclosing the independent variable (time) in
xt 
parentheses ()
t
− A discrete-time signal is represented by
enclosing the independent variable (index) in
square brackets [] xn
n
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