Signals & Systems Spring

2009 Instructor: Mian Shahzad Iqbal 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 & 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 & Discrete-time Systems 4

Books

Signal Processing First

Mark A. Yoder  Text book by James H. McClellan, Ronald W. Schafer,

Signals & Systems (Second Edition)

S. Hamid Nawab  Reference book by Alan V. Oppenheim, Alan S. Willsky, 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

 The Speech Signal

Signal

 The ECG Signal 8

 The image

Signal

9

 The image

Signal

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 & light signal 11

System

− An entity that responds to a signal

system

output input − Examples  Circuit 12

 The camera

System

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 !!

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Mathematical Representation

− A signal can be represented as a function of one or more independent variables − Examples t

v

   sin 0 

t

 2  15

s



Mathematical Representation

The image is a function of two spatial variables

s

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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 & 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) 19

Notation

− A continuous-time signal is represented by enclosing the independent variable (time) in parentheses ()

x

 

t

− A discrete-time signal is represented by square brackets []

x

 

n

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