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Signals & Systems Spring 2009

Instructor: Mian Shahzad Iqbal UET TAXILA

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Today's lecture −The course−Course contents−Recommended books−Course structure −Assessments breakdown−Before we start…−Introduction to signals and systems

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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

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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

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BooksSignal Processing First Text

bookby

James H. McClellan, Ronald W. Schafer, Mark A. Yoder

Signals & Systems (Second Edition) Reference

bookby

Alan V. Oppenheim, Alan S. Willsky,S. Hamid Nawab

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Assessments

Quizzes 10%Assignments 2%Sessionals 36%Matlab 2%Final Exam 50%

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Signal−What is a signal−A description of how one parameter is

related to another parameter −Examples

The voltage varies with time

tv

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Signal The Speech Signal

The ECG Signal

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Signal The image

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Signal The image

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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

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System−An entity that responds to a signal

−Examples Circuit

system

input output

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System The camera

The Speech Recognition System

Identified

Image

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System The audio CD-player

−Block Diagram representation of a system Visual representation of a system

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 !!

systemInput Signal Output Signal

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Mathematical Representation− A signal can be represented as a function of one

or more independent variables− Examples

20sin tttv

t

ts

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Mathematical Representation The image is a function of two spatial variables

yxs ,

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Continuous-time signals− A value of signal exists at every instant of time

tIndependent variable

Independent variablet

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Discrete-time signals−The value of signal exists only at equally

spaced discrete points in time

Independent variable

Independent variable

t

t

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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)

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Notation−A continuous-time signal is represented by

enclosing the independent variable (time) in parentheses ()

−A discrete-time signal is represented by enclosing the independent variable (index) in square brackets []

tx

t

nx

n