Signals and Linear System

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  • Topic: Digital signal processing, Fourier transform, Laplace transform
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  • Published : December 18, 2012
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EE2 Signals and Linear Systems

Pier Luigi Dragotti Electrical & Electronic Engineering Department Imperial College London

URL: http://www.commsp.ee.ic.ac.uk/~pld/Teaching/ E-mail: p.dragotti@imperial.ac.uk

PLD Autumn 2012
Thursday, 27 September 12

Signals and Linear Systems

Lecture 1

Aims and Objectives

“The concepts of signals and systems arise in a variety of fields and the techniques associated with these notions play a central role in many areas of science and technology such as, for example, communications, aeronautics, bio-engineering, energy, circuit design, ect. Although the physical nature of the signals and systems involved in these various disciplines are different, they all have basic features in common. The aim of the course is to provide the fundamental and universal tools for the analysis of signals, and for the analysis and design of basic systems and this independently of the domain of application.”

PLD Autumn 2012
Thursday, 27 September 12

Signals and Linear Systems

Lecture 1 Slide 2

Aims and Objectives

By the end of the course, you will have understood:

-Basic signal analysis (mostly continuous-time) -Basic system analysis (also mostly continuous systems) -Time-domain analysis (including convolution) -Laplace Transform and transfer functions -Fourier Series (revision) and Fourier Transform -Sampling Theorem and signal reconstructions -Basic z-transform

PLD Autumn 2012
Thursday, 27 September 12

Signals and Linear Systems

Lecture 1 Slide 3

About the course
•Lectures - 15-16 hours over 10 weeks •Problem Classes – 8 hours over 10 weeks •Office Hours – 2 hrs in week 7 and 8 •Assessment – 100% examination in June •Handouts in the form of pdf slides also available at http:// www.commsp.ee.ic.ac.uk/~pld/Teaching/ •Text Book: - Recommended Text Book: B.P. Lathi, “Linear Systems and Signals”, 2nd Ed., Oxford University Press - Also useful: A.V. Oppenheim & A.S. Willsky “Signals and Systems”, Prentice Hall

PLD Autumn 2012
Thursday, 27 September 12

Signals and Linear Systems

Lecture 1 Slide 4

Lecture 1 Basics about Signals (Lathi 1.1-1.5)

Pier Luigi Dragotti Electrical & Electronic Engineering Department Imperial College London

URL: http://www.commsp.ee.ic.ac.uk/~pld/Teaching/ E-mail: p.dragotti@imperial.ac.uk

PLD Autumn 2012
Thursday, 27 September 12

Signals and Linear Systems

Lecture 1

Outline

Examples of Signals Some useful Signal Operations Classification of Signals Some useful Signals

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Unit Step Function Unit Impulse Function The Exponential Function

PLD Autumn 2012
Thursday, 27 September 12

Signals and Linear Systems

Lecture 1 Slide 6

Examples of Signals (1)
Electroencephalogram (EEG) Signal

PLD Autumn 2012
Thursday, 27 September 12

Signals and Linear Systems

Lecture 1 Slide 7

Examples of Signals (2)
Stock Market Data as a discrete-time signal

PLD Autumn 2012
Thursday, 27 September 12

Signals and Linear Systems

Lecture 1 Slide 8

Examples of Signals (3)
Magnetic Resonance Image (MRI) as a 2-dimensional signal

PLD Autumn 2012
Thursday, 27 September 12

Signals and Linear Systems

Lecture 1 Slide 9

Examples of Signals (4)
Multiple View Images as a 3-dimensional signal

PLD Autumn 2012
Thursday, 27 September 12

Signals and Linear Systems

Lecture 1 Slide 10

Examples of Signals (4)
Multiple View Images as a 3-dimensional signal

PLD Autumn 2012
Thursday, 27 September 12

Signals and Linear Systems

Lecture 1 Slide 11

Examples of Signals (4)
Multiple View Images as a 3-dimensional signal

PLD Autumn 2012
Thursday, 27 September 12

Signals and Linear Systems

Lecture 1 Slide 11

Useful Signal Operations: Time Shifting

Signal may be delayed by time T:

or advanced by time T: (t – T) = x (t)

L1.2.1
PLD Autumn 2012
Thursday, 27 September 12

Signals and Linear Systems

Lecture 1 Slide 12

Useful Signal Operations: Time...
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