Pier Luigi Dragotti Electrical & Electronic Engineering Department Imperial College London
URL: http://www.commsp.ee.ic.ac.uk/~pld/Teaching/ Email: 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, bioengineering, 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 continuoustime) Basic system analysis (also mostly continuous systems) Timedomain analysis (including convolution) Laplace Transform and transfer functions Fourier Series (revision) and Fourier Transform Sampling Theorem and signal reconstructions Basic ztransform
PLD Autumn 2012
Thursday, 27 September 12
Signals and Linear Systems
Lecture 1 Slide 3
About the course
•Lectures  1516 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 1.11.5)
Pier Luigi Dragotti Electrical & Electronic Engineering Department Imperial College London
URL: http://www.commsp.ee.ic.ac.uk/~pld/Teaching/ Email: 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

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 discretetime 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 2dimensional 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 3dimensional 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 3dimensional 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 3dimensional 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...