Course introduction (after class version)

Course introduction (after class version) - ECSE-303...

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Unformatted text preview: ECSE-303 Signals and Systems I Monday, January 04, 2010 Course outline Martin Rochette (martin.rochette@mcgill.ca) Department of Electrical and Computer Engineering McGill University, Montreal What is a signal ? A system ? What is a signal ? A system ? In the fields of communications, signal processing and engineering, a signal is any time-varying quantity. A system is an assembly of entities/objects interacting with at least one component/element. vin (t ) R 1/4/2010 C + vout (t ) 3 ECSE 303-Signals and systems Signals and systems can be represented in different dimensions like the time domain, the frequency domain resulting from a Fourier transformation, and the Laplace domain resulting from a Laplace transformation. The frequency and the Laplace domains are conveniently used for signal processing and systems analysis. 1/4/2010 4 Textbooks Main textbook: Signals and Systems, 2nd Ed. by Oppenheim, Willsky and Nawab, Prentice-Hall, 1997, ISBN 0-13814757-4 Chapters 1-3, 6, 9 Complementary textbook: Fundamentals of Signals and Systems, 1st Ed. by B. Boulet, Da Vinci Engineering Press, 2005, ISBN 1584503815. Chapters 1-9 1/4/2010 5 Course plan 1. Elementary Continuous-Time and Discrete-Time Signals and Systems (4 hours) 2. Linear Time-Invariant (LTI) Systems (6 hours) 3. Differential and Difference LTI Systems (2 hours) 4. Fourier Series Representation of Periodic, Continuous-Time Signals (5 hours) 5. The Continuous-Time Fourier Transform (5 hours) 6. The Laplace Transform (5 hours) 7. Application of the Laplace Transform to LTI Differential Systems (3 hours) 8. Time and Frequency Analysis of Bounded-Input Bounded-Output (BIBO) stable, continuous-time LTI systems (5 hours) 9. Application of Laplace Transform Techniques to Electric Circuit Analysis (4 hours) 1/4/2010 6 Classes and tutorials Classes Mon, Wed, Fri, 2:35-3:25 ENGTR 0100 Tutorials Mon, 3:35-5:25 ENGTR 2100 Thu, 4:05-5:55 ENGTR 2100 Beginning in week of Jan 11 Dehkordi, Vahid Raissi Ahmad, Raja Modirnia, Seyed-Rahi Shang, Fang 1/4/2010 7 WebCT • Material from last year will be available online • This year’s material will be posted after every class. • Use martin.rochette@mcgill.ca for fast email reply 1/4/2010 8 Evaluation 1. Five assignments worth a total of 20% 2. Mid-term 1 is worth 20% and covers chapters I-II of Oppenheim 3. Mid-term 2 is worth 30% and covers chapters I-IV of Oppenheim 3. A final examination worth 30% covering all the material seen during the semester 1/4/2010 9 Assignments They must be deposited into the Signals and systems I mailbox in the first floor of the Trottier building. This must be done before the beginning of the class at the specified return date. A late assignment will lead to a penalty of 35% per day passed the deadline. To be considered for marking, a late assignment must be handed at the ECSE department reception in McConnell. 1/4/2010 10 Review of complex numbers Oscillatory signal V ( t ) = V0 cos (ω t + ϕ ) ⎡V0 e j (ωt +ϕ ) + V0 e − j (ωt +ϕ ) ⎤ V (t ) = ⎣ ⎦ 1⎡ V ( t ) = ⎣V0 (ω ) e j (ωt +ϕ ) + cc ⎤ ⎦ 2 1 2 cc : complex conjugate Or also { V ( t ) = Re V0 (ω ) e 1/4/2010 ECSE-303A j ( ω t +ϕ ) } 13 Cartesian form vs polar form Ae jφ = A ( cos φ + j sin φ ) M + jN = M + N e 2 1/4/2010 ECSE-303A 2 jφ N φ = atan( ) M 14 Question 1 Express the following numbers in Cartesian form x+jy: 1 2 e − jπ e − jπ 2 Ans: -0.5 and sqrt(1/2)[1-j] 1/4/2010 ECSE-303A 15 Question 2 Express the following numbers in polar form Aejφ: (1 − j ) 2 1+ j 1− j Ans: 2e-jπ/2 and ejπ/2 1/4/2010 ECSE-303A 16 You may review complex numbers in “Mathematical review” pp. 71-73 of Oppenheim 1/4/2010 ECSE-303A 17 ...
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This note was uploaded on 04/07/2010 for the course ELEC ecse 303 taught by Professor Rochette during the Winter '10 term at McGill.

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