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Unformatted text preview: ECSE303 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 timevarying 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 303Signals 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,
PrenticeHall, 1997, ISBN 0138147574
Chapters 13, 6, 9
Complementary textbook:
Fundamentals of Signals and
Systems, 1st Ed. by B. Boulet, Da
Vinci Engineering Press, 2005,
ISBN 1584503815.
Chapters 19
1/4/2010 5 Course plan
1. Elementary ContinuousTime and DiscreteTime Signals and
Systems (4 hours)
2. Linear TimeInvariant (LTI) Systems (6 hours)
3. Differential and Difference LTI Systems (2 hours)
4. Fourier Series Representation of Periodic, ContinuousTime
Signals (5 hours)
5. The ContinuousTime 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 BoundedInput BoundedOutput
(BIBO) stable, continuoustime 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, 2:353:25 ENGTR 0100 Tutorials
Mon, 3:355:25 ENGTR 2100
Thu, 4:055:55 ENGTR 2100
Beginning in week of Jan 11
Dehkordi, Vahid Raissi
Ahmad, Raja
Modirnia, SeyedRahi
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. Midterm 1 is worth 20% and covers
chapters III of Oppenheim
3. Midterm 2 is worth 30% and covers
chapters IIV 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 ECSE303A 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
ECSE303A 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)[1j]
1/4/2010
ECSE303A 15 Question 2
Express the following numbers in polar form
Aejφ: (1 − j ) 2 1+ j
1− j Ans: 2ejπ/2 and ejπ/2
1/4/2010
ECSE303A 16 You may review complex numbers in
“Mathematical review” pp. 7173 of
Oppenheim 1/4/2010
ECSE303A 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.
 Winter '10
 Rochette

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