PDS 11/12 
Processamento Digital de Sinais  Digital Signal Processing
Instructor
Pedro M. Q. Aguiar. Office 7.24, north tower, 7th floor. Office hours:
door is always open but please use email (aguiar at isr dot ist dot utl dot pt) to schedule appointments.
TA
Cláudia Soares.
Please use email (csoares at isr
dot ist dot utl dot pt) to
schedule appointments.
Course webpage
http://www.isr.ist.utl.pt/~aguiar/pds1112.HTM (this page)
Description
The course deals with
computer processing of discretetime signals. It is tailored to Eng&Sc MSc students (but also
attended by a few PhD candidates), in particular of Electrical and Computer
Eng., Biomedical Eng., Physics, and Informatics. Students will have handson
experience, through laboratory assignments. Course topics:
& Discretetime signal
representations (transforms) and linear systems
ü
Discretetime signals and systems. Discretetime signals: sequences. Discretetime systems.
Linear timeinvariant (LTI) systems. Properties of LTI systems. Linear
constantcoefficient difference equations. Frequencydomain representation of
discretetime signals and systems. Fourier transform. Properties of the Fourier
transform.
ü
Sampling of continuoustime signals. Periodic sampling. Frequencydomain representation of
sampling. Reconstruction. Discretetime processing of continuoustime signals.
ü
The ztransform. Definition.
Properties of the region of convergence. The inverse ztransform. Properties of
the ztransform.
ü
The discrete Fourier transform (DFT). Representation of periodic sequences: the discrete
Fourier series (DFS). Properties of the DFS. The Fourier transform of periodic
signals. Sampling the Fourier transform. Fourier representation of
finiteduration sequences: the DFT. Properties of the DFT. Linear filtering
using the DFT.
ü
Fourier analysis of signals using the DFT. DFT analysis of sinusoidal signals. The timedependent
Fourier transform. Fourier analysis of nonstationary
signals.
ü
Digital filters. Block diagram
representation. Direct form I and II.
Canonic forms. Flow graph representation. Transposed forms. Digital filter design
techniques. Design of IIR filters from continuoustime filters. Design of FIR
filters using windows.
& Statistical signal
processing
ü
Random signals and parameter estimation. Estimation in signal processing. Random variables. Gaussian
distribution. Random vectors. Multivariate Gaussian. Conditional probability
and independency. Random processes. Gaussian random processes. White noise.
Time series models. The estimation problem. Assessing estimator performance.
ü
Minimum variance unbiased (MVU) estimation. Unbiased estimators. Minimum variance criterion.
Existence of MVU estimator. Finding the MVU estimator.
ü
CramerRao (CR) lower bound. Estimator accuracy considerations. CR lower bound (CRLB)
and its derivation. CRLB for signals in white Gaussian noise. CRLB for
transformed parameters. CRLB bound for parameter vectors. The Fisher
information matrix. Signal processing examples.
ü
Maximum likelihood (ML) estimators. Definition of the ML estimator (MLE). Finding the MLE.
MLE for signals in white Gaussian noise and relation to LS. Properties of the
MLE. MLE for transformed parameters. MLE for parameter vectors. Numerical
determination of MLE. Signal processing examples.
ü
Least squares (LS). The
LS approach. Linear LS. Geometrical interpretations. Weighted LS.
Orderrecursive LS.
ü
Bayesian estimation. Prior
knowledge and estimation. Choosing a prior. The Gaussian case. Bayesian linear
model. Risk functions. Minimum mean square error (MMSE) estimators. Maximum a
posteriori (MAP) estimators. Linear MMSE estimation. Geometrical
interpretations. Signal processing examples.
Lectures
Class meets twice a
week: Tuesdays, 9:3011:00, room EA3, and Thursdays, 11:0012:30, room EA5.
Clearing doubts meeting: Tuesdays, 11:0012:30 and 15:3017:00 (please send
email in advance).
Readings
& [OS] "DiscreteTime Signal Processing", A.
Oppenheim and R. Schafer, Prentice Hall, 2nd Edition, 1999, chapters 2, 3, 4,
6, 7, 8, and 10, particularly the sections pointed out in the schedule below.
& [K] "Fundamentals of Statistical Signal Processing 
Estimation Theory", S. Kay, Prentice Hall, 1993, chapters A1.2, 1, 2, 3,
7, 8, 10, 11, 12, particularly the sections pointed out in the schedule below.
Before each lecture,
students should read the corresponding book sections. Good practice is at least read them after the lecture. A
very important complement is to solve the problems at the end of the
corresponding book chapter (some of them will be solved during the lectures).
Good practice is at least solve the
problems pointed out in the schedule below. Problems not included in the
textbooks above, sample slides, and previous tests and exams are linked below.
·
[A] "Additional
Problems", 2012.
·
[R] "Random
signals", 2012.
·
Test #1 (2010/2011) Example of solution
·
Test #2 and Exam
(2010/2011) Example of
solution
Labs
Students should team
up (teams of two) at the beginning of the semester and register for one of
three available weekly lab sessions (Tuesdays, 12:3014:00 and 14:0015:30, and
Wednesdays, 14:0015:30). There will be 6 lab assignments. Each team of two
students should deliver a lab report corresponding to each assignment, at the
end of the corresponding lab session. Lab room: LSDC1
(north tower, 5th floor).
Grading
Final grade is 30% on
labs and 70% on exam (or two tests: midterm and final), with the requirement
for approval of the minimum grade of 9.5 for both components. The lab grade is
the average of the grades of the lab assignments (each assignment grade is
based on both the report and lab class participation).
Schedule (tentative)
and summary
Lecture, date 
Topic 
Readings 
Problems 
Labs 
#1, Feb 14 
Course presentation 
Registration (Feb
22) 

#2, Feb 16 
Discrete signals and systems 
[OS] ch 2
(2.12.5) 
[OS] 2.4,2.24,2.39 

#3, Feb 23 
Discrete signals and systems 
[OS] ch 2
(2.62.9) 
[OS] 2.6,2.45.2.70 

#4, Feb 28 
Sampling 
[OS] ch4 (4.14.4) 
[OS] 4.2,4.8,4.25 

#5, Mar 1 
ztransform 
[OS] ch 3
(3.1,3.2) 
[OS] 3.1,3.4 

#6, Mar 6 
ztransform 
[OS] ch 3
(3.3,3.4) 
[OS] 3.6,3.8,3.36 

#7, Mar 8 
DFT 
[OS] ch 8
(8.18.4) 
[OS] 8.2,8.4 

#8, Mar 13 
DFT 
[OS] ch 8
(8.5,8.6) 
[OS] 8.5 

#9, Mar 15 
DFT  consolidation 
[OS] ch 8
(8.5,8.6) 
[OS] 8.7,8.32,8.57 

#10, Mar 20 
DFT 
[OS] ch 8
(8.7) 
[OS] 8.27,8.36,8.39 

#11, Mar 22 
Signal analysis using DFT 
[OS] ch 10
(10.110.3,10.5) 
[OS] 10.1,10.2,10.3 

#12, Mar 27 
Digital filters 
[OS] ch 6
(6.06.4), ch
7 (7.07.2) 
[OS] 6.1,6.23,7.23,7.32 

#13, Mar 29 
Random signals and parameter
estimation 
[K] ch 1
(1.1), [R] 
[A] 1,2 

Apr 2, 20:00, Rooms E3 and E4, Test #1 (material of lectures #2 #12) Grades 

#14, Apr 3 
Random signals and parameter
estimation 
[K] ch
A1.2, ch 1 (1.2,1.3) 
[K] 1.2,1.4 

#15, Apr 12 
MVU estimation 
[K] ch 2 
[K] 2.1,2.4,2.10 

#16, Apr 17 
CR lower bound 
[K] ch 3 (3.3,3.4,3.A,3.5) 
[A] 4, [K] 3.3 

#17, Apr 19 
CR lower bound 
[K] ch 3
(3.6,3.7,3.11) 
[A] 6,7, [K] 3.9 

#18, Apr 24 
ML estimators 
[K] ch 7
(7.4,7.5) 
[A] 10,11, [K] 7.2 

#19, Apr 26 
ML estimators 
[K] ch 7
(7.6,7.8) 
[K] 7.8,7.9,7.10,7.20,7.21 

#20, May 3 
ML estimators / Least squares 
[K] ch 8
(8.3,8.4) 
[A] 17,19,20 

#21, May 8 
ML estimators / Least squares 
[K] ch 7
(7.7,7.10) 
[K] 7.13,7.24, [A] 13,15,16 

#22, May 10 
Least squares 
[K] ch 8
(8.5,8.6) 
[K] 8.1,8.5 

#23, May 15 
Bayesian estimation 
[K] ch 10
(10.310.6) 
[K] 10.11,10.12,10.14 

#24, May 17 
Bayesian estimation 
[K] ch 11
(11.311.5) 
[K] 11.1,11.4,11.16, [A] 21,23,24 

#25, May 22 
Wrapup 
all the above 
all the above 

#26, May 24 

Jun 5, 8:00, Rooms V1.08 and V1.09, Test #2 (material of lectures #13  #24) and Exam #1
Grades 

Jul 17, 15:00, Room F3, Special Exam ("Época Especial") Grades 