PDS 10/11 
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.
Course webpage
http://www.isr.ist.utl.pt/~aguiar/pds1011.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
Extracting information from signals and LS. Estimation in signal processing. The Least Squares (LS)
approach. Linear LS. Geometrical interpretations. Weighted LS. Orderrecursive
LS.
ü
Random signals and parameter estimation. 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
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 EA2.
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, (1st Edition, 1989), chapters 2, 3, 4, 6, 7, 8,
and 10 (11), 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, 10, 11, 12, particularly the sections pointed out in the schedule below.
Whenever possible,
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.
Labs
Students should team
up (teams of two) at the beginning of the semester and register for a weekly
lab session. There will be an introductory lab session, followed by 8 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 7 best 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 (week) 
#1, Feb 15 
Course presentation 

#2, Feb 17 
Discrete signals and systems 
[OS] ch 2
(2.12.5) 
[OS] 2.4,2.24,2.39 (2.3,2.7,2.14,2.16) 

#3, Feb 22 
Discrete signals and systems 
[OS] ch 2
(2.62.9) 
[OS] 2.6,2.45.2.70 (2.18,2.24,2.37) 

#4, Feb 24 
Sampling 
[OS] ch4 (4.14.4) (3.13.4) 
[OS] 4.2,4.8,4.25 (3.1,3.4,3.11) 

Feb 28 

Mar 1 

#5, Mar 1 
ztransform 
[OS] ch 3
(3.1,3.2) (4.1,4.2) 
[OS] 3.1,3.4 (4.1,4.6) 

#6, Mar 3 
ztransform 
[OS] ch 3
(3.3,3.4) (4.34.7) 
[OS] 3.6,3.8,3.36 (4.8,4.24,4.26) 

#7, Mar 10 
DFT 
[OS] ch 8
(8.18.4) (8.18.5) 
[OS] 8.2,8.4 (8.2,8.9) 

#8, Mar 15 
DFT 
[OS] ch 8
(8.5,8.6) (8.68.8) 
[OS] 8.5 (8.11,8.13) 

#9, Mar 17 
DFT  consolidation 
[OS] ch 8
(8.5,8.6) (8.68.8) 
[OS] 8.7,8.32,8.57 (8.17,8.18,8.36) 

#10, Mar 22 
DFT 
[OS] ch 8
(8.7) (8.9) 
[OS] 8.27,8.36,8.39 (8.34,8.39,8.40) 

#11, Mar 24 
Signal analysis using DFT 
[OS] ch 10
(10.110.3,10.5) (11.111.3,11.5) 
[OS] 10.1,10.2,10.3 (11.1,11.2,11.7) 

#12, Mar 29 
Digital filters 
[OS] ch 6
(6.06.4), ch
7 (7.07.2) (7.0,7.1,7.4) 
[OS] 6.1,6.23,7.23,7.32 (6.1,6.7,7.7,7.23) 

#13, Mar 31 
Extracting info from signals, LS 
[K] ch 1
(1.1), ch 8 (8.3,8.4) 
pLS
(1,5,6) 

#14, Apr 5 
Extracting info from signals, LS 
[K] ch 8
(8.5,8.6) 
[K] 8.1,8.5 

#15, Apr 7 
Random signals 
pPTCRB
(PT1,2) 

Apr 8 

#16, Apr 12 
Seminar  Brain signal analysis and
computational models, by Prof. Lopes da Silva, University of Amsterdam 

#17, Apr 14 
Random signals 
[K] ch A1.2,
ch 1 (1.2,1.3) 
[K] 1.2,1.4 

#18, Apr 19 
MVU estimation 
[K] ch 2 
[K] 2.1,2.4,2.10 

#19, Apr 28 
CR lower bound 
[K] ch 3
(3.3,3.4,3.A,3.5) 
pPTCRB
(CRB1), [K] 3.3 

#20, May 3 
CR lower bound 
[K] ch 3
(3.6,3.7,3.11) 
pPTCRB
(CRB4,5), [K] 3.9 

#21, May 5 
ML estimators 
[K] ch 7
(7.4,7.5) 
pML
(1,3), [K] 7.2 

#22, May 10 
ML estimators 
[K] ch 7
(7.6,7.8) 
[K] 7.8,7.9,7.10,7.20,7.21 

#23, May 12 
ML estimators 
[K] ch 7
(7.7,7.10) 
[K] 7.13,7.24, pML
(4,5,7) 

#24, May 17 
Bayesian estimation 
[K] ch 10
(10.310.6) 
[K] 10.11,10.12,10.14, pB
(3,4) 

#25, May 19 
Bayesian estimation 
[K] ch 11
(11.311.5) 
[K] 11.1,11.4,11.16, pB
(1,5,6,7) 

#26, May 24 
Wrapup 
all the above 
all the above 

#27, May 26 

Jun 3 
Exam #1 and Test #2
(material of lectures #13  #25) (solEx) (grades) 

Jun 25 