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1 Introduction September 7, 2017
EE4C03 STATISTICAL DIGITAL SIGNAL PROCESSING (2017)
Alle-Jan van der Veen and Geert Leus
Summary
This is a second course in discrete-time signal processing:
Modeling discrete-time signals (and random processes),
Designing optimal filters and related adaptive filters (LMS, RLS, Kalman)
Estimation of the power spectrum of a random process
These are important topics that are frequently encountered in professional engi-
neering, and major applications such as digital communication, array processing,
and multimedia (speech and audio processing, image processing).
The course complements ET 4147 Signal Processing for Communications and
ET 4386 Estimation and detection.
1
1 Introduction September 7, 2017
EE4C03: STATISTICAL DIGITAL SIGNAL PROCESSING
Weight: 26 class hours + lab/ 5 EC credit points / 140 study hours
Classes: Wednesday 10:45, Friday 10:45
Week 1,2: Introduction; recapitulation of prior knowledge ( � -transform, discrete-
time Fourier transform, linear algebra); random processes
Week 3: Signal modeling, linear prediction
Week 3: Lunch meetings regarding lab assignments
Week 4: Examples and take-home Matlab exercise (1)
Week 4,5: Signal/system identification (Levinson, Schur algorithm)
Week 5: Spectrum estimation; frequency estimation (Pisarenko, MUSIC algo-
rithm)
Week 6: Optimal filtering (Wiener and Kalman filters)
Week 7,8: Adaptive filters (LMS, RLS algorithm)
Week 8: Examples and exercises (2)
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1 Introduction September 7, 2017
EE4C03: STATISTICAL DIGITAL SIGNAL PROCESSING
Book:
Monson H. Hayes, "Statistical digital signal processing and modeling", John Wiley
and Sons, New York, 1996. ISBN: 0-471 59431-8
The website indicates which sections are part of the course.
Slides
The slides and video recordings of the course can be found on
� � � � � � �� �� � � � � � �� � �� � � �� � � �� � � � � � �� � � � �� �
Exam:
Written (open book); Friday 10 November 2017, 13:30-16:30. The resit is in Jan-
uary 2018. Register at least 2 weeks in advance.
The website has examples of past exams (identical to ET4235). Questions will be
similar to those in the book.
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1 Introduction September 7, 2017
EE4C03: STATISTICAL DIGITAL SIGNAL PROCESSING
Lab assignment:
The course also contains a lab assignment with size 1 EC (=28 study hours).
In week 3, we have lunch meetings introducing the (track-dependent) assignments.
In week 4, select one of the available options. Work in groups of 2. Most assign-
ments have the following structure:
Problem analysis, find related literature
“Solve” problem (Matlab)
Write a compact report
The assignment is pass/fail (need to pass), furthermore its grade counts for 20% of
your final grade.
Deadline for handing in the report: 15 November 2017.
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1 Introduction September 7, 2017
1. Introduction
The (relative) importance of signal processing
IEEE has about 400,000 members. There are 42 Societies, and Signal Processing
is the 4rd largest (19,000 members), after Computers, Communications and Power
Electronics.
Downloads of articles from IEEE journals (2004):
1. Solid state circuits 1,500,000
2. Microwave technology 1,030,000
3. Signal processing 930,000
4. Magnetics 790,000
5. � � �
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1 Introduction September 7, 2017
1. Introduction
Signal Processing:
Techniques and Methods
– DFT, filters, filter banks (signal analysis and reconstruction)
– Statistical signal processing (parameter estimation, detection)
– Adaptive filters, neural networks
– Analytical techniques (e.g. linear algebra, optimization)
– DSP hardware, fast algorithms/architectures (implementation)
Applications
– Communication, radar, sonar, sensor arrays (multichannel signal processing),
information theory
– Speech and audio processing
– Image, video and multimedia processing
– Biomedical/bioinformatics
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1 Introduction September 7, 2017
1. Introduction
Speech and Audio Processing
The vowel /a/: � � � analog time, ��� � discrete time: 4 kHz, ��� � quantized (4 bits)
Examples: Compression (MP3), interference suppression (microphone arrays), speech
synthesis and understanding, wavefield synthesis
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1 Introduction September 7, 2017
1. Introduction
Sensor Array Processing
Examples: radio astronomy, seismic arrays, sonar arrays, synthetic aperture radar
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1 Introduction September 7, 2017
1. Introduction
Signal Processing for Communication
INFORMATIONTHEORY
SIGNALPROCESSING
ELEKTRO-MAGNETISM
channel inversion(equalization)
parameter estimationdetection
SIGNALPROCESSING
ELEKTRONICS
TELECOM
ELEKTRONICS
coder
source/channel
�� �� �
D/AA/DBPFA/D
� �� �
DSPD/A
� ���
� � �
� ���
Examples: multi-user multi-antenna (MIMO) communication, channel estimation,
baseband receiver design, VDSL, cognitive radio (compressive sensing), � � �
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1 Introduction September 7, 2017
1. Introduction
This course
We consider mostly random signals (as opposed to deterministic signals):
Signals described by statistical properties: mean, variance, correlation, power
spectrum (i.e., just 2nd order statistics)
Signals often modeled by filters (output of filtered white noise)
• Prediction filters: minimize prediction error
• Optimal filters (Wiener/Kalman): minimize mean square error
• Adaptive filters (LMS/RLS)
Estimation of signal properties via filter parameter estimation
• Spectrum analysis
• Estimation of frequencies
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1 Introduction September 7, 2017
1. Introduction
0 20 40 60 80 100−4
−3
−2
−1
0
1
2
3noisy time domain signal
time0 0.1 0.2 0.3 0.4 0.5
0
5
10
15
20
25
30
35
40
45
50corresponding frequency domain signal
normalized frequency
Two sinusoids buried in noise (e.g., a noisy music signal)
Modeling: what is a good (stochastic) model to describe the signal? How do we
estimate the model parameters?
Filtering: can we filter the noise away? Reconstruct the clean signal?
Spectrum: What is a good estimate of the spectrum? Resolution vs. noise aver-
aging: Can we detect the number of sinusoids and identify the two frequencies?
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