et 4235 Digital signal processing (2011-2012)

Introduction

This is a second course in discrete-time signal processing, with a focus on random signals. It provides a comprehensive treatment of signal processing algorithms for modeling discrete-time signals, designing optimum filters, estimation of the power spectrum of a random process, and implementing adaptive filters. These are important topics that are frequently encountered in professional engineering, and major applications such as digital communication, array processing, and multimedia (speech and audio processing, image processing).

The course provides a framework that connects signal models to filter structures, formulates filter design as an optimization problem, solved in turn via linear algebra techniques applied to structured matrices. The connections between these topics are strong, and provide insights that can also be used in other disciplines.

The course treats:

• Background in DSP, linear algebra and random processes;
• Linear prediction, parametric methods such as Pade approximation, Prony's method and ARMA models;
• The Yule-Walker equations, the Levinson algorithm, the Schur algorithm;
• Wiener and Kalman filtering;
• Spectrum estimation (nonparametric and parametric), frequency estimation (Pisarenko, MUSIC algorithm);
• Adaptive filtering (LMS, RLS).

The course complements ET 4147 Signal Processing for Communications.

Preliminary knowledge

To follow the course with profit, you will need the background knowledge provided by an elementary course in Signals and Systems, in particular you need to know what is a Laplace and a z-transform and what are their properties. This can be found, e.g., in J.G. Proakis and D.G. Manolakis (Prentice Hall, 2007), chapters 2--4 (viz. course ET 2405-D1). In addition, you need basic notions of random signals and of Linear Algebra.

Exam

The exam is written, open-book. For the exam, you can bring the book (or a print-out of the pdf) and copies of the slides. No written notes or other materials are allowed.

The next exam is Tuesday 8 November 2011, 14:00-17:00. The resit is Tuesday 24 January 2012, 09:00-12:00.

Books

Monson H. Hayes, "Statistical digital signal processing and modeling", John Wiley and Sons, New York, 1996. ISBN: 0-471 59431-8

(A pdf version of the book can probably be found on the internet.)

Instructors

dr.ir. Geert Leus (GL) and prof.dr.ir. Alle-Jan van der Veen (AJ).

Exercise sessions by dr.ir. Toon Van Waterschoot (TVW).

Schedule

The schedule for 2011 is as follows. Classes on Monday are 8:45-10:30 in EWI room B, classes on Tuesday are 8:45-10:30 in EWI room A.

 

	Date			Book	Slides
	Mon 5 Sep		No class
	Tue 6 Sep		No class
1.	Mon 12 Sep	GL	Introduction to the course. Background: z-transform, DTFT principles, matrix algebra, complex gradients	Ch.2	Ch.1 slides Ch.2 slides
2.	Tue 13 Sep	GL	Random processes, power spectra, spectral factorization, Yule-Walker equations	Ch.3	Ch.3 slides
3.	Mon 19 Sep	TVW	Examples and (hands-on) matlab exercises		slides, matlab scripts
4.	Tue 20 Sep	AJ	Signal modeling (deterministic): Pade, Prony	Ch.4.1-4.4, 4.6	Ch.4a slides
5.	Mon 26 Sep	GL	Signal modeling (stochastic): all-pole modeling, ARMA models	Ch.4.7	Ch.4b slides
6.	Tue 27 Sep	TVW	Examples and (online) matlab exercises		slides, matlab scripts
7.	Mon 3 Oct	AJ	The Levinson algorithm.	Ch.5 (skip 5.2.5, 5.2.9; 5.4)	Ch.5a slides,
8.	Tue 4 Oct	AJ	The Schur algorithm; Cholesky decomposition	Ch. 5.2.6, 5.2.7	(Schur)
9.	Mon 10 Oct	AJ	Nonparametric spectrum estimation	Ch.8.2 (skip 8.2.6)	Ch.8.2 slides
10.	Tue 11 Oct	AJ	Minimum variance spectrum estimation, Parametric spectrum estimation, Frequency estimation: Pisarenko, MUSIC	Ch.8.3, 8.5, 8.6	slides
11.	Mon 17 Oct	GL	Optimal FIR filtering: The Wiener filter, prediction, deconvolution, ...	Ch.7 (skip 7.4)	Ch.7 slides
12.	Tue 18 Oct	GL	Adaptive filters: LMS	Ch.9.1, 9.2 (skip 9.2.7, 9.2.8)	slides
13.	Mon 24 Oct	GL	Adaptive filters: RLS, the Kalman filter	Ch.9.4; Ch.7.4	slides ; Ch.7.4 slides
14.	Tue 25 Oct	AJ/GL	Applications: selection of radio astronomy, GSM speech coding, cognitive radio, ...		radio astronomy speech coding
	(skipped)		Optimal IIR filtering: noncausal and causal IIR filtering	Ch.7.3

Previous exams

Before 2009, the course had oral exams, hence there are not many examples of written exams yet.

Exam and solutions of January 2012.

Exam and solutions of November 2011.

Exam and solutions of January 2011.

Exam and solutions of November 2010.

Exam and solutions of January 2010.

Exam and solutions of November 2009.

Exercises

The book contains very many exercises. Below is a list of suggested problems. A pdf of the Solutions Manual can probably be found on the internet.

Chapter 3:	3.2; 3.3; 3.8; 3.11; 3.13; 3.25
Chapter 4:	4.1; 4.2; 4.4; 4.5; 4.12; 4.14; 4.18; 4.20; 4.23
Chapter 5:	5.5; 5.6; 5.8; 5.11; 5.14; 5.18; 5.20
Chapter 7:	7.2; 7.5; (7.7; 7.12); 7.15; 7.17; 7.18 ; 7.20
Chapter 8:	8.1; 8.2; 8.3; 8.5; 8.22 (b), (c)
Chapter 9:	9.1; 9.3; 9.7; 9.8; 9.10; 9.11; 9.16; 9.17; 9.19