Signal Processing Systems
Dept. of Microelectronics

EE4C03 Statistical digital signal processing and modeling

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, biomedical signal 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:

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

The course complements ET4386 Estimation and detection and 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 discrete-time Fourier transform (DTFT), a z-transform, and their properties. This can be found, e.g., in J.G. Proakis and D.G. Manolakis (Prentice Hall, 2007), chapters 2-4. You may consult the course EE2S11 Signals and Systems (video lectures in english available). In addition, you need basic notions of random signals, as shown in the course EE2S31 Signal Processing, and of Linear Algebra.

Exam and lab assignments

For details, see the Brightspace page of this course.

Book

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

Instructors

prof.dr.ir. Geert Leus (GL), dr. Geethu Joseph (GJ), dr. Raj Thilak Rajan (RR).

Schedule

In 2024, classes are on Wednesdays 13:45-15:30 and Fridays 8:45-10:30. The complete schedule, slides as well as the latest recordings can be found on Brightspace.

Exercises

The book contains 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