Statistical signal and data processing through applications

Summary

Building up on the basic concepts of sampling, filtering and Fourier transforms, we address stochastic modeling, spectral analysis, estimation and prediction, classification, and adaptive filtering, with an application oriented approach and hands-on numerical exercises.

Content

Keywords

Statistical tools, spectral analysis, prediction, estimation, annihilating filter, mixture models, principal component analysis, stochastic processes, hidden Markov models, adaptive filtering, mathematical computing language (Matlab, Python, or similar).

Learning Prerequisites

Required courses

Stochastic Models in Communications (COM-300), Signal Processing for Communications (COM-303) / Signal Processing (COM-202).

Important concepts to start the course

Calculus, Algebra, Fourier Transform, Z Transform, Probability, Linear Systems, Filters.

Learning Outcomes

By the end of the course, the student must be able to:

• Choose appropriate statistical tools to solve signal processing problems;
• Analyze real data using a mathematical computing language;
• Interpret spectral content of signals;
• Develop appropriate models for observed signals;
• Assess / Evaluate advantages and limitations of different statistical tools for a given signal processing problem;
• Implement numerical methods for processing signals.

Transversal skills

• Use a work methodology appropriate to the task.
• Demonstrate the capacity for critical thinking
• Access and evaluate appropriate sources of information.
• Make an oral presentation.
• Write a scientific or technical report.

Teaching methods

Ex cathedra with exercises and numerical examples.

Expected student activities

Attendance at lectures, completing exercises, testing presented methods with a mathematical computing language (Matlab, Python, or similar).

Assessment methods

• 20% midterm
• 20% mini project
• 60% Final exam

Supervision

Resources

Bibliography

Background texts

• P. Prandoni, Signal Processing for Communications, EPFL Press;
• P. Bremaud, An Introduction to Probabilistic Modeling, Springer-Verlag, 1988;
• A.V. Oppenheim, R.W. Schafer, Discrete Time Signal Processing, Prentice Hall, 1989;
• B. Porat, A Course in Digital Signal Processing, John Wiley & Sons,1997;
• C.T. Chen, Digital Signal Processing, Oxford University Press;
• D. P. Bertsekas, J. N. Tsitsiklis, Introduction to Probability, Athena Scientific, 2002 (excellent book on probability).

More advanced texts

• L. Debnath and P. Mikusinski, Introduction to Hilbert Spaces with Applications, Springer-Verlag, 1988;
• A.N. Shiryaev, Probability, Springer-Verlag, New York, 2nd edition, 1996;
• S.M. Ross, Introduction to Probability Models, Third edition, 1985;
• P. Bremaud, Markov Chains, Springer-Verlag, 1999;
• P. Bremaud, Mathematical Principles of Signal Processing, Springer-Verlag, 2002;
• S.M. Ross, Stochastic Processes, John Wiley, 1983;
• B. Porat, Digital Processing of Random Signals, Prentice Hall,1994;
• P.M. Clarkson, Optimal and Adaptive Signal Processing, CRC Press, 1993;
• P. Stoïca and R. Moses, Introduction to Spectral Analysis, Prentice-Hall, 1997.

Ressources en bibliothèque

• Probability / Shiryaev
• Stochastics Processes / Ross
• Discrete Time Signal Processing / Oppenheim
• Introduction to Spectral Analysis / Stoïca
• Digital Processing of Random Signals / Porat
• Introduction to Probability / Bertsekas
• Introduction to Hilbert Spaces with Applications / Debnath
• Signal Processins for Communications / Prandoni
• An Introduction to Probabilistic Modeling / Bremaud
• A Course in Digital Signal Processing / Porat
• Optimal and Adaptive Signal Processing / Clarkson
• Digital Signal Processing / Chen
• Introduction to Probability Models / Ross

Notes/Handbook

• Slides handouts;
• Collection of exercises.

Moodle Link

• https://go.epfl.ch/COM-500