# Coursebooks 2016-2017

## Statistical signal and data processing through applications

Ridolfi Andrea

English

#### Summary

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

#### Content

1. Fundamentals of Statistical Signal Processing : Signals and systems from the deterministic and stochastic point of view.

2. Models, Methods, and algorithms :Parametric and non-parametric signal models (wide sense stationary, Gaussian, Markovian, auto regressive and white noise signals); Linear prediction and estimation (orthogonality principale and Wiener filter); Maximum likehood estimation and Bayesian a priori.

3. Statistical Signal Processing Tools for Spread Spectrum wireless transmission :Coding and decoding of information using position of pulses (annihilating filter approach); Avoiding interference with GPS(spectral mask and periodogram estimation); Spectrum estimation for classical radio transmissions (estimating frequencies of a harmonic signal).

4. Statistical Signal Processing Tools for the Analysis of Neurobiological Signals :Identification of spikes (correlation-bases methods); Characterization of multiple state neurons (Markovian models and maximum likelihood estimation); Classifying firing rates of neuron (Mixture models and the EM algorithm); Principal Component Analysis.

5. Statistical Signal Processing Tools for Echo cancellation :Adaptive filtering (least mean squares and recursive least squares).

#### Keywords

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

#### Learning Prerequisites

##### Required courses

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

##### Recommended courses

Mathematical Foundations of Signal Processing (COM-514).

##### Important concepts to start the course

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;
• 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.

#### Teaching methods

Ex cathedra with exercises, numerical examples, computer session.

#### Expected student activities

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

#### Assessment methods

• Midterm exam enabling to get a bonus grade from 0 to 1 to be added to the final grade;
• Final exam enabling to obtain a final grade between 1 and 6.

#### Resources

##### Bibliography

Background texts

• P. Prandoni, Signal Processing for Communications, EPFL Press;
• 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).

• 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, An Introduction to Probabilistic Modeling, Springer-Verlag, 1988;
• 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.

##### Notes/Handbook

• Slides handouts;
• Lecture notes;
• Collection of exercises.

### Reference week

MoTuWeThFr
8-9
9-10
10-11
11-12
12-13
13-14
14-15   INM202
15-16
16-17   INM202
17-18
18-19
19-20
20-21
21-22

Lecture
Exercise, TP
Project, other

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• Autumn semester
• Winter sessions
• Spring semester
• Summer sessions
• Lecture in French
• Lecture in English
• Lecture in German