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# Coursebooks 2016-2017

## Statistical signal and data processing through applications

#### COM-500

#### Lecturer(s) :

Ridolfi Andrea#### Language:

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).

**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,
*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.

##### 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;
- Lecture notes;
- Collection of exercises.

### In the programs

- Computer Science, 2016-2017, Master semester 2
**Semester**Spring**Exam form**Written**Credits**

5**Subject examined**

Statistical signal and data processing through applications**Lecture**

2 Hour(s) per week x 14 weeks**Exercises**

2 Hour(s) per week x 14 weeks

- Communication Systems - master program, 2016-2017, Master semester 2
**Semester**Spring**Exam form**Written**Credits**

5**Subject examined**

Statistical signal and data processing through applications**Lecture**

2 Hour(s) per week x 14 weeks**Exercises**

2 Hour(s) per week x 14 weeks

- Communication Systems - master program, 2016-2017, Master semester 4
**Semester**Spring**Exam form**Written**Credits**

5**Subject examined**

Statistical signal and data processing through applications**Lecture**

2 Hour(s) per week x 14 weeks**Exercises**

2 Hour(s) per week x 14 weeks

- Communication systems minor, 2016-2017, Spring semester
**Semester**Spring**Exam form**Written**Credits**

5**Subject examined**

Statistical signal and data processing through applications**Lecture**

2 Hour(s) per week x 14 weeks**Exercises**

2 Hour(s) per week x 14 weeks

### Reference week

Mo | Tu | We | Th | Fr | |
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14-15 | INM202 | ||||

15-16 | |||||

16-17 | INM202 | ||||

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20-21 | |||||

21-22 |

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