# Traitement du Signal

## In brief

• Number of hours : 7 lectures, 7 sessions of practical work
• Teaching language : french
• Teaching method : En présence
• Code : N5EN05A

## Objectives

Two parts in this course: 1) Introduce theoretical tools for signal processing, 2) Digital signal processing (implementation).

Objectives for the first part (theoretical tools) :

- Understand the different classes of deterministic and random signals with the definitions of the autocorrelation function and the power spectrum density

- Understand the concept of linear filtering and the Wiener Lee relationships

- Understand the principles of sampling and the Shannon theorem

- Understand the interest of non-linear transformations applied to deterministic and random signals and how to apply Price’s theorem

Objectives for the second part (digital signal processing) :

- To be able to correctly sample a signal and to generate simple digital signals.

- To be able to estimate digitally the aucorrelation function and to perform a frequency representation (Fourier transform, Power Spectral Density) of a signal.

- To be able to determine impulse responses for simple filters (Finite Impulse Response, or FIR, filters) and to synthesize them, meaning to choose their parameters to meet some requirements.

- To be able to filter a signal and to analyze the obtained result.

## Description

For the first part (theoretical tools) :

- Autocorrelation and power spectral density

- Sampling

- Linear Filtering

- Non-linear transformations and Price’s theorem

For the second part (digital signal processing) :

- Sampling and quantization.

- From theoretical to digital tools for the autocorrelation function and the Fourier transform : what are the approximations to be done ? what are their consequences ?

- Digital filters (FIR and IIR) and FIR synthesis.

## Targeted skills

For the first part (theoretical tools) :

Computation of autocorrelation functions and power spectrum densities for deterministic signals and stationary random processes

Shannon theorem

Compute the autocorrelation function and the power spectrum density at the ouput of a linear filter

Apply Price’s theorem to stationary random processes

For the second part (digital signal processing) :

- Perform a basic signal analysis using digital estimations in terms of autocorrelation function, Fourier Transform, Power Spectral Density.

- Implement simple digital filters (FIR) to analyze, generate or modify signals.

## Bibliography

- Athanasios Papoulis and S. Unnikrishna Pillai, Probability, Random Variable and Stochastic Processes, McGraw Hill Higher Education, 4th edition, 2002.

- Simon Haykin and Barry Van Veen, Signal and Systems, Wiley Alan V.  Oppenheim and Ronald W. Schafer, Digital Signal Processing, Prentice-Hall.

## Needed prerequisite

Bases on deterministic signals (energy, power, periodicity)

Random variables and vectors

### Session 1 ou session unique - Contrôle des connaissances

ModalitéNatureCoefficientRemarques
CC (contrôle continu) Oral/Ecrit50%Examen-TSI
CC (contrôle continu) Travaux Pratiques50%TP-TSI

### Session 2 - Contrôle des connaissances

ModalitéNatureCoefficientRemarques
CC (contrôle continu) Oral/Ecrit50%Examen-TSI
CC (contrôle continu) Travaux Pratiques50%TP-TSI

## Contact(s)

### THOMAS Nathalie

Phone : 2236

Email : Nathalie.Thomas @ enseeiht.fr

### TOURNERET Jean-yves

Phone : 2224

Email : Jean-Yves.Tourneret @ enseeiht.fr

THOMAS NATHALIE

## Places

• Toulouse

### Contact

The National Institute of Electrical engineering, Electronics, Computer science,Fluid mechanics & Telecommunications and Networks

2, rue Charles Camichel - BP 7122
31071 Toulouse Cedex 7, France

+33 (0)5 34 32 20 00