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# Cours - 9P-440-SCI : Fundamentals of estimation and detection - Voies 2&4

## Descriptif

Most signal processing methods consist in extracting a piece of information from the observed signal. This information extraction step is necessary, and often difficult, because all signals arising from physical measurements are affected by noise, that is, a random signal that perturbs the useful one. The whole purpose of signal processing is to extract the useful information from a noisy signal. The objective of this course is to introduce the methods that make it possible to perform this task.

## Objectifs pédagogiques

Introduce the basis of estimation and detection theory.

30 heures en présentiel
réparties en:
• Travaux pratiques : 15
• Cours magistral : 15

Numérique sur 20

## Pour les étudiants du diplôme Diplôme d'ingénieur de l'Institut d'Optique Théorique et Appliquée

Le rattrapage est autorisé (Note de rattrapage conservée écrêtée à une note seuil de 12)
• le rattrapage est obligatoire si :
Note initiale < 6

Le coefficient de l'UE est : 20

### Programme détaillé

The main addressed topics are the following:

1. Basics of random variable and functions. These notions are assumed to be known. One will only remind the essential results without demonstrating them but insisting on their practical applications. Since signal processing deals with noisy signals that are represented by random variables or random functions, good knowledge of these concepts is essential to understand the sequel of this course.
2. Estimation theory. Estimation is the operations that consists in extracting information from a noisy signal. This information is represented by one or several numerical parameters. The objective of estimation theory is to perform this task in an "optimal" way. The main results of this theory will be applied during the laboratory works associated with this course.
3. Detection theory. In many cases, the information that is sought in the signal is of binary nature. For example, in digital communications, one needs to know if the current bit is 0 or 1. The methods used in such applications are similar to those used in estimation theory, but they present enough specificities to deserve a separated presentation.