# Parcours électifDiscipline Specifics ModulesSystem identification and sparse decompositions

Lecturer(s): Julien HUILLERY, Laurent BAKO, Marc JACOB
Course ⋅ 16 hStudy ⋅ 12 h

## Objectives

The understanding of physical phenomena coupled with the advancement of observation technologies, the needs of analysis, diagnosis and control of engineering systems make more and more use of experimental modeling. This modeling work is a prerequisite for the synthesis of control laws of dynamic systems or the analysis and processing of signals. The goal of this course is to provide advanced principles and methods of signal and system modeling. "System identification" aims to associate a mathematical model with a dynamic system on the basis of noisy data measured with sensors. The "sparse decomposition of signals" aims at a compact modeling of a signal via its decomposition in a dictionary.

## Keywords

experimental modeling, system identification, parametric estimation, sparsity, dictionary of signals, time-frequency representations, compressed sensing, optimization

## Programme

Part I: Systems Identification Introduction to Signal and System Modeling: System Point of View Concept of model structure: definition and examples Estimation methods based on the minimization of the prediction error Elements for the analysis: identifiability, persistence of excitation, frequency richness of a signal Asymptotic properties of the estimators: consistency, convergence in distribution

Part II: Sparse Decomposition of Signals Introduction to Signal and System Modeling: Signal Point of View Sparse decomposition of signals: principle and algorithms Dictionaries of representation: time-frequency and wavelets Compressed sensing: a new paradigm for measurement

## Learning Outcomes

• To understand the application issues of signals and systems modeling
• To construct and identify a model of system from experimental measurements
• To know the usual bases of representation of signals
• To determine a sparse representation of a signal

## Assesment

Final mark = 50% knowledge + 50% know-how Knowledge = 100% final exam Know-how = 100% continuous assessment