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Mathematics of Random Signal

Code UE : USEEJ1

  • Cours
  • 6 crédits

Responsable(s)

Dariush GHORBANZADEH

Public, conditions d’accès et prérequis

Bachelor Mathematics level

Objectifs pédagogiques

The primary objective of this course is to provide mathematical background and sufficient experience so that the student can understand sentences in the language of probability theory, as well as solve probabilistic problems in Telecommunications Engineering programs and applied science. Broad range of topics, such as random vectors, random sequences, convergence of random sequences, random processes and correlation are introduced.

Compétences visées

Upon completion of the subject, students will be able to understand:
  • The concepts surrounding probability and random processes such as the sample space, conditional probability, total probability, Bayes theorem, and independence.
  • One Random Variable and One Function of One Random Variable.
  • One function of two random variables, two functions of two random variables, moments, covariance and correlation, joint characteristic functions, conditional distributions and moments and minimum mean-square-error (MSE) estimation.
  • Sequences of Random Variables. Distributions and densities, independence, M functions of M random variables, covariance and correlation matrices and joint characteristic functions.
  • Limit Theorems. The Law of Large Numbers. The Central Limit Theorem
  • Random process. Stationarity : strict sense and wide sense. Ergodicity. Poisson Processes. Markov Processes.
  • Students will be able to understand the applications and practical issues such as the numerical simulation of random phenomena using  python.

Mots-clés

Contenu

1. Foundations of Probability Theory
2. Random Variables
3. Distribution and Density Functions
4. Functions and Sequences of Random Variables
5. Expectation. Conditional Expected
6. Characteristic Functions and Moment Generating Functions
7. Ordered Statistics
8. Multivariate normal distribution
9. Elements of Random  Processes
10. Limit Theorems
11. Simulation (using numerical Python)

Modalité d'évaluation

Validation will be done through final exam and projects

Bibliographie

  • Ghorbanzadeh.D : Probabilités. Exercices corrigés. ISBN : 9782710807476.
  • Ghorbanzadeh.D. , Marry.P. , Point.N., Vial.D : Eléments de Mathématiques du Signal. Exercices résolus. 3° édition. EAN13 : 9782100519361
  • Venkatarama Krishnan, Kavitha Chandra : Probability and Random Processes 2nd Edition. ISBN: 978-0-471-99828-0.
  • Scott Miller , Donald Childers : Probability and Random Processes, Second Edition: With Applications to Signal Processing and Communications 2nd Edition. ISBN-13: 978-0123869814 .

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Contact

EPN03 - Easy
292 rue Saint-Martin 11-B-2
75141 Paris Cedex 03
Tel :01 40 27 24 81
Virginie Dos Santos Rance

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