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Digital Signal Processing : Models and Applications (SIGMA)

The target is to obtain a broad vision of modern signal processing techniques and related application fields. The courses combine 1) a methodological approach to learn fundamental theoretical tools 2) an exploration of their use through a selection of relevant professional fields and 3) the learning of a « savoir-faire » by means of recurrent practical works and personal projects.

Various applications fields are investigated, including :speech processing, multimedia compression, dictionary learning, sensor networks, target tracking, source separation and the indexation of musical files.

2nd year courses

2nd year program

192 hours
Fall semester Spring semester
Period 1 Period 2 Period 3 Period 4
Time slot B1 SIGMA201 (a) Representation of signals SIGMA201 (b) Representation of signals SIGMA203 Adaptive signal processing SIGMA 205 Personal project
Time slot B2 SIGMA202 (a) Time series SIGMA202 (b) Time series SIGMA204 Bayesian methods and Kalman filtering SIGMA206 Speech and audio processing
SIGMA207 Multimedia

Details :

Fall semester

  • SIGMA 201 Representation of signals (48 hrs) (Bertrand David)
    A signal is a mapping which generally depends on time or space. It is seen as a data sequence which is meant to be analyzed, transformed, interpreted or synthetized. Representing the data as a function of time and space is generally not the right way to proceed. More relevant representations exist; think for instance of the representation of a sinusoid as a single real number in the Fourier basis. You will discover how the use of sparse signal representations can be used to analyze, de-noise or compress signals of various nature (audio, biological, etc.) This course addresses theoretical notions of (non differentiable) optimization. On the otherhand, simple notions in compressive sensing will be provided: compressive sensing theory has been at the origin of a deep revolution of the signal processing world over the last decade. Practical works will be at the heart of the course.
  • SIGMA 202 Time series (48 hrs) (François Roueff)
    Time series are used for modeling numerical sequences. They consist in a sequence of statistically dependent random variables. In this course, we focus on the concepts used for describing second order properties : autocovariance function, spectral density measure or function, linear prediction, innovation process, as well as the most popular linear models: AR, MA, and ARMA processes. The second part of the course is devoted to spectral analysis techniques. Various applications are targeted, including speech synthesis, sismology or radar.

Spring semester, period 3

  • SIGMA 203 Adaptive signal processing (24 hrs) (Slim Essid)
    This course targets adaptive methods. By this, we mean algorithms that are able to provide results in real time, while new data enter the system. The focus is put on stochastic optimization methods allowing for the solution ofa programming problem « on-line » . Archetypal examples are the Least Mean Square (LMS) and Recursive Least Square (RLS) estimators. Practical works permanently illustrate the course.
  • SIGMA 204 Bayesian methods and Kalman filtering (24 hrs) (Anne Sabourin)
    The course introduces the fundamental tools in Bayesian estimation and detection. The aim is to estimate an unknown quantity (a source signal, the location of a target) based on noisy observation and a possible a priori on the distribution of the unknown. Popular estimators (Minimum Mean Square Error, Maximum A Posteriori) are reviewed. Next, the problem of inference in hidden Markov models is posed. The celebrated Kalman filter is presented. Practical applications to autonomous navigation are proposed as practical works.

Spring semester, period 4

  • SIGMA 205 Personal project (24 hrs) (Pascal Bianchi)
    The methods learned in the courses are applied by means of a personal project. The nature of the project depends on the option chosen by the student : audio, statistical signal processing or multimedia.
  • SIGMA 206 Speech and audio processing (24 hrs) (Chloé Clavel)
    The course goes from the basic methodological tools to the applications of speech and audio processing. Speech and Audio signals are ubiquitous on the web. Their analysis is a crucial step before their indexation, which then allows social networks to organize and aggregate them. Speech signal analysis is also essential in “speech analytics” applications and human-machine interactions (google voice, siri). Finally, Audio-frequency signals have given rise to many current developments targeting our personal life (music, home studio, home cinema, etc.).
  • SIGMA 207 Introduction to multimedia processing (24 hrs) (Marco Cagnazzo)
    This course introduces the tools for effective processing, storage and transmission of multimedia signals, in particular for video. The following topics will be tackled: Lossless coding - Video and motion estimation - Hybrid vidéo coding - Streaming and IP transmission - File formats - MPEG2-TS - Scene description.

3rd year options

The SIGMA education track includes a large number of programs in the third year that can be selected by the students. The second semester is an intership. 

  • You can apply for one of several Master of Science (M2) offered by Paris-Saclay University (UPSAy) or other Universities in Paris  (most of them are in English): 

    • MVA  Mathématiques, Vision et Apprentissage (UPSAy) Mathematics and applications School
    • DATA   DataSciences  (UPSA Mathematics and applications School)
    • ATSI ,  Automatic Control and signal and image processing (UPSAy Electrical EngineeringSchool) 
    • MN , Multimedia Networking (UPSAy Electrical EngineeringSchool) located at Telecom-Paristech
    • AIC , Machine Learning, Information and Content (Computer Science School)
    • ATIAM , Acoustique, traitement du signal et informatique appliqués à la musique  (Université Pierre et Marie Curie)
    • BIM  Bio-imaging (Université Paris-Descartes)

  • Or stay in the school for one of these programs :

    • TSS Traitement statistique du signal 
    • Parole et Audio
    • MM Multimedia (in English)