Digital signal processing

I'm the teaching instructor for the 1st year Master degree unit in digital signal processing, supervised with my colleague Pr. RĂ©gis Marchiano.

This unit is in French, so sorry folks if you were looking for an English version of this 🤷‍♂️.

Pedagogical objectives

This teaching unit aims at training the students to digital signal processing, starting from an analog information, and by studying then all the elements of a data acquisition chain and data processing required for the signal exploitation. More precisely, this teaching unit describes all the methods and techniques allowing to understand and formalize:

  • the acquisition of an analog signal, 
  • the frequency analysis of the resulting digital signal by using discrete Fourier transform and fast Fourier transform,
  • discrete linear systems, with the introduction of finite/infinite impule response (FIR/IIR) systems,
  • digital filters synthesis.

Competences acquired by the student

At the end of this teaching unit, the students will be capable of:

  • modelizing and analyzing a digital acquisition chain of an analog signal,
  • analyzing the frequency content of a digital signal,
  • modelizing and analyzing a digital system, more particularily in terms of digital filtering,
  • synthesizing digital filters with given specifications,

in order to apply all these skills to industrial and/or research projects.


1st part (3 lecture courses et 2 tutorials) : sampling and frequency analysis

  • a short review of continuous time signal processing (Fourier series and tranform, Laplace transform, notion of continuous system, transfer function),
  • data sampling: the Shannon theorem
  • frequency analysis of descrete-time signals: discrete Fourier transform, fast Fourier transform

2nd part (1 lecture courses et 1 tutorial) : mathematical tools

  • discrete systems, stability
  • Z-transform
  • discrete systems characterization: impulse/indicial response, reccurence, frequency response, transfer function

3rd part (2 lecture courses et 2 tutorials) : applications of digital signal processing

  • digital filters: FIR, IIR systems, frequency responses
  • digital filter synthesis

Pedagogical data (in French)

  1. Courses slides:
  2. Tutorials: a bunch of exercises on the 6 courses, to be done during the 5 tutorial sessions.
  3. Practicals (python's workbooks): 
    • Practical 1: FFT in practice
    • Practical 2: digital filter synthesis

Code ressources are not online, but do not hesitate to contact me if you want them!

This article was updated on March 29, 2022