Digital signal processing

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

Curriculum

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:
   • Course 1: recall on continuous time signal and system processing
   • Course 2: signal sampling and the Shannon theorem
   • Course 3: digital signal frequency analysis - towards FFT
   • Course 4: Z-transform
   • Course 5: digital filters
   • Course 6: digital filter synthesis (IIR only)
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!