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Digital signal processing

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  • Lecturer: Olivier BETHOUX (olivier.bethoux@sorbonne-universite.fr)
  • Course code: UM4RBT14
  • Student workload: 12h of lectures, 10h of tutorials, 6h of labs
  • Credits: 3 ECTS
  • Specialization tracks:
  • Semester offered: S1 S2 S3 S4
  • Language of instruction: French English
  • Targeted audience: Eng. Sc. department Other :
  • Localization : PMC Campus Other :

Course Overview

This course aims to train students in the analysis of digital data and their processing. The teaching focuses on discrete frequency analysis on the one hand, and on the synthesis of digital filters on the other.

Mots-clés : Signal processing, sampling, discrete Fourier and FFT analysis, discrete systems and digital filter analysis, digital filter synthesis.

Prerequisites

Students should have previously acquired the following prerequisites to follow this course:

  • Analog signal processing: convolution, series and continuous-time Fourier transform;
  • Continuous-time systems: Laplace transform, frequency response, transfer function, analog filter synthesis.

Intended Learning Outcomes

By the end of this course, students will be able to:

  1. Define the Fourier transform of a 1D signal to be used according to the continuous or discrete nature of the signal;
  2. Explain the effects of sampling an analog signal (Shannon's theorem);
  3. To know the definition and properties of the Fourier transform of a discrete signal, and the effects of its different parameters (number of points, windowing, etc.) on the resolution/accuracy of the frequency analysis;
  4. Analyze the result of a Fourier transform calculation (e.g., associating the temporal and frequency properties of signals, identifying the frequency support of information, etc.)
  5. Determine the Z transform of any discrete signal;
  6. Calculate the input/output relationship of a linear and invariant discrete system, in the time and frequency domain;
  7. Recognize a discrete system such as FIR or IIR;
  8. Use these relationships to characterize the properties of a linear and invariant discrete system (stability, velocity, filtering, etc.);
  9. Synthesize a digital filter on the basis of specifications;
  10. Write a a Matlab or a Python program to display and analyze the spectrum of a signal;
  11. Write a Matlab or a Python Python program to design and use a numerical filter based on the software tools provided.

Indicative Teaching Sequence and Methods

Week C/TD/TP* Content Preparation Learn.\ outc.
S1 C1 Reminders about continuous time AAV1
S2 C2 Sampling AAV2
S3 C3 / TD1 Frequency analysis Preparatory video for TD1 AAV1, AAV3-4
S4 TD2 Windowing Preparatory video for TD2 AAV3-4
S5 TP1 FFT and windowing Review FFT and its properties AAV4, AAV10
S6 C4 Z-Transform AAV5
S7 C5 / TD3 Discrete Time Systems / Discrete Systems Analysis Preparatory video for TD3 AAV6-8
S8 C6 Synthesis of digital filters AAV8-9
S9 TD4 Synthesis of digital filters Preparation for TD4 AAV9
S10 TP2 Using a synthesis tool in Python Review FFT and FIR/IIR synthesis AAV10-11
S11 TD5 Last year final exam AAV1-11
  • C/TD/TP respectively corresponds to lectures, tutorials and lab sessions.

Sequence of the unit

The UE takes place in 3 successive sequences:

  • Sequence 1: recalls, sampling and frequency analysis of discrete signals (C1/2/3 + TD1/2 + TP1 + Quiz1)

  • Sequence 2: mathematical tools and discrete time systems (C4/5 + TD3 + Quiz 2)

  • Sequence 3: synthesis of digital filters (C6 + TD4/5 + TP2)

Indicative Assessment of Intended Learning Outcomes (1st session)

Week Individ./group In-person/remote Type of exam Evaluated outcomes Scale %
S11 Individual In-person Practical AAV 10-11 30%
S12 Individual In-person Written AAV 1-9 70%

2nde session

Session Individ./group In-person/remote Type of exam Evaluated outcomes Scale %
2 Individual In-person Written AAV 1-11 70%
1 Individual In-person Practical AAV 10-11 30%

Bibliographic references

  • A.W.M. Van Den Henden, N.A.M Verhoeckx, Traitement numérique du signal : une introduction. Masson.
  • M. Bellanger, Traitement numérique du signal. Dunod.
  • Etienne Tisserand, Jean-François Pautex, Patrick Schweitzer, "Analyse et traitement des signaux - Méthodes et applications au son et à l'image", Dunod, EAN 9782100524372

Logo SDI Date of generation of this unit description: 14/01/2026 Logo SDI