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Semestre 5
Intersemestre
Semestre 6
 
 
 
Semestre 7
 
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Semestre 9
 
 
Intersemestre

Course unit

Signal processing

Last updated: 09/12/2024

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Course Director(s):

KRÉMÉ Marina LAKHMI Riadh

General Description:

The aim of this unit is to provide the fundamental bases of deterministic signal processing.

Initially the Fourier series and Fourier transform of continuous signals will be studied in order to determine the frequency content of signals. These tools will then be extended to discrete signals (sampled and limited duration) in order to introduce the discrete Fourier transform. Finally with a view to filtering signals, the characterisation of systems will be investigated via. impulse response, frequency response and the transfer function. More particularly linear invariant systems (IIRF/FIR filters) will be studied, in both the temporal and frequency domains.

These different notions will be subject to practical application with practical courses on Matlab in order to understand the advantages and limits of the processing and numerical analysis of signals.

Key words:

Fourier series Gibbs phenomenon Shannon’s theorem Fourier/Laplace transforms Z transforms convolution Discrete filters Impulse response Frequency response Transfer function IIRF/FIR filters Sampling

Number of teaching hours

13

Fields of study

Mathematics

Teaching language

French

Intended learning outcomes

On completion of the unit, the student will be capable of: Classification level Priority

Learning assessment methods

Percentage ratio of individual assessment Percentage ratio of group assessment
Written exam: 100 % Project submission: 0 %
Individual oral exam: 0 % Group presentation: 0 %
Individual presentation: 0 % Group practical exercise: 0 %
Individual practical exercise: 0 % Group report: 0 %
Individual report: 0 %
Other(s): 0 %

Programme and content

Type of teaching activity Content, sequencing and organisation
Course

3 Courses of 1h30 / 4h30

  • Fourier series, Fourier transforms of continuous signals
  • Sampling, discrete signals, discrete Fourier transform
  • Systems, impulse response, frequency response, transfer function, IIRF/FIR filters
Practical courses

4 Practical courses of 1h30 with Matlab / 6h00

  • Study of Tuning Forks (Simulink
  • Sampling and Gibbs phenomenon
  • Discrete Fourier transform
  • Discrete filters