Signal processing
Summary
Signal processing theory and applications: discrete and continuous time signals; Fourier analysis, DFT, DTFT, CTFT, FFT, STFT; linear time invariant systems; filter design and adaptive filtering; sampling; interpolation and quantization; image processing, data communication and control systems.
Content
Signal processing is an engineering discipline that studies how to analyze, modify, and transmit information using mathematical models, practical devices, and numerical algorithms.
The class will cover the following topics:
1. Basic discrete- and continuous-time signals and systems: signal classes and operations on signals, signals as vectors in a vector space
2. Fourier Analysis: properties of Fourier transforms, DFT, DTFT, CTFT; practical Fourier analysis (FFT, STFT)
3. LTI systems: properties and composition, convolution, application of Fourier analysis to LTI System, Laplace and z-Transforms.
4. Analog vs Digital: sampling, interpolation and quantization.
5. Applications: adaptive filtering; image processing, data communication and control systems.
Learning Prerequisites
Required courses
Linear Algebra, Programming (Python), Analysis II
Recommended courses
Analyse III (concurrently), Probability theory (concurrently)
Important concepts to start the course
Vectors and vector space, functions and sequences, infinite series
Learning Outcomes
By the end of the course, the student must be able to:
- Identify signals and signal types
- Describe properties of LTI systems
- Analyze LTI systems by spectral analysis
- Recognize signal processing problems
- Apply the correct analysis tools to specific signals
- Implement signal processing algorithms
- Design digital filters
- Interpret complex signal processing systems
Teaching methods
This course will weave together theoretical analysis in course lectures with practical hands-on labs using Python (via Jupyter notebooks) and more traditional exercise sessions.
Expected student activities
Study class material; complete weekly homework sets (with solutions discussed in subsequent exercise sessions) and participate in Python applied labs.
Assessment methods
The final grade will be almost fully determined by the final exam, with a small grade component based on compilation of weekly laboratory and homework assignments.
Supervision
| Office hours | Yes |
| Assistants | Yes |
| Forum | Yes |
Dans les plans d'études
- Semestre: Printemps
- Forme de l'examen: Ecrit (session d'été)
- Matière examinée: Signal processing
- Cours: 4 Heure(s) hebdo x 14 semaines
- Exercices: 2 Heure(s) hebdo x 14 semaines
- Labo: 2 Heure(s) hebdo x 14 semaines
- Type: obligatoire
- Semestre: Printemps
- Forme de l'examen: Ecrit (session d'été)
- Matière examinée: Signal processing
- Cours: 4 Heure(s) hebdo x 14 semaines
- Exercices: 2 Heure(s) hebdo x 14 semaines
- Labo: 2 Heure(s) hebdo x 14 semaines
- Type: optionnel
- Semestre: Printemps
- Forme de l'examen: Ecrit (session d'été)
- Matière examinée: Signal processing
- Cours: 4 Heure(s) hebdo x 14 semaines
- Exercices: 2 Heure(s) hebdo x 14 semaines
- Labo: 2 Heure(s) hebdo x 14 semaines
- Type: optionnel
- Semestre: Printemps
- Forme de l'examen: Ecrit (session d'été)
- Matière examinée: Signal processing
- Cours: 4 Heure(s) hebdo x 14 semaines
- Exercices: 2 Heure(s) hebdo x 14 semaines
- Labo: 2 Heure(s) hebdo x 14 semaines
- Type: optionnel