Signal Processing

This teaching unit complements basic training in signal processing with in-depth knowledge of deterministic or random digital signals. This knowledge is essential in all engineering sciences, as digital signal processing is currently used in the majority of applications.

In the first part (10.5 hours of lectures, 6 hours of practical work), the course covers the sampling and quantification of continuous signals and the relationship between digital signals and the original continuous signal. It defines the discrete Fourier transform of digital signals, its estimation, and its use on real deterministic signals.

The second part of the course (9 hours of lectures, 4.5 hours of tutorials, 3 hours of practical work) is dedicated to random signals and how the properties of certain random signals can be used either to reduce the random part of a signal whose deterministic part we wish to favor (filtering, increasing the signal-to-noise ratio, etc.) or to improve information transmission or even identify complex linearized systems.

 

The objective of this module is to familiarize students with the processing of digital signals (i.e., quantized and sampled), whether deterministic or random. By the end of this module, students will be able to design a system for digitally acquiring and processing signals from an analog sensor. They will also know how to use this knowledge to exploit the random properties of signals.

 

Level 3 knowledge of continuous and sampled signal processing.

Recommended prerequisites:

Have a basic understanding of analog signal processing

 

Final assessment based on a 70% exam and 30% practical work evaluation 

Conversion of continuous-time signals into discrete-time signals and vice versa.

Signal digitization: sampling, quantization: theoretical reminders and practical implementation.

A/D and D/A converters, encoding dynamics.

Discrete Fourier transform (tools), windowing, theory and practical implementation, application to spectral analysis.

Multi-frequency systems.

Deterministic description of random signals: statistical moments and temporal moments.

Useful properties of random signals: stationarity and ergodicity.

Relationship between random signals: correlation and covariance.

Random process: AR, MA, and ARMA models.

Concept of adaptive filtering.

Identification of a transfer function using random signals.

 

CM: 7:30 p.m.

Tutorial: 4.5 hours

Practical work: 9 hours