Signal processing

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

The first part (10:30 h lecture, 6 h hands-on) covers the sampling and quantization of continuous signals, and the relationship between digital signals and the original continuous signal. We define the discrete Fourier transform of digital signals, its estimation and its use on real deterministic signals.

The second part of the course (9h Lecture, 4h30 TD, 3h TP) 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 emphasize (filtering, increasing the signal-to-noise ratio, etc.) or to improve the transmission of information or identify complex linearized systems.

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

L3-level knowledge of continuous and sampled signal processing.

Recommended prerequisites* :

Basic knowledge of analog signal processing

Final examination 70% and practical work assessment 30%. 

Convert continuous-time signals into discrete-time signals and vice versa.

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

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

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

Multi-clocked 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 processes: AR, MA and ARMA models.

Notion of adapted filtering.

Identify a transfer function using random signals.

CM: 7:30 p.m.

TD: 4h30

Practical work: 9h