Continuous signals

After a refresher course on mathematical concepts such as scalar products and distributions, the course introduces the subject of signal and image processing, and its applications in radar, GPS navigation, speech, audio and biomedical applications, as well as links with current issues such as IoT and artificial intelligence. The course then introduces the tools for characterizing and processing deterministic signals. This module serves as a pre-requisite for the Digital Signal Processing course in semester 6, and is also relevant to the Digital Communications course. Finally, this module will be complemented in semester 6 by the Random Processes and Signals module.

Basic mathematics at BAC+2 level.

* Reminder of the mathematical concepts required to understand signal processing * General information on signals and systems Illustrative examples * Temporal characterization of deterministic signals Definition and classification Examples (gate function, etc.) and special signals (Dirac pulse, step, ramp, etc.) * Characterization by mean, energy and autocorrelation function Intercorrelation and intercovariance functions. Method for calculating the autocorrelation function * Frequency characterization of deterministic signals: Fourier analysis (Fourier series development), Fourier transform, properties and method of calculation of spectral density and interspectrum, Wiener-Khintchine theorem * Filtering of linear invariant signals/systems: Definition of a filter, time and frequency characterization, linear phase filter, introduction to Butterworth and Chebyshev filters * Other basic processing: windowing, sampling and modulation.

Signal processing

Exercise handouts and summary of main results.