Signal Processing

This course completes a basic training in signal processing with a thorough 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 a first part (10h30 lecture, 6h lab), the course deals with the sampling and quantization aspects of continuous signals and the relation between digital signals and original continuous signals. We define the discrete Fourier transform of digital signals, its estimation and its use on real deterministic signals.

The second part of the course (9 hours lecture, 4.5 hours lab, 3 hours lab) is dedicated to random signals and how the properties of some random signals can be used either to reduce the random part of a signal whose deterministic part is to be privileged (filtering, increase of the signal-to-noise ratio, ...) or to improve the transmission of information or to identify complex linearized systems.

 

The objective of this module is to familiarize students with the processing of digital signals (i.e. quantified and sampled) whether they are deterministic or random. At the end of this module, students will be able to design a digital acquisition and processing system for a signal from an analog sensor. They will also be able to use this knowledge to exploit the random properties of signals.

 

Knowledge of L3 level in continuous and sampled signal processing.

Recommended prerequisites*:

Have a basic knowledge of analog signal processing

 

Final control by an exam 70% and evaluation of the practical work 30%. 

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

Digitization of signals: sampling, quantization: theoretical reminders 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-timing 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.

Notion of adapted filtering.

Identification of a transfer function by using random signals.

 

CM: 7:30 pm

TD : 4h30

Practical work : 9h