Signal Processing

This course complements a basic education in signal processing with in-depth knowledge of deterministic and random digital signals. This knowledge is essential in all engineering disciplines, as digital signal processing is currently used in the majority of applications.

In the first part (10:30 a.m. lectures, 6 hours of lab work), the course covers the sampling and quantization 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 application to real deterministic signals.

The second part of the course (9 hours of lectures, 4 hours and 30 minutes of tutorials, 3 hours of lab) is devoted to random signals and how the properties of certain random signals can be used either to reduce the random component of a signal when the deterministic component is of primary interest (filtering, increasing the signal-to-noise ratio, etc.), to improve information transmission, or to identify linearized complex systems.

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

Bachelor's-level knowledge of continuous and sampled-signal processing.

Recommended prerequisites*:

Have a basic understanding of analog signal processing

Final assessment consisting of an exam (70%) and lab work evaluation (30%) 

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

Signal Digitization: Sampling and Quantization: Theoretical Overview 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.

The concept of adaptive filtering.

Identification of a transfer function using random signals.

CM: 7:30 p.m.

TD: 4:30

Practical Training: 9:00 a.m.