UE E6-A - Mathematics, Signal, Automation

Level of knowledge :

N1: beginner
N2: intermediate
N3: confirmed
N4: expert

The knowledge (skills) expected at the end of the UE

Acquire notions on specific mathematical tools complementary to those of UE E5-A, function vector spaces, Bessel functions, distribution theory, complex functions of the complex variable: (C1, N1)
Acquire notions of fundamental methods for modeling and controlling continuous-time or sampled dynamic systems (C1,N1)
Know the definitions and physical meaning of quantities characterizing the continuous-time signal, such as average, energy, power and functions of auto or intercorrelation, auto or intercovariance, etc.. (C1, N1)
Know the definitions, properties and interpretation of tools for characterizing continuous-time signals in the frequency domain, in particular the gate function (C1, N1)
Know the basic processing of a continuous-time signal, such as windowing and filtering (C1, N1)

Learning outcomes in terms of abilities, skills and attitudes expected at the end of the course

Know how to carry out calculations within the framework of distribution theory: (C1, N1)
Apply the properties of Bessel functions to practical cases: (C1, N1)
Calculate projections of functions onto orthogonal function bases: (C1, N1)
Analyze the analytical properties of complex functions of the complex variable: (C1,N1)
Apply the residue theorem.
Be able to develop a function in Laurent series and calculate Z-transforms: (C1, N1)
Be able to identify areas of application in signal processing: (C1, N1)
Depending on the nature of the signals (random/deterministic, periodic or not, with finite energy or not, etc.), be able to characterize the signals to be processed.), be able to characterize continuous-time signals both in terms of their correlation and their frequency richness (C1, N1)
Be able to evaluate the impact of simple processing such as modulation, windowing and linear filtering on a signal, in both time and frequency domains: (C1, N1)