Department of Fundamental Education in Science and Technology

https://www.univ-soukahras.dz/en/dept/st

Lecturer
Information	Bachelor - Second Year : Electronic Department of Fundamental Education in Science and Technology Website : https://www.univ-soukahras.dz/en/module/5041 Semester : S4 Unit : UEF 2.2.2 Credit : 4 Coefficient: 2
Content	Chapter 1: Fundamentals of Signals (3 Weeks) Objectives of signal processing. Application domains. Classification of signals (morphological, spectral, etc.). Deterministic signals (periodic and non-periodic) and random signals (stationary and non-stationary). Causality. Notions of power and energy. Basic functions in signal processing (measurement, filtering, smoothing, modulation, detection, etc.). Examples of basic signals (rectangular pulse, triangular, ramp, step, sign, Dirac, etc.) Chapter 2: Fourier Analysis (4 Weeks) Introduction. Mathematical reminders (dot product, Euclidean distance, linear combination, orthogonal basis, etc.). Approximation of signals by a linear combination of orthogonal functions. Fourier series, Fourier transform, Properties. Parseval\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\'s theorem. Fourier spectrum of periodic (discrete spectrum) and non-periodic (continuous spectrum) signals. Chapter 3: Laplace Transform (3 Weeks) Definition. Properties of the Laplace transform. Signal/system relationship. Application to linear systems and time/frequency analysis of SLIT (Shifted Linear Invariant Systems). Chapter 4: Convolution Product (2 Weeks) Formulation of convolution product. Properties of convolution product. Convolution product and Dirac impulse. Chapter 5: Signal Correlation (3 Weeks) Signals with finite total energy. Signals with finite average power. Inter-correlation between signals. Auto-correlation. Properties of correlation function. Energy spectral density and power spectral density. Wiener-Khintchine theorem. Case of periodic signals.
Evaluation	Continuous control: 40%; Final exam: 60%.