Fourier Analysis of analog deterministic signals.
Definition and analysis of simple LTI systems.
Complex envelope of band-pass signals.
Sampling of band-limited signals. Aliasing.
Definition of random process, stationary random processes, Gaussian random processes.
Random processes through LTI systems.
White noise, Statistical characteristics of narrow-band Gaussian noise.
Monica Gherardelli, Mario Fossi
"Appunti di Teoria dei Segnali",
Editrice Esculapio
ISBN 9788874888351
Reference books:
Simon Haykin, Michael Moher: “Introduzione alle telecomunicazioni analogiche e digitali”
Casa Editrice Ambrosiana
J.G Proakis, M. Salehi::”Communication Systems Engineering“,
Prentice Hall International Editions
A. Papoulis: "Probability, Random variables and Stochastic processes",
Ed. Mc Graw-Hill (3* edizione).
Learning Objectives
Knowledge and knowing how to apply the fundamental methodological tools for
description, analysis and modeling of deterministic signals and of
random signals
Knowing how to apply methodological tools to the study of simple linear systems and theirs
behavior in the presence of input signals
Knowing, understanding and interpreting the effects of sampling time-continuous signals.
Prerequisites
Limits, series, integrals. Linear Algebra. Complex Algebra. Trigonometry.
Analytic Geometry. Probability Theory.
Teaching Methods
Classroom lectures or distance lessons in streaming; possibility of accessing the recordings of lessons already held.
Further information
Further information is available at the website e-l.unifi.it
Type of Assessment
Oral exam that consists of four questions for verifying:
-learning the fundamental methodological tools for
description, analysis and modeling of deterministic signals and of
random signals;
- ability to apply methodological tools to the study of the behavior of simple linear systems in the presence of input signals;
-knowing, understanding and interpreting the effects of sampling the time-continuous signals.
At the student's choice, some questions may be replaced by partial written tests in progress.
Course program
Introduction
Definitions of information, signal and communication system.
Classifications of signals - Deterministic and random signals; energy signals and power signals; analog signals, discrete-time signals and digital signals; periodic signals, no-periodic signals and cyclic signals. Examples.
Deterministic signals
Fourier analysis - Complex exponential Fourier series of periodic and energy signals. Fourier transform; graphic evaluation of convolution integral; autocorrelation, cross-correlation and Parseval theorem. Dirac Delta: definition and properties. Fourier transforms of generalized functions: Dirac delta, complex exponential function, signum function, unit step function, periodic functions, Dirac Comb. Definition of bandwidth of a signal. Autocorrelation and Spectral power density of power signals.
Linear transformations of analog signals – Classification of electrical systems: linear systems, Time-invariant systems, casual systems, stable systems, active and passive systems. Analytical characterization of LTI systems. Physical reliability. LTI system analysis in the frequency domain: frequency response or transfer function of a system, frequency response theorem, I/O relation, relation between I/O power spectral densities. Distortionless transmission: linear distortions, amplitude and phase distortions. Power gain of a LTI system. Filtering systems: band-pass filters, low-pass filters, definition of filter bandwidth.
Complex envelope of a band-pass signal - Hilbert transform. Complex envelope of finite energy signal. Canonical representation of band-pass signals. Examples.
Sampling of signals – Sampling theorem of finite energy and band-limited signals: Fourier transform of the sampled signal, Nyquist rate, analog signal reconstruction by mean of interpolation formula. Aliasing. Sampling by switching circuit. Sample-hold sampling. Sampling of band-pass signals. Examples.
Random vectors - Covariance matrix, Joint distribution function and joint probability density function. Gaussian vectors, linear transformations of n jointly Gaussian random variables.
Random processes – Definition. Nth order distribution function of a process, Nth order probability density function of a process. Multi-dimensional processes. Complex processes. Mean, autocorrelation and auto-covariance functions. Cross-correlation and cross-covariance functions of two processes. Uncorrelated processes, orthogonal processes, statistically independent processes. Gaussian processes. Stationary processes: stationarity in the strict sense and in the wide sense, joint stationarity. Autocorrelation and power spectral density of stationary processes. Cross correlation and cross spectrum of stationary processes. Linear transformation of random processes. Ergodic processes.
Noise – White noise , white gaussian noise through a low-pass filter: ideal and real cases (RC filter). Noise equivalent bandwidth and decorrelation time. Matched filter. Statistical characteristics of Gaussian narrow-band: properties of the in-phase and quadrature components, properties of the envelope and phase.