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Signal sampling, discrete-time systems and discrete spectral analysis Spectral analysis of random processes ans series in linear and non-linear systems Using Matlab for digital signal processing. Luise, G. Educational objectives To understand the meaning of spectral content associated with continuous and discrete signals, both deterministic and random, described when possible by single-valued functions typically in the time-domain.

To understand the concept of signal processing by a device linear and non-linear that is capable to modify the signal shape in time and its spectral content: continuous and discrete filters and frequency-domain system response.

First practical implementation of digital signal processing algorithms and filter design, by using Matlab. About 20 hours are dedicated to solutions of exercises with variable difficulty, which are spread across all the course. About 12 hours are dedicated to verifying by Matlab and audio processing boards, practical computer aided implementation of some of the spectral analysis and filter design techniques that are taught during the course.

The 2 exercises of the written test, which are open answers and do not include the part of digital signal processing, aim to verify the student capability to analyse interconnected systems that process signals either deterministic or random , both in the time and the frequency domain, including basic operations such as linear time-invariant filtering, instantaneous non-linearity, modulation and demodulation, sampling and reconstruction of analog signals.

The oral exam always begins with a question on digital signal processing and one or two successive questions on analogic signals and random processes. The goal is to verify the student level of knowledge and comprehension of the methodological and theoretical content of the class, and particularly to verify the capability of the student of autonomous elaboration of the concepts.

During the oral exam, the capability of autonomous exposition of the concepts and the language appropriateness will be also evaluated. Extended program Concept of signal continuous, discrete, periodic.

Energy, Power, mean value. Operations with signals. Elementary signals. Fourier series expansion of periodic signals: convergence, orthogonality, spectrum lines amplitude and phase , link between power and Fourier series coefficients. Continuous spectrum for aperiodic signals.

Parseval's Theorem. CFT computation of important signals. CTF computation by the derivative method. Linear and non-linear systems: causality, time invariance. Cascade and parallel of LTI systems.

Examples: RC CR filters, ideal integrator, differentiator, two-path wireless channel model, square law, modulus law. Definition and properties of energy and power cross-correlation integral. PSD and power autocorrelation function of periodic signals.

Signal sampling: the Nyquist-Shannon sampling theorem proof for energy signals , reconstruction, aliasing and anti-aliasing filtering. Inverse ZT and residue theorem. Connections with the Laplace transform LT for sampled sequences. DTFT and ZT main properties and transform of important sequences Kroneker delta, constant, monolateral decaying exponential, complex exponential.

Discrete-time LTI systems: discrete convolution and transfer function H z. H z region of convergence and stability. Fundamental property of the DFT: the circular convolution. DFT spectral resolution of a sampled signal: time-domain zero-padding. Frequency-domain zero-padding and time-domain interpolation.

Vector-matrix representation of: discrete convolution linear and circular and DFT. Diagonalization of circulant matrices by DFT: concept of eigen-vectors of circulant systems and similarities with eigen-functions of time-continuous convolutive linear systems. Resume of: continuous and discrete random variables definition, CDF, pdf, mean value, mean squared value, variance ,. Discrete -time RP filtering, connections between mean values and covariance matrices of the input and output vectors, decorrelation of statistically correlated samples.

Covariance matrix of y and colour introduced by H. Energy and Power computation. Graphical representation by Matlab commands plot, stem, subplot, etc. Application to audio signal. Equiripple Parks-McLellan filter design by Matlab. Application to audio and music signal filtering, equalizer design by DFT processing.

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Selezionando 'Nego' i suddetti cookie non verranno utilizzati e i contenuti di terze parti non verranno mostrati. For more information read our privacy policy Accept Deny. Go top Table of content Table of content. Computer science and electronic engineering. Continuous-time signals and spectral analysis: Fourier series and transform- Continuous signals in linear and non-linear systems.

To understand the meaning of spectral content associated with continuous and discrete signals, both deterministic and random, described when possible by single-valued functions typically in the time-domain. Mandatory: Mathematical Analisis I e II functions, limits, derivatives, integrals, series, function series expansions Mandatory: Linear Algebra I vectors, spaces, cartesian products, orthogonality, Higly Recommended: Foundations of Probability Theory probability of events, random variables, marginal, joint, and conditional probability density functions, transformation of random variables, random process definition Useful: Linear Algebra II spectral decomposition of symmetric Hermitian matrices, eigenvalues and eigenvectors.

Concept of signal continuous, discrete, periodic.

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## Marco Luise

The goal of this module is to provide the fundamental set of concepts and techniques that relate to the analysis of signals in the broad area of information engineering. On successful completion of this module, the student should understand i the fundamental concepts of representation of signals in both the time and the frequency domain and their relation, ii how signals get processed by both linear and non-linear systems, iii the characterization of random signals in both time and frequency domain. The student is finally introduced to digital representation and processing of signals, and becomes confident with practical operations through specific computer-assisted tools. The module is tightly connected with the modules in System Theory, Electronics, Object programming, that are thaugth in the same semester, and to the module of Communication Systems that is thaught in the 3rd year.

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## ISBN 13: 9788838608094

He's been the Technical Co-Chair of the 7th Int. He has contributed to establish the Association ToscanaSpazio , which is currently chairing. I contributed to establish new scientific journals, associations, and consulting companies including WISER srl. Bacci, M. Assessment Method:. Recently, game theory has emerged as an effective framework for the network design, since it provides analytical tools to predict the outcome of interactions among rational entities. This tutorial provides an overview of the relevant applications of game theory, focusing on state-of-the-art techniques for resource allocation in wireless and wired communication networks.

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## Teoria dei segnali

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## Università degli Studi di Perugia

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