Ing Ind - Inf (Mag.)(ord. 270) - CR (263) MUSIC AND ACOUSTIC ENGINEERING
052845 - SIGNALS AND SYSTEMS
This course focuses on the analysis of signals (sound, acoustic pressure, voltage, images, etc.) and the systems that act on them (acoustic resonators and environments, circuits, mechanical devices, etc.). We concentrate on the Fourier Transform and Linear-Time Invariant Systems, providing the fundamental mathematical tools for sampling, manipulating, preserving, and interpreting information signals.
This second module of the course is dedicated to discrete-time signals and systems.
Risultati di apprendimento attesi
Lectures and excercise sessions will allow students to:
- understand the fundamental mathematical tools for the representation and decomposition of discrete-time signals and systems
- understand analogies and differences with continuous-time analysis tools;
- derive suitable models of linear-time invariant discrete-time systems, and appropriate representations of the related signals in time- and frequency-domain
- analyze and design discrete-time filters
- understand and apply the theory of discrete random processes for spectral estimation and for designing simple adaptive filters
Discrete-Time Signals and Systems – Some useful Discrete-Time signal models; sampling Continuous-Time sinusoids and aliasing; useful signal operations; examples of Discrete-Time systems.
Time-Domain Analysis of Discrete-Time Systems – Discrete-Time system equations; system response to internal conditions: Zero-Input Response; Unit Impulse Response h[k]; System Response to External Input: Zero-State Response; classical solution of linear difference equations; system stability; determining Impulse Response.
Fourier Analysis of Discrete-Time Signals – Periodic signal representation by Discrete-Time Fourier Series; aperiodic signal representation by Fourier integral; properties of DTFT; DTFT connection with the Continuous-Time Fourier Transform; Discrete-Time linear system analysis by DTFT;
The Discrete Fourier Transform (DFT): numerical computation of Fourier Transform: the Discrete Fourier Transform (DFT); the Fast Fourier Transform (FFT); signal processing using DFT and FFT; convolution in the frequency domain; convolution via overlap-and-add; the short-time Fourier Transform (STFT); windowing: spectral leakage, spectral resolution, zero-padding.
Discrete-Time system analysis using the Z-transform – generalization of DTFT to the Z-transform; The Z-Transform; some properties of the Z-transform; Z-transform solution of linear difference equations system realization; connection between the Laplace and the Z-Transform; the bilateral Z-transform.
Frequency Response and Digital Filters – Frequency response of discrete-time systems; frequency response from pole-zero location; digital filters; filter design criteria; recursive filter design: the impulse invariance method; recursive filter design: the bilinear transformation method; nonrecursive filters; nonrecursive filter design.
Introduction to multirate systems – Downsampling and upsampling; decimation and interpolation; resampling.
Fundamentals of statistical signal processing – Random sequences: expectation, i.i.d sequences, jointly distributed random sequences; correlation and covariance sequences; time averages and ergodicity.
Introduction to spectral estimation: power spectral density, bias and variance of an estimator, periodogram, correlogram
Introduction to adaptive filtering: Wiener-Hopf equation and Wiener filtering; linear prediction.
A certain familiarity with fundamentals of calculus is recommended, particularly on: derivatives, integrals, and integro-differential equations, series.
Modalità di valutazione
The exam consists of a written test based on the topics taught in the course, including a mixture of theoretical questions (~55%) and exercises (~45%).
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Tipo Forma Didattica
Ore di attività svolte in aula
Ore di studio autonome
Laboratorio Di Progetto
Informazioni in lingua inglese a supporto dell'internazionalizzazione
Insegnamento erogato in lingua
Disponibilità di materiale didattico/slides in lingua inglese
Disponibilità di libri di testo/bibliografia in lingua inglese
Possibilità di sostenere l'esame in lingua inglese
Disponibilità di supporto didattico in lingua inglese