Ing Ind - Inf (Mag.)(ord. 270) - MI (263) MUSIC AND ACOUSTIC ENGINEERING

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052845 - SIGNALS AND SYSTEMS

Obiettivi dell'insegnamento

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.

The course is divided in two modules. Module 1 is dedicated to continuous-time (analog) signals and systems. Module 2 focuses on discrete-time (digital) signals and systems.

Risultati di apprendimento attesi

The students will acquire the fundamental tools for describing and analyzing continous-time and discrete-time signal systems; they will acquire the ability to use such tools for designing and describing systems with prescribed transfer functions / frequency responses.

Argomenti trattati

Module 1: continuous-time signals and systems

Overview of Signals and Systems – Signals: size and classification of signals, operations on signals, examples of signal models, symmetries. Systems: classification of systems, system models: Input-Output description.

Time-Domain Analysis of Continuous-Time Systems – System response to internal conditions: Zero-Input Response, the Unit Impulse Response; system response to external input: Zero-State Response. Classical solution of differential equations, system stability, intuitive insights into system behavior, determining the impulse response.

Signal Representation by Fourier Series – Signals and vectors; signal comparison: correlation; signal representation by orthogonal signal set; trigonometric Fourier series; exponential Fourier series; numerical computation of the coefficients; LTIC system response to periodic inputs.

Continuous-Time Signal Analysis: The Fourier Transform – Aperiodic signal representation by Fourier integral; transform of some useful functions; some properties of the Fourier transform; signal transmission through LTIC systems; ideal and practical systems; signal energy; application to communications: amplitude modulation; angle modulation; windowing.

Continuous-Time System Analysis Using the Laplace Transform – The Laplace transform; some properties of the Laplace transform; solution of differential and integro-differential equations; block diagrams; system realization; application to feedback and controls; the bilateral Laplace transform.

Frequency Response and Analog Filters – Frequency response of an LTIC system; filter design by placement of poles and zeros of h(s); Butterworth filters; Chebyshev filters; frequency transformations; filters that satisfy distortionless transmission conditions.

Sampling of continuous-time signals - Sampling period and sampling frequency; the sampling theorem; anti-aliasing low-pass filter; perfect signal reconstruction via sinc interpolation.

Module 2: discrete-time signals and systems

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.

Prerequisiti

A certain familiarity with fundamentals of calculus is recommended, particularly on: derivatives, integrals, and integro-differential equations, series, linear algebra.

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%).

Bibliografia

B. P. Lathi, Signal processing and linear systems, Editore: Berkeley-Cambridge Press, Anno edizione: 1998
Slides of the coursehttp://beep.metid.polimi.it/P. S. R. Diniz, E. A. B. da Silva, S. L. Netto, Digital signal processing Editore, Editore: Cambridge University Press, Anno edizione: 2010

Software utilizzato

Nessun software richiesto

Forme didattiche

Tipo Forma Didattica

Ore di attività svolte in aula

(hh:mm)

Ore di studio autonome

(hh:mm)

Lezione

60:00

90:00

Esercitazione

40:00

60:00

Laboratorio Informatico

0:00

0:00

Laboratorio Sperimentale

0:00

0:00

Laboratorio Di Progetto

0:00

0:00

Totale

100:00

150:00

Informazioni in lingua inglese a supporto dell'internazionalizzazione

Insegnamento erogato in lingua
Inglese

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