Ingegneria Elettronica | SIGNAL THEORY

cod. 0612400007

SIGNAL THEORY

	0612400007
	DIPARTIMENTO DI INGEGNERIA INDUSTRIALE
	EQF6
	ELECTRONIC ENGINEERING
	2016/2017

PERCORSO COMUNE Cohort 2015/2016

	OBBLIGATORIO
	YEAR OF COURSE 2
	YEAR OF DIDACTIC SYSTEM 2012
	SECONDO SEMESTRE

TEACHING UNITS

	SSD	CFU	HOURS	ACTIVITY	TYPE OF ACTIVITY
1	TEORIA DEI SEGNALI
	SECS-S/02	6	60	LESSONS	BASIC COMPULSORY SUBJECTS
2	TEORIA DEI SEGNALI
	ING-INF/03	3	30	LESSONS	COMPULSORY SUBJECTS, CHARACTERISTIC OF THE CLASS

PROFESSORS

	CONSOLATINA LIGUORI2 T Curriculum
	FLAMINIO FERRARA1 Curriculum

	Objectives
	THE AIM OF THE COURSE IS TWOFOLD: INTRODUCING THE BASIC NOTIONS OF THE PROBABILITY THEORY, IN ORDER TO MODEL AND ANALYSE RANDOM PHENOMENA TYPICALLY OBSERVED IN THE REAL WORLD AND, IN PARTICULAR, IN THE COMMUNICATION SYSTEMS, AND PROVIDING THE MAIN SIGNAL PROCESSING TECHNIQUES TO TREAT SIGNALS PRESENT IN COMPUTER ENGINEERING APPLICATION, IN CASE OF BOTH WAVEFORMS AND DIGITAL SIGNALS. KNOWLEDGE AND UNDERSTANDING: BASIC NOTIONS OF PROBABILITY AND COMBINATORIAL CALCULUS. RANDOM VARIABLES. SIGNAL PROCESSING TECHNIQUES IN THE TIME AND FREQUENCY DOMAINS. UNDERSTANDING THE EFFECT OF SYSTEMS ON BOTH ANALOG AND DIGITAL SIGNALS. DIGITAL-TO-ANALOG CONVERSION. DISCRETE FOURIER TRANSFORM AND FAST FOURIER TRANSFORM. APPLIED KNOWLEDGE AND UNDERSTANDING: ABILITY TO MODEL AND ANALYSE RANDOM EVENTS. ABILITY TO CHARACTERIZE ANALOG AND DIGITAL SIGNALS AND SYSTEMS. ABILITY TO DESIGN AND PERFORM SIMPLE SIGNAL PROCESSING PROCEDURES. ABILITY TO APPLY THE SAMPLING THEOREM. PERSONAL JUDGMENTS: ABILITY TO SELECT THE MOST APPROPRIATE METHODS TO ANALYSE A RANDOM PHENOMENON AND THE BEST REPRESENTATIONS OF THE SIGNALS AND SYSTEMS IN ORDER TO STUDY THEIR INTERACTION. ABILITY TO AVOID ARTIFACTS AND UNWANTED EFFECTS INTRODUCED BY THE DISCRETIZATION OF ANALOG SIGNALS. COMMUNICATION SKILLS: BEING ABLE TO VERBALLY EXPLAIN OR WRITE A TOPIC OF THE COURSE, BY USING SUITABLE MATHEMATICAL STATEMENTS. LEARNING SKILLS: BEING ABLE TO APPLY THE ACQUIRED KNOWLEDGE TO DIFFERENT CONTEXTS FROM THOSE PRESENTED DURING THE COURSE, AND TO DEEPEN THE TOPICS USING MATERIALS OTHER THAN THOSE PROPOSED FOR THE COURSE.

THE AIM OF THE COURSE IS TWOFOLD: INTRODUCING THE BASIC NOTIONS OF THE PROBABILITY THEORY, IN ORDER TO MODEL AND ANALYSE RANDOM PHENOMENA TYPICALLY OBSERVED IN THE REAL WORLD AND, IN PARTICULAR, IN THE COMMUNICATION SYSTEMS, AND PROVIDING THE MAIN SIGNAL PROCESSING TECHNIQUES TO TREAT SIGNALS PRESENT IN COMPUTER ENGINEERING APPLICATION, IN CASE OF BOTH WAVEFORMS AND DIGITAL SIGNALS.
KNOWLEDGE AND UNDERSTANDING:
BASIC NOTIONS OF PROBABILITY AND COMBINATORIAL CALCULUS. RANDOM VARIABLES. SIGNAL PROCESSING TECHNIQUES IN THE TIME AND FREQUENCY DOMAINS. UNDERSTANDING THE EFFECT OF SYSTEMS ON BOTH ANALOG AND DIGITAL SIGNALS. DIGITAL-TO-ANALOG CONVERSION. DISCRETE FOURIER TRANSFORM AND FAST FOURIER TRANSFORM.
APPLIED KNOWLEDGE AND UNDERSTANDING:
ABILITY TO MODEL AND ANALYSE RANDOM EVENTS. ABILITY TO CHARACTERIZE ANALOG AND DIGITAL SIGNALS AND SYSTEMS. ABILITY TO DESIGN AND PERFORM SIMPLE SIGNAL PROCESSING PROCEDURES. ABILITY TO APPLY THE SAMPLING THEOREM.
PERSONAL JUDGMENTS:
ABILITY TO SELECT THE MOST APPROPRIATE METHODS TO ANALYSE A RANDOM PHENOMENON AND THE BEST REPRESENTATIONS OF THE SIGNALS AND SYSTEMS IN ORDER TO STUDY THEIR INTERACTION. ABILITY TO AVOID ARTIFACTS AND UNWANTED EFFECTS INTRODUCED BY THE DISCRETIZATION OF ANALOG SIGNALS.
COMMUNICATION SKILLS:
BEING ABLE TO VERBALLY EXPLAIN OR WRITE A TOPIC OF THE COURSE, BY USING SUITABLE MATHEMATICAL STATEMENTS.
LEARNING SKILLS:
BEING ABLE TO APPLY THE ACQUIRED KNOWLEDGE TO DIFFERENT CONTEXTS FROM THOSE PRESENTED DURING THE COURSE, AND TO DEEPEN THE TOPICS USING MATERIALS OTHER THAN THOSE PROPOSED FOR THE COURSE.

	Prerequisites
	FOR THE SUCCESSFUL ACHIEVEMENT OF THE OBJECTIVES, A SUITABLE KNOWLEDGE OF MATHEMATICS IS REQUIRED, AS GUARANTEED BY THE MATHEMATICS III COURSE.

	Contents
	THE COURSE OF SIGNAL THEORY IS COMPOSED BY TWO UNITS. ELEMENTS OF PROBABILITY THEORY: ELEMENTS OF PROBABILITY THEORY AND COMBINATORIAL CALCULUS. AXIOMS OF PROBABILITY. CONDITIONAL PROBABILITY AND INDEPENDENCE. TOTAL PROBABILITY THEOREM. BAYES THEOREM. COMBINATORIAL CALCULUS. (HOURS: LESSONS/EXERCISES/LABORATORY 5/4/0) RANDOM VARIABLES. DEFINITION OF A RANDOM VARIABLE (R.V.) AND ITS PROBABILITY DISTRIBUTION AND PROBABILITY DENSITY FUNCTION. MEAN AND VARIANCE OF A R.V.. FUNCTIONS OF A RANDOM VARIABLE. COUPLES OF R.V.’S AND THEIR JOINT AND MARGINAL DISTRIBUTIONS. COVARIANCE. DISTRIBUTIONS OF DISCRETE AND CONTINUOUS R.V.’S OF COMMON USE. (HOURS: LESSONS/EXERCISES/LABORATORY 5/3/0) BASIC LAWS OF PROBABILITY THEORY. TRANSFORMATION OF DISCRETE AND CONTINUOUS R.V.’S. BOTH IN ONE- AND TWO-DIMENSIONAL CASE. SUM OF INDEPENDENT R.V.’S. SAMPLE MEAN AND SAMPLE VARIANCE. LARGE NUMBER LAW CENTRAL LIMIT THEOREM. (HOURS: LESSONS/EXERCISES/LABORATORY 5/3/0) INTRODUCTION TO STOCHASTIC PROCESSES. DEFINITION OF A STOCHASTIC PROCESS AND ITS PROPERTIES: STATIONARITY, WEAK-SENSE STATIONARITY, AND ERGODICITY. GAUSSIAN PROCESSES.. (HOURS: LESSONS/EXERCISES/LABORATORY 3/2/0) SIGNAL ANALYSIS: SIGNALS AND SYSTEMS IN THE TIME DOMAIN. CLASSIFICATION AND BASIC OPERATIONS OF DISCRETE-TIME AND CONTINUOUS-TIME SIGNALS. TIME AVERAGES, ENERGY AND POWER OF DETERMINISTIC SIGNALS. PERIODIC SIGNALS. CORRELATION FUNCTION AND ITS PROPERTY. SYSTEM ANALYSIS IN TIME DOMAIN. SYSTEM PROPERTIES AND LINEAR TIME-INVARIANT (LTI) SYSTEMS. CONVOLUTION INTEGRAL AND SUM. (HOURS: LESSONS/EXERCISES/LABORATORY 15/5/0) SIGNALS AND SYSTEMS IN THE FREQUENCY DOMAIN. EIGENFUNCTIONS OF LTI SYSTEMS. FREQUENCY-DOMAIN REPRESENTATION OF SYSTEMS AND SIGNALS: FOURIER TRANSFORM AND ITS PROPERTIES. POISSON SUM AND FOURIER SERIES. FREQUENCY-DOMAIN LTI SYSTEM ANALYSIS. ENERGY AND POWER SPECTRA OF SIGNALS. INPUT-OUTPUT RELATIONSHIP FOR ENERGY AND POWER SPECTRA AND CORRELATION FUNCTIONS. (HOURS: LESSONS/EXERCISES/LABORATORY 10/5/0) DIGITAL SIGNAL PROCESSING. RELATIONSHIP BETWEEN SAMPLING OPERATION AND REPLICATION OF SIGNALS INTRODUCED BY FOURIER TRANSFORM. NYQUIST-SHANNON SAMPLING THEOREM AND ITS PRACTICAL IMPLEMENTATIONS: ANTI-ALIASING FILTER, SAMPLE & HOLD SAMPLING PROCEDURE. DIGITAL PROCESSING OF ANALOG SIGNALS. ANALOG-TO-DIGITAL CONVERSION. (HOURS: LESSONS/EXERCISES/LABORATORY 8/2/0) DISCRETE FOURIER TRANSFORM. DEFINITION OF DISCRETE FOURIER TRANSFORM (DFT) AND ITS PROPERTIES. CIRCULAR CONVOLUTION. DECIMATION-IN-TIME FAST FOURIER TRANSFORM (FFT) ALGORITHM. I-FFT ALGORITHM AND DECIMATION-IN-FREQUENCY FFT ALGORITHM. IMPLEMENTING LTI SYSTEMS USING THE DFT. (HOURS: LESSONS/EXERCISES/LABORATORY 10/5/0) TOTAL HOURS: 90 (HOURS: LESSONS/EXERCISES/LABORATORY 61/29/0)

Contents

THE COURSE OF SIGNAL THEORY IS COMPOSED BY TWO UNITS.
ELEMENTS OF PROBABILITY THEORY:
ELEMENTS OF PROBABILITY THEORY AND COMBINATORIAL CALCULUS. AXIOMS OF PROBABILITY. CONDITIONAL PROBABILITY AND INDEPENDENCE. TOTAL PROBABILITY THEOREM. BAYES THEOREM. COMBINATORIAL CALCULUS. (HOURS: LESSONS/EXERCISES/LABORATORY 5/4/0)
RANDOM VARIABLES. DEFINITION OF A RANDOM VARIABLE (R.V.) AND ITS PROBABILITY DISTRIBUTION AND PROBABILITY DENSITY FUNCTION. MEAN AND VARIANCE OF A R.V.. FUNCTIONS OF A RANDOM VARIABLE. COUPLES OF R.V.’S AND THEIR JOINT AND MARGINAL DISTRIBUTIONS. COVARIANCE. DISTRIBUTIONS OF DISCRETE AND CONTINUOUS R.V.’S OF COMMON USE. (HOURS: LESSONS/EXERCISES/LABORATORY 5/3/0)
BASIC LAWS OF PROBABILITY THEORY. TRANSFORMATION OF DISCRETE AND CONTINUOUS R.V.’S. BOTH IN ONE- AND TWO-DIMENSIONAL CASE. SUM OF INDEPENDENT R.V.’S. SAMPLE MEAN AND SAMPLE VARIANCE. LARGE NUMBER LAW CENTRAL LIMIT THEOREM. (HOURS: LESSONS/EXERCISES/LABORATORY 5/3/0)
INTRODUCTION TO STOCHASTIC PROCESSES. DEFINITION OF A STOCHASTIC PROCESS AND ITS PROPERTIES: STATIONARITY, WEAK-SENSE STATIONARITY, AND ERGODICITY. GAUSSIAN PROCESSES.. (HOURS: LESSONS/EXERCISES/LABORATORY 3/2/0)
SIGNAL ANALYSIS:
SIGNALS AND SYSTEMS IN THE TIME DOMAIN. CLASSIFICATION AND BASIC OPERATIONS OF DISCRETE-TIME AND CONTINUOUS-TIME SIGNALS. TIME AVERAGES, ENERGY AND POWER OF DETERMINISTIC SIGNALS. PERIODIC SIGNALS. CORRELATION FUNCTION AND ITS PROPERTY. SYSTEM ANALYSIS IN TIME DOMAIN. SYSTEM PROPERTIES AND LINEAR TIME-INVARIANT (LTI) SYSTEMS. CONVOLUTION INTEGRAL AND SUM. (HOURS: LESSONS/EXERCISES/LABORATORY 15/5/0)
SIGNALS AND SYSTEMS IN THE FREQUENCY DOMAIN. EIGENFUNCTIONS OF LTI SYSTEMS. FREQUENCY-DOMAIN REPRESENTATION OF SYSTEMS AND SIGNALS: FOURIER TRANSFORM AND ITS PROPERTIES. POISSON SUM AND FOURIER SERIES. FREQUENCY-DOMAIN LTI SYSTEM ANALYSIS. ENERGY AND POWER SPECTRA OF SIGNALS. INPUT-OUTPUT RELATIONSHIP FOR ENERGY AND POWER SPECTRA AND CORRELATION FUNCTIONS. (HOURS: LESSONS/EXERCISES/LABORATORY 10/5/0)
DIGITAL SIGNAL PROCESSING. RELATIONSHIP BETWEEN SAMPLING OPERATION AND REPLICATION OF SIGNALS INTRODUCED BY FOURIER TRANSFORM. NYQUIST-SHANNON SAMPLING THEOREM AND ITS PRACTICAL IMPLEMENTATIONS: ANTI-ALIASING FILTER, SAMPLE & HOLD SAMPLING PROCEDURE. DIGITAL PROCESSING OF ANALOG SIGNALS. ANALOG-TO-DIGITAL CONVERSION. (HOURS: LESSONS/EXERCISES/LABORATORY 8/2/0)
DISCRETE FOURIER TRANSFORM. DEFINITION OF DISCRETE FOURIER TRANSFORM (DFT) AND ITS PROPERTIES. CIRCULAR CONVOLUTION. DECIMATION-IN-TIME FAST FOURIER TRANSFORM (FFT) ALGORITHM. I-FFT ALGORITHM AND DECIMATION-IN-FREQUENCY FFT ALGORITHM. IMPLEMENTING LTI SYSTEMS USING THE DFT. (HOURS: LESSONS/EXERCISES/LABORATORY 10/5/0)
TOTAL HOURS: 90 (HOURS: LESSONS/EXERCISES/LABORATORY 61/29/0)

	Teaching Methods
	THE COURSE INCLUDES THEORETICAL LESSONS AND CLASSROOM EXERCISES.

	Verification of learning
	THE FINAL EXAM IS ONE AND CONTAINS BOTH UNITS. ITS GOAL IS THE EVALUATION OF THE KNOWLEDGE AND UNDERSTANDING OF THE CONCEPTS PRESENTED DURING THE COURSE, THE ABILITY TO APPLY THAT KNOWLEDGE TO SOLVE PROBLEMS ON PROBABILITY, ON THE ANALYSIS OF SIGNALS AND SYSTEMS BOTH IN TIME AND FREQUENCY DOMAINS, ON THE SAMPLING OF TIME-CONTINUOUS SIGNALS. FURTHERMORE, THE PERSONAL JUDGEMENT, THE COMMUNICATION SKILLS AND THE LEARNING ABILITIES ARE ALSO EVALUATED.THE FINAL EXAM CONSISTS OF A WRITTEN TEST AND AN ORAL INTERVIEW:A) THE WRITTEN TEST AIMS TO ASSESS THE ABILITY TO SOLVE PROBLEMS ABOUT THE TOPICS PRESENTED DURING THE COURSE; B) THE ORAL INTERVIEW AIMS TO VERIFY THE ACQUIRED KNOWLEDGE ALSO ON THE TOPICS NOT COVERED BY THE WRITTEN TEST. THE ORAL EXPOSITION AND THE MATHEMATICAL ARGUMENTS ARE CREDITED WITH HIGHER SCORES.

Verification of learning

THE FINAL EXAM IS ONE AND CONTAINS BOTH UNITS. ITS GOAL IS THE EVALUATION OF THE KNOWLEDGE AND UNDERSTANDING OF THE CONCEPTS PRESENTED DURING THE COURSE, THE ABILITY TO APPLY THAT KNOWLEDGE TO SOLVE PROBLEMS ON PROBABILITY, ON THE ANALYSIS OF SIGNALS AND SYSTEMS BOTH IN TIME AND FREQUENCY DOMAINS, ON THE SAMPLING OF TIME-CONTINUOUS SIGNALS. FURTHERMORE, THE PERSONAL JUDGEMENT, THE COMMUNICATION SKILLS AND THE LEARNING ABILITIES ARE ALSO EVALUATED.THE FINAL EXAM CONSISTS OF A WRITTEN TEST AND AN ORAL INTERVIEW:A) THE WRITTEN TEST AIMS TO ASSESS THE ABILITY TO SOLVE PROBLEMS ABOUT THE TOPICS PRESENTED DURING THE COURSE; B) THE ORAL INTERVIEW AIMS TO VERIFY THE ACQUIRED KNOWLEDGE ALSO ON THE TOPICS NOT COVERED BY THE WRITTEN TEST. THE ORAL EXPOSITION AND THE MATHEMATICAL ARGUMENTS ARE CREDITED WITH HIGHER SCORES.

	Texts
	ELEMENTS OF PROBABILITY THEORY: LECTURE NOTES ON PROBABILITY AND COMBINATORIAL CALCULUS (IN ITALIAN).S. M. ROSS, PROBABILITÀ E STATISTICA PER L’INGEGNERIA E LE SCIENZE, APOGEO, 2008.COMPLEMENTARY BOOK:A. PAPOULIS, S. U. PILLAI, PROBABILITY, RANDOM VARIABLES AND STOCHASTIC PROCESSES, 4TH ED., MCGRAW-HILL, 2001. SIGNAL ANALYSIS: E. CONTE, LEZIONI DI TEORIA DEI SEGNALI, LIGUORI, 1996, M. LUISE, G. M. VITETTA, TEORIA DEI SEGNALI, 3RD ED., MCGRAW-HILL, 2009. COMPLEMENTARY BOOKS: C. PRATI, , SEGNALI E SISTEMI PER LE TELECOMUNICAZIONI, 2ND ED., MCGRAW-HILL, 2010. V. OPPENHEIM, A. S. WILLSKY, S. HAMID NAWAB, SIGNALS & SYSTEMS, 2ND ED., PRENTICE-HALL, 1997.

Texts

ELEMENTS OF PROBABILITY THEORY:
LECTURE NOTES ON PROBABILITY AND COMBINATORIAL CALCULUS (IN ITALIAN).S. M. ROSS, PROBABILITÀ E STATISTICA PER L’INGEGNERIA E LE SCIENZE, APOGEO, 2008.COMPLEMENTARY BOOK:A. PAPOULIS, S. U. PILLAI, PROBABILITY, RANDOM VARIABLES AND STOCHASTIC PROCESSES, 4TH ED., MCGRAW-HILL, 2001.
SIGNAL ANALYSIS:
E. CONTE, LEZIONI DI TEORIA DEI SEGNALI, LIGUORI, 1996,
M. LUISE, G. M. VITETTA, TEORIA DEI SEGNALI, 3RD ED., MCGRAW-HILL, 2009.
COMPLEMENTARY BOOKS:
C. PRATI, , SEGNALI E SISTEMI PER LE TELECOMUNICAZIONI, 2ND ED., MCGRAW-HILL, 2010.
V. OPPENHEIM, A. S. WILLSKY, S. HAMID NAWAB, SIGNALS & SYSTEMS, 2ND ED., PRENTICE-HALL, 1997.