FUNDAMENTALS OF SIGNAL ANALYSIS

Flaminio FERRARA FUNDAMENTALS OF SIGNAL ANALYSIS

0612400056
DIPARTIMENTO DI INGEGNERIA INDUSTRIALE
EQF6
ELECTRONIC ENGINEERING
2021/2022

OBBLIGATORIO
YEAR OF COURSE 2
YEAR OF DIDACTIC SYSTEM 2018
SECONDO SEMESTRE
CFUHOURSACTIVITY
2FONDAMENTI DI ANALISI DEI SEGNALI MODULO DI (FONDAMENTI DI ANALISI DEI SEGNALI)
330LESSONS
1FONDAMENTI DI ANALISI DEI SEGNALI MODULO DI (FONDAMENTI DI ANALISI DEI SEGNALI)
660LESSONS
Objectives
THE COURSE IS METHODOLOGICAL AND AIMS TO PROVIDE BASIC TOOLS AND METHODS FOR DESCRIBING AND ANALYSING NON-DETERMINISTIC PHENOMENA AND TO INTRODUCE THE MAIN SIGNAL ANALYSIS AND PROCESSING TECHNIQUES, WITH EMPHASIS ON THE TIME-FREQUENCY DUALITY. THE PRESENTED TOOLS AND METHODS HAVE WIDESPREAD APPLICATION IN THE ELECTRONIC AND TELECOMMUNICATION ENGINEERING.

KNOWLEDGE AND UNDERSTANDING
AT THE END OF THE COURSE THE STUDENT, IN HIS CULTURAL BAGGAGE, HAS:
THE UNDERSTANDING THE BASIC TERMINOLOGY USED IN PROBABILITY THEORY;
THE KNOWLEDGE OF RANDOM VARIABLES MODELS AND RELATED TRANSFORMATIONS, AS WELL AS NOTIONS OF STOCHASTIC PROCESSES AND COMBINATORIAL CALCULUS;
THE KNOWLEDGE OF SIGNAL PROCESSING TECHNIQUES IN THE TIME AND FREQUENCY DOMAINS, FOR CONTINUOUS AS WELL AS FOR DISCRETE TIME SIGNALS;
THE KNOWLEDGE OF LINEAR SYSTEMS ANALYSIS IN THE TIME AND FREQUENCY DOMAINS;
THE KNOWLEDGE OF THE TECHNIQUES TO PERFORM THE DIGITAL-TO-ANALOG CONVERSION;
NOTIONS ON THE DISCRETE FOURIER TRANSFORM

APPLIED KNOWLEDGE AND UNDERSTANDING
AT THE END OF THE COURSE THE STUDENT IS ABLE:
TO MODEL AND ANALYZE RANDOM EVENTS, IN CONNECTION TO REAL-WORLD PHENOMENA;
TO CHARACTERIZE SYSTEMS IN TERMS OF INPUT/OUTPUT RELATIONSHIPS, ESPECIALLY AS REGARDS LTI SYSTEMS;
TO DESIGN AND PERFORM SIMPLE SIGNAL PROCESSING TECHNIQUES, IN CONNECTION TO SIGNALS OF PRACTICAL INTEREST;
TO PERFORM SAMPLING AND RECONSTRUCTION OF AN ANALOG SIGNAL;
TO PERFORM SIMPLE SIGNALS PROCESSINGS;
TO APPLY THE BASIC CONCEPTS OF ANALOG/DIGITAL SIGNAL CONVERSION.

PERSONAL JUDGMENTS
THE STUDENT IS ABLE:
TO SELECT THE MOST APPROPRIATE METHODS TO ANALYSE A RANDOM PHENOMENON;
TO SELECT THE BEST REPRESENTATIONS OF THE SIGNALS AND SYSTEMS IN ORDER TO STUDY THEIR INTERACTION;
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;
BEING ABLE TO EXPOSE THE TOPICS OF SIGNAL ANALYSIS IN A CLEAR AND CONCISE MANNER, MAKING USE OF AN ADEQUATE SCIENTIFIC TERMINOLOGY AND OF THE TOOLS OF THE MATHEMATICAL AND GRAPHIC REPRESENTATION OF THE PHENOMENA EXPOSED.

LEARNING SKILLS
BEING ABLE TO APPLY THE ACQUIRED KNOWLEDGE TO DIFFERENT CONTEXTS FROM THOSE PRESENTED DURING THE COURSE;
BEING ABLE 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 4/4/0)
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 5/4/0)
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 10/5/0)
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 8/2/0)
Teaching Methods
THE COURSE INCLUDES THEORETICAL LESSONS (60 HOURS) AND CLASSROOM EXERCISES (30 HOURS) ON THE TOPICS PROPOSED DURING THE THEORETICAL LESSONS.
DURING THE LESSONS THE TOPICS COVERED ARE PRESENTED WITH GRADUALLY INCREASING THEIR COMPLEXITY. IN THE EXERCISES, THE STUDENT IS ASKED TO SOLVE PROBLEMS RELATED TO THE TOPICS COVERED IN THE THEORETICAL LESSONS. THE RESOLUTION METHOD CONSISTS OF UNDERSTANDING THE PROBLEM, PLANNING THE SOLUTION, AND FINALLY THE RESOLUTION ITSELF. DURING THIS LAST STEP, THE HABIT OF EVALUATING THE REASONABLENESS OF THE RESPONSE AND VERIFYING ITS CONSISTENCY IS PROMOTED.
Verification of learning
THE FINAL EXAM IS AIMED TO EVALUATE 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 EVALUATION GRADE RANGES FROM 18/30 TO 30/30 CUM LAUDE. THE FINAL EXAM CONSISTS OF A WRITTEN TEST AND AN ORAL INTERVIEW. TO ACCESS THE ORAL EXAM, THE WRITTEN TEST MUST BE PASSED WITH A MINIMUM GRADE OF 18/30. DURING THE COURSE IT IS POSSIBLE TO PERFORM TWO PARTIAL EXONERATIVE WRITTEN TESTS, RESPECTIVELY AFTER ONE HALF OF THE LESSONS AND AT THE END OF THE COURSE.
THE WRITTEN TEST AIMS TO ASSESS THE ABILITY TO SOLVE PROBLEMS ABOUT THE TOPICS PRESENTED DURING THE COURSE. IT CONSISTS OF AT LEAST TWO EXERCISES: THE FORMER ON ANALYSIS OF SIGNALS AND SYSTEMS BOTH IN TIME AND FREQUENCY DOMAINS, THE LATTER ON THE PROBABILITY AND COMBINATORIAL CALCULUS
THE ORAL INTERVIEW AIMS TO VERIFY THE ACQUIRED KNOWLEDGE ALSO ON THE TOPICS NOT COVERED BY THE WRITTEN TEST AND, EVENTUALLY, TO PLUG THOSE GAPS FOUND IN THE WRITTEN TEST.
TO PASS THE EXAM (MINIMUM GRADE 18/30) THE STUDENT WILL HAVE TO DEMONSTRATE, AS MUCH AS POSSIBLE, TO BE ABLE TO ANALYSE A SIGNAL AND KNOW HOW TO SET THE SOLUTION TO A PROBLEM OF SIGNAL PROCESSING.
THE MAXIMUM GRADE (30/30) IS ATTRIBUTED WHEN THE STUDENT DEMONSTRATES A COMPLETE AND IN-DEPTH KNOWLEDGE OF THE VARIOUS TOPICS COVERED IN THE THEORETICAL LESSONS AND IS ABLE TO TREAT, ACCURATELY AND EFFICIENTLY, SIGNALS (DETERMINISTIC AND RANDOM) AND LTI SYSTEMS BOTH IN THE TIME DOMAIN (CONTINUOUS OR DISCRETE) AND IN THE FREQUENCY DOMAIN.
MOREOVER, TO BE AWARDED CUM LAUDE, IT WILL BE TAKEN INTO ACCOUNT:
THE QUALITY OF ORAL EXPOSITION, IN TERMS OF THE USE OF AN APPROPRIATE SCIENTIFIC LANGUAGE;
THE ABILITY OF CROSS-CORRELATION BETWEEN THE DIFFERENT TOPICS OF THE COURSE AND, WHEN POSSIBLE, WITH THOSE OF OTHER DISCIPLINES;
THE DEMONSTRATED PERSONAL JUDGMENT.
Texts
S. M. ROSS, PROBABILITÀ E STATISTICA PER L’INGEGNERIA E LE SCIENZE, APOGEO, 2008.
A. PAPOULIS, S. U. PILLAI, PROBABILITY, RANDOM VARIABLES AND STOCHASTIC PROCESSES, 4TH ED., MCGRAW-HILL, 2001.
E. CONTE, LEZIONI DI TEORIA DEI SEGNALI, LIGUORI, 1996,
M. LUISE, G. M. VITETTA, TEORIA DEI SEGNALI, 3RD ED., MCGRAW-HILL, 2009.
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
More Information
FRONTAL LESSONS ARE PROVIDED. ITALIAN IS THE LANGUAGE OF THE COURSE
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