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Signal Theory

Maurizio LONGO Signal Theory

0612700010
DIPARTIMENTO DI INGEGNERIA DELL'INFORMAZIONE ED ELETTRICA E MATEMATICA APPLICATA
EQF6
COMPUTER ENGINEERING
2015/2016

OBBLIGATORIO
YEAR OF COURSE 2
YEAR OF DIDACTIC SYSTEM 2012
SECONDO SEMESTRE
CFUHOURSACTIVITY
1ELEMENTI DI PROBABILITÀ
660LESSONS
2ANALISI DEI SEGNALI
660LESSONS


FABIO POSTIGLIONE21 T Curriculum
MAURIZIO LONGO2 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.
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 OF 60 HOURS EACH.

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 6/3/0)

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 10/5/0)

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 10/5/0)

INTRODUCTION TO STOCHASTIC PROCESSES. DEFINITION OF A STOCHASTIC PROCESS AND ITS PROPERTIES: STATIONARITY, WEAK-SENSE STATIONARITY, AND ERGODICITY. GAUSSIAN PROCESSES. MARKOVIAN PROCESSES AND MARKOV CHAINS. (HOURS: LESSONS/EXERCISES/LABORATORY 6/3/0)


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. ARMA SYSTEMS. (HOURS: LESSONS/EXERCISES/LABORATORY 16/8/0)

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: T/N CONVERSION AND QUANTIZATION. DISCRETE-TIME PROCESSING OF CONTINUOUS-TIME SIGNALS AND IMPULSE INVARIANCE. DOWNSAMPLING. (HOURS: LESSONS/EXERCISES/LABORATORY 12/6/0)

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. NOTIONS OF SPECTRAL ANALYSIS. EVALUATION OF SPECTRA AND SIMPLE EXAMPLES OF SPECTRAL ANALYSIS. (HOURS: LESSONS/EXERCISES/LABORATORY 10/5/0)

TOTAL HOURS: 120 (HOURS: LESSONS/EXERCISES/LABORATORY 80/40/0)
Teaching Methods
THE COURSE INCLUDES THEORETICAL LESSONS AND CLASSROOM EXERCISES. SOME CLASSROOM EXERCISES CAN BE SOLVED BY USING MATLAB DURING THE LABORATORY ACTIVITY; THE ROUTINES ARE THEN DISTRIBUTED TO THE STUDENTS.
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, SUCH AS: 1) PROBABILITY AND COMBINATORIAL CALCULUS; 2) ANALYSIS OF SIGNALS AND SYSTEMS BOTH IN TIME AND FREQUENCY DOMAINS; 3) SAMPLING OF TIME-CONTINUOUS SIGNALS. THE WRITTEN TEST IS EVALUATED ON THE BASIS OF THE CORRECTNESS OF THE APPROACH AND RESULTS ACCORDING TO THE FOLLOWING SCALE: “EXCELLENT”, “GOOD”, “FAIR”, “SUFFICIENT”, “BARELY SUFFICIENT”, “INSUFFICIENT”. THE “INSUFFICIENT” SCORE IMPLIES THE WRITTEN TEST REPETITION. THE “BARELY SUFFICIENT” SCORE CORRESPONDS TO A LAME WRITTEN TEST AND IMPLIES THAT THE STUDENT SHOULD MAKE UP THE PROBLEMS OF HIS/HER TEST DURING THE ORAL INTERVIEW.
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. AN ORAL INTERVIEW THAT IS NOT CONSIDERED SUFFICIENT IMPLIES THE REPETITION OF THE WRITTEN TEST, TOO.
C) CONCERNING THE FINAL SCORE, EXPRESSED OUT OF THIRTY, THE WRITTEN TEST CONTRIBUTES FOR 40% WHILE THE ORAL INTERVIEW FOR 60%. FULL MARKS WITH DISTINCTION MAY BE GIVEN TO STUDENTS WHO DEMONSTRATE THAT THEY CAN APPLY THE ACQUIRED KNOWLEDGE WITH CONSIDERABLE AUTONOMY TO EXERCISES AND THEORETICAL ISSUES.

DURING THE CLASSROOM EXERCISES, SOME (OPTIONAL) WRITTEN TESTS (HENCEFORTH CLASSROOM TESTS) ARE PROVIDED TO THE STUDENTS, CONTAINING BOTH EXERCISES AND QUESTIONS ABOUT THEORETICAL ISSUES, IN ORDER TO EVALUATE THE ACQUIRED KNOWLEDGE OF THE STUDENTS AT THAT MOMENT. ALL THE CLASSROOM TESTS BUT THE LAST ONE ARE EVALUATED ACCORDING TO THE SCALE PROVIDED IN A). IT IS POSSIBLE TO PARTICIPATE TO THE LAST CLASSROOM TEST IF ALL THE PREVIOUS TEST HAVE BEEN CREDITED WITH A SCORE OF “BARELY SUFFICIENT” OR HIGHER. A POSITIVE RESULT OF THE LAST CLASSROOM TEST PROVIDES A FINAL SCORE, EXPRESSED OUT OF THIRTY. THE STUDENT CAN ALSO CHOOSE TO HAVE AN ORAL INTERVIEW: IN THAT CASE, THE SCORE OF CLASSROOM TESTS IS CONSIDERED AS THAT OBTAINED BY A WRITTEN TEST AND THE ORAL INTERVIEW FOLLOWS THE RULES LISTED IN B) AND C).
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:
V. OPPENHEIM, A. S. WILLSKY, S. HAMID NAWAB, SIGNALS & SYSTEMS, 2ND ED., PRENTICE-HALL, 1997.
V. K. INGLE, J. G. PROAKIS, DIGITAL SIGNAL PROCESSING USING MATLAB, 3RD ED., CENGAGE LEARNING, 2011.
More Information
FRONTAL LESSONS ARE PROVIDED. ITALIAN IS THE OFFICIAL LANGUAGE.
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