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Professor
DANILO PANI (Tit.)
Period
Second Semester 
Teaching style
Convenzionale 
Lingua Insegnamento
 



Informazioni aggiuntive

Course Curriculum CFU Length(h)
[70/75]  BIOMEDICAL ENGINEERING [75/00 - Ord. 2014]  PERCORSO COMUNE 5 50

Objectives

The main objective of the Electronic Signal Processing course is to provide the instruments needed to understand the fundamental principles of signal analysis and processing. This means that the students are required to learn the methods and, moreover, the fundamentals such methods are based on, in order to be able to easily extend to more complex problems related to the signal analysis and processing what they have learnt, in further studies and in the professional activity. Signal analysis and processing is a fundamental aspect of information engineering.

Acquiring knowledge and understanding. At the end of the course it is expected that the students know:
- the time and frequency representation domains, the main techniques allowing to switch between the them, and the basic operations they can apply in such domains, beyond important characteristics in the two domains of some biomedical signals
- the issues related to the correct sampling and quantization of signals
- the basic concepts related to signal filtering, both in the discrete and continuous time, and some tools that can be used to analyze digital filters and to filter biosignals
- the fundamentals of probability theory and are able to deal with random variables (continuous and discrete)
- the Matlab language fundamentals (variables, indexing, operations, scripts and functions).

Applying knowledge and understanding. At the end of the course it is expected that the students are able to:
- correctly operate in both time and frequency domain on unidimensional signals of different nature
- choose adequate sampling and quantization parameters for a given application
- analyze the basic characteristics of a digital filter, identifying pros and cons, and to adequately apply it to biomedical signals
- apply the basic theoretical concepts of probability theory to the analysis of random variables in simple problems, and as a basis for the study of stochastic processes
- are able to write Matlab scripts and functions for basic data processing, and to perform simple Matlab processing on biosignals.

Making judgments. At the end of the course it is expected that the students are able to autonomously identify and evaluate the data needed to identify and solve technical/scientific problems, related to biomedical signals analysis and processing, by proposing possible ways for the signal acquisition (sampling and quantization), analysis (representation domain and the related issues) and enhancement (identification of a simple filtering strategy).

Communication. At the end of the course it is expected that the students have acquired the correct use of language, related to the course contents, so to be able to clearly communicate without misunderstandings with a speaker with technical skills, and to convey the main concepts to a speaker without technical skills.

Learning skills. At the end of the course it is expected that the students have the skills and methods needed to study further autonomously or in Master studies, improving their skills about stochastic processes and advanced biomedical signal processing. Particularly, the students will be able to interpret the information they have in order to identify and fill the gaps in their skills by means of a focused study, not only theoretic, but also including the technical documentation available for a specific problem.

Prerequisites

There are prerequisites enforced by the course of study: being a course of the II year, it is required to have already passed the exams of Physics I and Mathematical Analysis I.

It is also required a familiarity with integral calculus, even in two dimensions. The familiarity with the elementary physics concepts and the wave theory ease the understanding of several parts of the course. Furthermore, the knowledge of the Fourier's Series and Transform, at mathematical level, is important since the course does not analyze in depth such aspects. In order to fruitfully attend the Matlab laboratory, the knowledge of a sequential imperative programming language (e.g.: C) and its characteristics is strongly recommended.

Contents

1. Fundamentals of probability theory and random variables (14 hours)
1.a (5 hours) Introduction to signals. Deterministic and random signals. Elements of combinatorial calculus (permutations, dispositions, combinations). Fundamentals of probability theory (probability definition, events and sample space. Conditional probability, independent events, Bayes formula and total probability law).
1.b (9 hours) Discrete and continuous random variables. Cumulative distribution function, Probability density function (for discrete and continuous random variables). Expected values and moments. Chebyshev's inequality. Quantiles, mode and median. Uniform, gaussian, binomial, Poisson distributions. Joint distributions. Covariance and correlation. Short introduction to random processes.

2. Methods and tools for signals analysis and processing (21 hours)
2.a (7 hours) Time-domain signals properties. Basic operations in the time domain: delay, mirroring, sum and product, convolution. Discrete convolution. Mean value, power and energy of a signal. Power and energy signals. Fundamental signals: step, impulse, rectangular pulse and complex exponentials. Phasors representation, line single-sided spectrum, line double-sided spectrum. Continuous time Fourier Series and Transform. Parseval's and Rayleigh's theorems. Properties of the continuous-time Fourier Transform, reciprocal spreading and modulation.
2.c (8 hours) Fourier Transform of a periodic signal and of a pulse train. Sampling theorem and aliasing. Normalized frequency. Quantization. Discrete time Fourier Transform (DTFT) and its properties, limits hampering its implementation. Discrete Fourier Transform (DFT), frequency resolution. Uncertainty principle and basic motivations of the Short Time Fourier Transform (STFT). Spectral leakage and hints on the time windowing. Examples on biomedical signals.
2.c (6 hours) LTI systems in the continuous time and in the discrete time. Series and parallel of systems. Stability and causality. Transfer function. Ideal filters. Group delay and phase distortion. Examples of real filters and hints on the main differences with respect to the ideal ones. FIR and IIR filters. Z-transform. Analysis and design in the Z domain.
2.c (6 hours) LTI systems in the continuous time and in the discrete time. Series and parallel of systems. Stability and causality. Transfer function. Ideal filters. Group delay and phase distortion. Examples of real filters and hints on the main differences with respect to the ideal ones. FIR and IIR filters. Z-transform. Analysis and design in the Z domain.

3. Lab (Matlab) (15 hours). Lab experiences with Matlab.

Teaching Methods

The course is based on a traditional teaching approach (lectures) joined to a significant amount of computer lab experiences and exercises on the all the topics in the program (exercises assigned and corrected in the classroom + interactive exercise sessions in the classroom). Lectures exploit a set of slides extracted from the lecture notes (available on the course website), complemented by dashboard explanations when relevant mathematical and conceptual steps or exercises are present. With the students’ collaboration, lectures aim to be interactive, stimulating the active participation of the students in the identification of possible solutions to new problems proposed in the lecture, in the creative solving of exercises, either on paper or with the computer, in the immediate application (exercise) of the concepts learnt during the lectures, also fixing the theoretical concepts by using Matlab in the lab.

During the lab experiences it is possible to deeply understand, through the direct experience, the theoretical concepts while learning the Matlab language and applying it to simple concrete exercises. Exercises and labs include a significant amount of explanation of the concepts behind the specific problem the students are dealing with.

In order to preserve the students' time for the individual study, there are no programmed tutoring activities. Nevertheless, the students can ask for more exercitations and tutoring activities (with the lecturer or with the tutor), depending on their needs.

An approximated division of the hours between the different activities is provided hereafter:
Lectures: 35 hours
Exercises and computer lab: 15 hours

Verification of learning

The exam consists of a written part (3 hours) and an optional oral test on a different day (which can also compromise the final result of the exam, and the two parts, written and oral, do not concur in the definition of the final score arithmetically). The written exam is usually composed of four exercises aiming to verify if the expectations of achievements and abilities have been acquired, involving the largest part of the program at different detail levels and including “mathematical” exercises, theoretical questions and Matlab code for simple applications, engineering problems at the student’s level, not requiring the trivial application of a formula but rather the context analysis in order to identify a correct solution.

The exam rating is objective, defined on the basis of the percentage of correctness of every single answer (to which is associated a defined score, unknown to the student, as a function of the difficulty level). The written exam is rated so that, even without an oral test, the best students can achieve the maximum score (30/30L). In order to pass the exam, it is mandatory that the Matlab exercise marks a sufficient score.

Students are motivated to go further the simple study aimed at the resolution of a given exercise, challenging themselves with problems requiring the ability to move from the abstract theoretical concept to its practical application. Students are required to motivate their answers, either by showing the mathematical steps carried out to obtain the final answer or b means of a clear comment. Such an approach makes it possible to assess the students’ knowledge and their capability to apply it to simple problems, at their level, but also allows evaluating the communication skills and the capability to make judgments.

During the semester, 3 short quizzes including 10 questions maximum are administered and concur to the definition of a score that is added to the one achieved in the written exam, limitedly to the first two exam dates of first exams session. The maximum score that can be acquired is 3 points.

The number of exams per year is defined according to the Faculty regulations. Extra dates can be requested to the lecturer by outside prescribed time students, for motivated reasons.

Texts

Lecture notes, freely provided to the students on the course web pages, updated every year.

Matlab Laboratory. It is strongly suggested to use this book:
* Rudra Pratap - Getting Started with MATLAB - Oxford University Press- ISBN: 9780199731244

For a deeper understanding of the theoretical parts, it is possible to have a look to the following textbooks:

Signals and systems (all the signals and systems books usually have a section on probability, which is also useful)
* Oppenheim-Willsky-Hamid - Signals & Systems (2nd edition) - Prentice Hall - ISBN 0-13-561175-9

* Oppenheim-Schafer- Discrete-Time Signal Processing - 3nd Edition - Prentice-Hall Signal Processing Series - ISBN 978-0131988422

* Carlson-Crilly- Communication Systems 5th edition - McGraw-Hill - ISBN 9788838606618

* Smith - The Scientist and Engineer's Guide to Digital Signal Processing - 2nd edition - California Technical Publishing - ISBN 0-9660176-6-8 (free download from http://www.dspguide.com/ chapter-wise, or on-line readable, but less useful than the others)

Probability
* Mood-Greybill-Boes - Introduzione alla statistica - Terza edizione - McGraw Hill ISBN 9788838606618

More Information

The teaching material (lecture notes) has been used by the lecturer to create the slides projected during the lecture. Since the last ones are too concise, they are not provided to the students. It is of paramount importance that the students take their own notes during the lecture, using them as a reference to cross check with the official material during their home study. Exercises are also provided to the students; they are corrected in the classroom during the lectures. Some exam exercises are also made available, along with the Matlab exercises performed in the lab and the associated material. Furthermore, an exam simulation is also proposed. There, the students can use their own material and cooperate each other to solve the assigned problems. All the material is in the pdf format (except the lab material), always protected by a password and not editable, to respect the copyright laws. The password is provided to the students during the first lectures.

Matlab licenses for students have been acquired by the University of Cagliari. Instructions to obtain your own copy of Matlab with the Campus license are available in the News section of the course website.

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