Learning objectives
Knowledge and understanding:
The main goal of this course is to provide the students with A refresher (with a reinforcement tailored towards the upcoming courses) of the key concepts in linear algebra, probability theory and system analysis they should have encountered in their Bachelor studies.
The refreshed mathematical tools will allow them to manage both deterministic and stochastic signals both in continuous- and discrete-time, as well as their linear transformations.
Applying knowledge and understanding:
The abilities to apply the acquired knowledge and understanding are:
PART 1:
- to understand and apply the basic concepts of linear vector spaces and their basic operations.
- to manipulate Hermitian, unitary, and projection matrices. To perform a spectral or singular value matrix decomposition
- to apply basic probabilty theory to solve practical problems
PART 2:
- to apply Fourier and Z transform techniques to solve linear filtering problems
- to calculate the spectral properties of filtered stochastic processes
- to use the complex equivalent lowpass representation of real bandpass stochastic processes
PART 3:
- to develop matlab programs to solve practical problems in linear algebra, probability theory and signal analysis.
Prerequisites
A very basic knowledge of linear spaces, matrix operations, basic probability and basic transform theory applied to linear systems analysis is assumed.
Course unit content
PART 1 (BONONI)
Basics of linear spaces
matrix theory, eigenvalues, eigenvectors, spectral decomposition, singular value decomposition
Introduction to probability theory. Basic concepts: conditioning, total probability, Bayes law
Scalar and muti-dimensional random variables
stochastic processes.
PART 2 (COLAVOLPE)
Wrapup of basic complex-number calculus
Continuous Fourier transform and its properties
Sampling and aliasing
Discrete Fourier transforms and its properties
Two-sided Z transform and its properties
Spectral analysis of stochastic processes: the Wiener Khinchin theorem.
Passband signals: lowpass equivalent.
PART 3 (UGOLINI)
Introduction to Matlab.
Matlab examples in linear algebra and matrix manipulation.
Matlab examples in probability theory and stochastic processes.
Matlab examples in signal analysis.
Full programme
PART 1 (BONONI)
Basics of linear spaces
matrix theory, eigenvalues, eigenvectors, spectral decomposition, singular value decomposition
Introduction to probability theory. Basic concepts: conditioning, total probability, Bayes law
Scalar and muti-dimensional random variables
stochastic processes.
PART 2 (COLAVOLPE)
Wrapup of basic complex-number calculus
Continuous Fourier transform and its properties
Sampling and aliasing
Discrete Fourier transforms and its properties
Two-sided Z transform and its properties
Spectral analysis of stochastic processes: the Wiener Khinchin theorem.
Passband signals: lowpass equivalent.
PART 3 (UGOLINI)
Introduction to Matlab.
Matlab examples in linear algebra and matrix manipulation.
Matlab examples in probability theory and stochastic processes.
Matlab examples in signal analysis.
Bibliography
TEXTBOOKS
[1] A. B. Carlson, Communication Systems: An Introduction to Signals and Noise in Electrical Communication. McGraw-Hill, 1986.
[2] A. Papoulis, Probability, Random Variables and Stochastic Processes. New York, NY: McGraw-Hill, 1991.
[3] A. V. Oppenheim and R. W. Schafer, Discrete-Time Signal Processing. New Jersey: Prentice Hall, 2nd ed., 1999.
Teaching methods
Lectures and exercises (approximately with a ratio 80%-20%)
Assessment methods and criteria
Exams will be oral with possibly written exercises.
Other information
1) Course structure
(each lecture 2 hours)
Part 1 will use 2 lectures per week and will finish at mid-semester.
Part 2 will use 1 lecture per week across the whole semester.
Part 3 will use 2 lectures per week starting from mid-semester.
This scheme will allow coordination of the 3-part contents.
A calendar of lectures for all 3 parts will be posted on the web-learning (Elly) site.
2) only in case COVID emergency persists:
All Classes will be held ALSO online on Teams.
3) Office hours:
You will be able to meet your teachers either physically at their office or remotely via Teams after making an appointment by email. Check the individual units for their official meeting days.
4) teaching material:
It will be posted on the (unique) Elly course website.
2030 agenda goals for sustainable development
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