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 tosolve linear filtering problems
- to calculate the spectral properties of filtered
stochastic processes
- to use the complex equivalent lowpass
representation of real bandpass stochastic
processes
Prerequisites
A very basic knowledge of linear spaces, matrix
operations and basic probability is
assumed.
Course unit content
PART 1 (FOGGI)
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 (PIEMONTESE)
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.
Full programme
PART 1 (FOGGI)
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 (PIEMONTESE)
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.
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)
Both parts will use 1 lecture per week and across the whole semester.
2) Office Hours
FOGGI:
Wednesday 15:00-17:00 (Scientific Complex, Building 2, floor 2).
PIEMONTESE:
Wednesday 14:00-16:00 (Scientific Complex, Building 2, floor 2).
You can also meet your instructor on Teams after making an appointment by email.
3) teaching material:It will be posted on the (unique) Elly course website.
2030 agenda goals for sustainable development
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