Acquisition of basic theoretical knowledge of signal theory, including the definition of a signal, its representation in the time and frequency domains, and the Fourier transform; knowledge of signal sampling and quantisation techniques, and the related issues of aliasing and noise; theoretical knowledge of fundamental notions of probability theory and random processes, for the representation of signals as their realisations; enabling the student to analyse and process biomedical signals using the signal theory methodologies.
Curriculum
teacher profile teaching materials
Axiomatic theory of probability. The axioms of probability. Bayes' theorem. Random variables. Distribution and probability density function. Mean, variance, moments, covariance matrix. Characteristic function. Functions of one random variable. Multiple random variables: joint distributions. Conditional distributions. Gaussian random variables: univariate and multivariate. Bernoulli random variable. Stochastic processes: general concepts. Stationary processes. Ergodic processes and related theorems. Parametric stochastic processes. Linear and non-linear transformation of stochastic ergodic processes. Continuous-time random processes; gaussian process, armonic process.
Probability, Random Variables, and Stochastic Processes, Athanasios Papoulis, S. Unnikrishna Pillai, McGraw-Hill 2002
Fruizione: 20810334 TEORIA DEI SEGNALI in Ingegneria elettronica L-8 CAMPISI PATRIZIO
Programme
Message and signal definition. Signal representations. Generalized Fourier Representation. Cross and auto-correlation function: definition and properties. Linear transformations. Linear and time-invariant systems. I/O relations: convolution integral and its properties. Fourier series expansion. Fourier Transform. Parseval and Wiener theorems. Energy and power spectral density. Limited bandwidth signals. Sampling theorem. Sub-sampling effects. Hilbert transform. Analytical signal, complex envelope and low-frequency components of a band-pass signal. Bandwidth limited signals linear transformations and their samples relations.Axiomatic theory of probability. The axioms of probability. Bayes' theorem. Random variables. Distribution and probability density function. Mean, variance, moments, covariance matrix. Characteristic function. Functions of one random variable. Multiple random variables: joint distributions. Conditional distributions. Gaussian random variables: univariate and multivariate. Bernoulli random variable. Stochastic processes: general concepts. Stationary processes. Ergodic processes and related theorems. Parametric stochastic processes. Linear and non-linear transformation of stochastic ergodic processes. Continuous-time random processes; gaussian process, armonic process.
Core Documentation
Roberto Cusani- Teoria dei Segnali - Edizioni EfestoProbability, Random Variables, and Stochastic Processes, Athanasios Papoulis, S. Unnikrishna Pillai, McGraw-Hill 2002
Attendance
Attendance is not mandatory but recommendedType of evaluation
During the course, ongoing tests will assess the student's preparation. There will be two written tests: a) the first aimed at assessing the student's ability to analyze b) the second aimed at evaluating the student's theoretical knowledge. teacher profile teaching materials
Axiomatic theory of probability. The axioms of probability. Bayes' theorem. Random variables. Distribution and probability density function. Mean, variance, moments, covariance matrix. Characteristic function. Functions of one random variable. Multiple random variables: joint distributions. Conditional distributions. Gaussian random variables: univariate and multivariate. Bernoulli random variable. Stochastic processes: general concepts. Stationary processes. Ergodic processes and related theorems. Parametric stochastic processes. Linear and non-linear transformation of stochastic ergodic processes. Continuous-time random processes; gaussian process, armonic process.
Probability, Random Variables, and Stochastic Processes, Athanasios Papoulis, S. Unnikrishna Pillai, McGraw-Hill 2002
Fruizione: 20810334 TEORIA DEI SEGNALI in Ingegneria elettronica L-8 CAMPISI PATRIZIO
Programme
Message and signal definition. Signal representations. Generalized Fourier Representation. Cross and auto-correlation function: definition and properties. Linear transformations. Linear and time-invariant systems. I/O relations: convolution integral and its properties. Fourier series expansion. Fourier Transform. Parseval and Wiener theorems. Energy and power spectral density. Limited bandwidth signals. Sampling theorem. Sub-sampling effects. Hilbert transform. Analytical signal, complex envelope and low-frequency components of a band-pass signal. Bandwidth limited signals linear transformations and their samples relations.Axiomatic theory of probability. The axioms of probability. Bayes' theorem. Random variables. Distribution and probability density function. Mean, variance, moments, covariance matrix. Characteristic function. Functions of one random variable. Multiple random variables: joint distributions. Conditional distributions. Gaussian random variables: univariate and multivariate. Bernoulli random variable. Stochastic processes: general concepts. Stationary processes. Ergodic processes and related theorems. Parametric stochastic processes. Linear and non-linear transformation of stochastic ergodic processes. Continuous-time random processes; gaussian process, armonic process.
Core Documentation
Roberto Cusani- Teoria dei Segnali - Edizioni EfestoProbability, Random Variables, and Stochastic Processes, Athanasios Papoulis, S. Unnikrishna Pillai, McGraw-Hill 2002
Attendance
Attendance is not mandatory but recommendedType of evaluation
During the course, ongoing tests will assess the student's preparation. There will be two written tests: a) the first aimed at assessing the student's ability to analyze b) the second aimed at evaluating the student's theoretical knowledge.