THEORY OF SIGNALS
*) Knowledge and understanding: Knowledge of the mathematical foundations for the representation and analysis of continuous-time and discrete-time signals, in time and frequency domain. Knowledge of the input-output relations for continuous-time and discrete-time time-invariant linear systems.
*) Applied knowledge and understanding: analyze a signal in time domain and in frequency domain; calculate the output of a linear time invariant system corresponding to an assigned input signal.
*) Making judgments: developing the ability of critically and synergistically using the various instruments for signal analysis and for calculating the output of systems.
*) Communication skills: Ability to present the topics in a clear and rigorous technical-scientific point of view. Knowing how to submit an application solution in a simple and comprehensive.
*) Learning skills: knowing how to integrate knowledge from various sources for the purpose of deepening. Knowing how to use the concepts covered for applications other than those disclosed.
There are no mandatory prerequisites.
Recommended prerequisites: Calculus I and II.
Definition of signals and systems. Deterministic and stochastic signals. Signal classification. Analog and digital signals. Classification of systems. Operations on signals. Transformations of the dependent and independent variable. Combination of elementary operations. Derivation, integration, first difference and sum. (8 hours)
Synthetic characterization of signals. Extent and duration. Signals of strictly limited. practically limited and not limited duration. Periodic signals. Area and time average. Alternating component. Energy and power signals. Mutual energy. RMS value. Relations between energy and power signals. Mutual power. Measure in dB of power and energy. Auto and mutual correlation functions of energy signals and power signals. (8 hours)
Properties od continuous-time and discrete-time systems. Input-output relationship. Interconnection of systems. Properties of the systems. Dispersivity. Causality. Invertibility. Time invariance. Stability. Linearity. LTI systems. Input-output relationship for a LTI system and impulse response. Convolution. Properties of convolution. Step response. Properties of the impulse response. Dispersivity. Causality. Invertibility. Stability. Frequency response of a LTI system. Response to a phasor TC and TD of a LTI system. Response to a sinusoid of a LTI system. (10 hours)
Fourier series for TC signals and conditions fi convergence. Reconstruction of a periodic signal with a finite number of harmonics. Fourier series for TD signals (DFS). Main properties of the Fourier series and the DFS. Linearity. Hermitian symmetry. Equality of Parseval. Response of an LTI system to a periodic signal. Frequency selectivity of the LTI and ideal filter systems. (10 hours)
Fourier transform for TC signals. Fourier transform for TD signals. Propertie of the Fourier transform. I-O relationship in the frequency domain. Convolution property. Existence and invertibility of the Fourier transform. Transient signals. spectral extension and bandwidth of a signal. Strictly band-limited, practically lband-imited and not band-limited signals- Properties of the Fourier transform. The dependent variable transformations. Transformations of the independent variable. Derivation and integration. Fourier transform of a TC periodic signal. Fourier transform of a TD periodic signal.S spectral extension and bandwidth of a periodic signal. Relations between series and Fourier transform. Energy spectral density and power spectral density for TC and TD signals, periodic and aperiodic. (18 hours)
Characterization and properties of LTI systems in the frequency domain. Separation of signals by filtering. Interconnections of LTI systems in the frequency domain. Properties of the frequency response of an LTI system. Instantaneity. Stability. Causality. Non-linear systems. Frequency response of non-linear systems. distorting systems and equalization.(10 hours)
Sampling and A / D conversion and D/A. Sampling and ideal interpolation. Sampling theorem. Ideal interpolation. Aliasing. Sampling and interpolation in practice. Sampling of non band limited signals. Non ideal Interpolation. (8 hours)
Definition of signals and systems. Classification of signals and systems (2 hours).
Operations on signals. Transformations of the dependent and independent variable (4 hours).
Synthetic characterization of signals. Energy and mutual power. Auto- and mutual correlation functions (10 hours).
Properties of systems. Relation i-u. and Interconnection of systems. (4 hours).
LTI Systems. i-u relationship and impulse response. (9 hours).
Frequency response of an LTI system. (3 hours).
Fourier series for TC signals. DFS. Main properties. Parseval Equality. (8 hours).
Fourier transform for TC and TD signals. Properties. (8 hours)
Bandwidth of a signal. Bandwidth of a periodic signal. Ideal filters (6 hours).
Relations between Fourier series and Fourier transform. Energy Spectral Density and Power Spectral Density (4 hours).
Properties of LTI systems in the frequency domain. Equalization. (8 hours).
Sampling and A/D and D/A conversion. Ideal sampling. Sampling theorem. (6 hours).
Classroom lectures and exercises.
Giacinto Gelli, Francesco Verde, ‘Segnali e sistemi’, Liguori Ed., 2014.
The objective of the examination test is to verify the level of achievement of the training objectives indicated above.
The examination is divided into 2 parts which take place on different days:
• A written test that aims to assess the level of understanding and the ability to use the instruments studied during the course; to pass the test it is necessary to acquire at least 15 points out of 30. The test time is 2 hours; books and notes cannot be consulted.
• An oral test in which the ability to connect and compare different aspects dealt with during the course will be evaluated; to pass the test it is necessary to acquire at least 18 points out of 30.
The final score is the average of the two scores. If the total mark is less than 18, all two tests must be repeated.