System Theory

Lecture 1. Definition of signals, systems and networks. Signal characterization - discrete and continuous time signals. Deterministic and stochastic signals. Special signals - step, impulse signals. Finite time, finite energy signals. Even and odd signals. Dirac delta (impulse) signal.

Lecture 2. System Classification. SISO, SIMO, MISO, MIMO systems. Causality, linearity, time invariance. Systems with memory. Deterministic and stochastic systems.

Lecture 3. Network characterization. Input and output of the netork. Basic operations on discrete time (DT) and continuous time (CT) signals. Time domain description of DT and CT systems. Impulse response, convolution.

Lecture 4. Input-output (BIBO) stability. Stability criteria of LTI systems using impulse response.

Lecture 5. State space representation, system response calculation using matrix functions. System eigenvalues - system response.

Lecture 6. Asymptotic stability. Asymptotic and BIBO stability.

Lecture 7. Engineering problems. Signal flow networks (SFN), signals low graphs. Feedback in networks - negative feedback.

Lecture 8. Sinusoidal signal description - complex phasor representation. System in steady-state. Transfer factor of system.

Lecture 9. Periodic signals - Fourier series. Periodic response of linear systems.

Lecture 10. Signal spectrum - Fourier transform. Band and time limited signals. Windowing of signals. Fourier transform, system transfer characteristics, distortionless signal transmission, Bode plot.

Lecture 11. Signal description in complex frequency domain. Laplace transform. Inverse Laplace transorm. Transfer function.

Lecture 12. Discrete time signal and system description - Z transform, inverse Z transform.

Lecture 13. Sampling of signals. Shannon sampling theorem.

Lecture 14. Control theory introduction - feedback, loop gain, phase margin.

Practicum

Practicum 1. Signal characterization - discrete and continuous time signals. Special signals - step, impulse signals. Even and odd signals. Dirac delta (impulse) signal.

Practicum 2. Impulse response. Convolution. Step response. Multipath channel impulse response.

Practicum 3. Impulse response and step response calculation for LTI systems. System response calculation using convolution.

Practicum 4. State space representation, system impulse response calculation using matrix functions. System eigenvalues - impulse response.

Practicum 5. State space representation, system response calculation.

Practicum 6. Signal flow networks (SFN), signals low graphs. Analogy of electrical, mechanical systems.

Practicum 7. Sinusoidal signal description - complex phasor representation. System in steady-state. Transfer factor of system.

Practicum 8. Periodic signals - Fourier series. Periodic response of linear systems. Realization of transfer characteristics - direct and cascade realization. FIR and IIR systems.

Practicum 9. Signal spectrum - Fourier transform. Band and time limited signals. Fourier transform, system transfer characteristics, distortionless signal transmission, Bode plot.

Practicum 10. Signal description in complex frequency domain. Laplace transform. Inverse Laplace transorm. Transfer function.

Practicum 11. Discrete time signal and system description - Z transform, inverse Z transform.

Practicum 12. Analysis in complex frequency domain - signal flow graph, state space model.

Practicum 13. Sampling of signals. Shannon sampling theorem.

Practicum 14. Simple control system model and analysis. Feedback, loop gain, phase margin