### Signal Theory

#### Signal Theory - BE5B31TES

 Credits 5 Semesters Summer Completion Assessment + Examination Language of teaching English Extent of teaching 2P+2C
Annotation
Course explains basic terms and methods for representation and analysis of continuous-time and discrete-time signals and systems. Representations of signals and systems in continuous and discrete-time is developed for time and frequency domains through the Fourier transform. Bode and Nyquist plots as well as the Laplace transform and the Z-transform are used for stability analysis of feedback systems. Linearization by small-signal analysis is introduced. Filtering and filter design, sampling and interpolation are discussed. Analog and pulse modulation fundamentals and their characteristics are introduced. Characteristics of band-pass signals are discussed, including Hilbert transform and complex envelope. Fundamentals of random signals and their parameters are reviewed.
Course outlines
1. Introduction, classification of signals, basic continuous (CTD) and discrete time domain (DTD) signals, basic time domain characteristics, energy, power. Complex exponential.
2. Correlation function, special CTD and DTD signals, Dirac delta, unit impulse, unit step, rectangular signal, sampling function.
3. Systems, their classification and properties, CTD and DTD linear time-invariant systems (LTI), convolution integral and convolution sum. System interconnection and eigensignals of LTI systems.
4. Frequency analysis of signals, Fourier series and Fourier transform.
5. Discrete Fourier transform DFT and its properties. Frequency analysis of signals, relationships between transforms FT, FS, DtFT, DtFS and DFT.
6. Systems described by differential and difference equations. State space representation.
7. Properties of Laplace transform and Z-transform and their application, system function, BIBO and asymptotic stability. Examples for 1st and 2nd order systems.
8. Frequency domain analysis of LTI systems, frequency response, Bode and Nyquist plots.
9. Linearization of nonlinear system by small-signal analysis.
10. Signal sampling and interpolation. CT system discretization.
11. Ideal filters, introduction to CTD and DTD filter design.
12. Band-pass signals, analytic signal, complex envelope, sampling of band-pass signals.
13. Analog and pulse modulation fundamentals.
14. Random variable, basic description, random process, ergodicity, white noise.
Literature
1. A. V. Oppenheim, A. S. Wilsky with S.H. Nawab: Signals and Systems, Prentice-Hall, Second Edition, 1997.
2. Hwei P. Hsu: Signals and systems. Schaums outlines, 3rd edition, Mc Graw Hill, 2014
3. J. R. Buck, M. M. Daniel, A. C. Winter: Computer Explorations in Signals and Systems Using MATLAB, Prentice-Hall, 1997.