# Popis předmětu - BE5B31TES

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BE5B31TES Signal Theory
Role:PV Rozsah výuky:2P+2C
Katedra:13131 Jazyk výuky:EN
Garanti:Bortel R. Zakončení:Z,ZK
Přednášející:Bortel R. Kreditů:5
Cvičící:Bortel R. Semestr:L

Webová stránka:

https://moodle.fel.cvut.cz/courses/BE5B31TES

Anotace:

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.

Osnovy přednášek:

 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.

Osnovy cvičení:

Literatura:

 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.