# Subject description - BE5B31TES

Summary of Study | Summary of Branches | All Subject Groups | All Subjects | List of Roles | Explanatory Notes               Instructions
BE5B31TES Signal Theory
Roles:PV Extent of teaching:2P+2C
Department:13131 Language of teaching:EN
Guarantors:Bortel R. Completion:Z,ZK
Lecturers:Bortel R. Credits:5
Tutors:Bortel R. Semester:L

Web page:

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

Anotation:

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.

Exercises outline:

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.

Requirements:

Subject is included into these academic programs:

 Program Branch Role Recommended semester BEECS Common courses PV 4 BPEECS_2018 Common courses PV 4

 Page updated 27.2.2024 09:56:34, semester: Z,L/2023-4, Z/2024-5, Send comments about the content to the Administrators of the Academic Programs Proposal and Realization: I. Halaška (K336), J. Novák (K336)