Popis předmětu - BE2B37SAS
BE2B37SAS | Signals and systems | ||
---|---|---|---|
Role: | Rozsah výuky: | 2p+2c | |
Katedra: | 13137 | Jazyk výuky: | EN |
Garanti: | Zakončení: | Z,ZK | |
Přednášející: | Kreditů: | 5 | |
Cvičící: | Semestr: | L |
Anotace:
Introductory course focused on a description of continuous- and discrete-time signals and systems in time and frequency domains. The course also introduces the basic characteristics of bandpass signals, analog modulations and random signals.Osnovy přednášek:
1. | Introduction, classification of signals in continuous and discrete time, description and meaning (deterministic, random, causal, finite, periodic), special signals (unit step, rectangular pulse, Dirac impulse, unit impulse, sinc function). | |
2. | Characteristics of signals in time domain (average value, energy, power, mutual energy and power, cross-correlation and autocorrelation). | |
3. | Spectral representation of continuous signals, orthogonal signals, basis. Fourier Series (FS). Physical meaning of harmonic components. | |
4. | Fourier transform (FT). Properties of FT, Parseval's theorem. Transformation of special signals. Energy and power spectrum and their relation with correlation function. | |
5. | Spectrum of modulated signals, introduction to analog modulation. | |
6. | Spectrum of discrete signals. Sampling theorem. Discrete Fourier Series (DFS) and Discrete time Fourier Transform (DtFT). Energy and power spectral densities. | |
7. | Ideal sampling and interpolation, aliasing. | |
8. | Relations of FT, FS, DtFT and DFS. Discrete Fourier Transform (DFT) and Fast Fourier Transform (FFT) used for the calculation of FT and FS. | |
9. | Classification of systems and their properties, description of linear time-invariant (LTI) systems in time domain, convolution, stability of the system. | |
10. | Description of linear and time-invariant (LTI) system in the frequency domain, transfer function and frequency response. | |
11. | Ideal filters, replacement of a continuous-time system using a discrete one. | |
12. | Passage of signals through nonlinear systems, intermodulation. | |
13. | Bandpass signals and their description, complex envelope, sampling of bandpass signals. | |
14. | Introduction to random signals, stationarity and ergodicity, white noise. |
Osnovy cvičení:
1. | Introduction and organization of the exercise. Review of required mathematical basics. Classification of signals in continuous and discrete-time. | |
2. | Characteristics of the signals in the time domain, signal energy and power in continuous and discrete-time. | |
3. | Characteristics of the signal in the time domain, autocorrelation and cross-correlation. | |
4. | Complex Fourier series (FS), spectrum of continuous periodic signals. | |
5. | First semester test. Power spectrum, relation to autocorrelation function. | |
6. | Fourier transform (FT), relationships signal - spectrum - autocorrelation function - energy/power spectral density. | |
7. | Fourier series and transformation of discrete-time signals DtFT and DtFS, relationships signal - spectrum - autocorrelation function - energy/power spectrum. | |
8. | Second semester test. Signal sampling. | |
9. | Classification of systems. Description of linear time-invariant (LTI) system in the time domain, convolution, stability. | |
10. | Description of linear time-invariant system (LTI) in frequency domain, transfer function and frequency response. | |
11. | Generation of basic signals, display, calculation of energy and power, calculation of autocorrelation function in Matlab. | |
12. | Calculation of the coefficients of Fourier series (FS and DtFS) and spectrum (FT and DtFT) using DFT/FFT, calculation of energy and power in the spectral domain in Matlab. | |
13. | LTI system, transfer function, poles and zeros, calculation of the response, characteristics of the input and output signals of the system in Matlab. | |
14. | Presentation of semester projects, assessment. |
Literatura:
[1] | Oppenheim, A. V., Willsky, A. S., Young, I. T., Signals and systems, Harlow: Pearson, 2013. | |
[2] | Taylor, F. J., Principles of Signals and Systems, McGraw-Hill, 1994. | |
[3] | Boulet, B., Fundamentals of Signals and Systems, Da Vinci Engineering Press, 2005. | |
[4] | Papoulis, A., Probability, random variables, and stochastic processes, McGraw-Hill, 2002. | |
[5] | Proakis, J. G., Salehi, M., Digital communications, Boston: McGraw - Hill, 2008. | |
[6] | Hrdina, Z., Vejražka, F., Signály a soustavy, Praha: ČVUT, 1998. |
Požadavky:
Knowledge of linear algebra and mathematical analysis, especially complex analysis and integral transforms.Klíčová slova:
Signály, soustavy, zpracování signálu, vzorkování, spektrum, Fourierova transformace.Předmět je zahrnut do těchto studijních plánů:
Plán | Obor | Role | Dop. semestr |
Stránka vytvořena 29.3.2024 12:50:51, semestry: Z/2024-5, Z,L/2023-4, připomínky k informační náplni zasílejte správci studijních plánů | Návrh a realizace: I. Halaška (K336), J. Novák (K336) |