Subject description - BE2B37SAS
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BE2B37SAS |
Signals and systems |
Roles: | |
Extent of teaching: | 2p+2c |
Department: | 13137 |
Language of teaching: | EN |
Guarantors: | |
Completion: | Z,ZK |
Lecturers: | |
Credits: | 5 |
Tutors: | |
Semester: | L |
Anotation:
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.
Course outlines:
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. |
Exercises outline:
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. |
Literature:
[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. |
Requirements:
Knowledge of linear algebra and mathematical analysis, especially complex analysis and integral transforms.
Keywords:
Signals, systems, signal processing, sampling, spectrum, Fourier transform.
Subject is included into these academic programs:
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Page updated 28.4.2024 12:51:31, semester: L/2023-4, Z/2024-5, Z/2023-4, Send comments about the content to the Administrators of the Academic Programs |
Proposal and Realization: I. Halaška (K336), J. Novák (K336) |