Signals and systems
Code  Completion  Credits  Range  Language 

BE2B37SAS  Z,ZK  5  2p+2c  English 
 Lecturer:
 Tutor:
 Supervisor:
 Department of Radioelectronics
 Synopsis:

Introductory course focused on a description of continuous and discretetime signals and systems in time and frequency domains. The course also introduces the basic characteristics of bandpass signals, analog modulations and random signals.
 Requirements:

Knowledge of linear algebra and mathematical analysis, especially complex analysis and integral transforms.
 Syllabus of lectures:

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, crosscorrelation 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 timeinvariant (LTI) systems in time domain, convolution, stability of the system.
10. Description of linear and timeinvariant (LTI) system in the frequency domain, transfer function and frequency response.
11. Ideal filters, replacement of a continuoustime 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.
 Syllabus of tutorials:

1. Introduction and organization of the exercise. Review of required mathematical basics. Classification of signals in continuous and discretetime.
2. Characteristics of the signals in the time domain, signal energy and power in continuous and discretetime.
3. Characteristics of the signal in the time domain, autocorrelation and crosscorrelation.
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 discretetime 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 timeinvariant (LTI) system in the time domain, convolution, stability.
10. Description of linear timeinvariant 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.
 Study Objective:
 Study materials:

[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, McGrawHill, 1994.
[3] Boulet, B., Fundamentals of Signals and Systems, Da Vinci Engineering Press, 2005.
[4] Papoulis, A., Probability, random variables, and stochastic processes, McGrawHill, 2002.
[5] Proakis, J. G., Salehi, M., Digital communications, Boston: McGraw  Hill, 2008.
[6] Hrdina, Z., Vejražka, F., Signály a soustavy, Praha: ČVUT, 1998.
 Note:
 Further information:
 No timetable has been prepared for this course
 The course is a part of the following study plans: