Signals and systems

Garant předmětu:

Přednášející:

Cvičící:

Předmět zajišťuje:

katedra radioelektroniky

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.

Požadavky:

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

Osnova 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.

Osnova 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.

Cíle studia:

Studijní materiály:

[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.

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