Předmět Signals and systems analysis (FEKT-CASS)

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Materiál	Typ	Datum	Počet stažení

Cíl

The aim of the course is to acquaint students with one-dimensional (1D) and two-dimensional (2D) signals and systems with continuous-time signals and discrete-time systems with pulse and digital signals and systems. It is also necessary to introduce the concept of spectrum 1D and 2D signals and emphasize its difference from the frequency characteristics of 1D and 2D system. Consequently, the aim is to provide students with basic information about random signals and their impact on systems bring analog and digital modulation and define description of the characteristics of communication systems.

Osnova

1. Signals and systems and their mathematical models Real signals and their mathematical continuous-time models. Basic signal operations (time scaling, flipping, time shifting translation, time shifting translation and flipping, convolution, correlation). Signal classification, unit impulse, unit step, harmonic signal. Real systems with continuous- and discrete-time. Dynamic system, its input and output, status. Linear time-invariant system. Impulse response. Response of LTI system using convolution, superposition.2. Periodic signals and their spectrum Function substitution by functional series. Periodic continuous-time signal, harmonic signal and its representation by phasors. Periodic and harmonic discrete-time signals. Fourier series, spectrum of periodic rectangular pulses, spectrum theorems.3. Fourier representation of aperiodic continuous-time signals Definition of the Fourier transform of aperiodic continuous-time signals. Spectra of selected signals. Spectrum theorems. Definition of the inverse Fourier transform. The inverse Fourier transform of rectangular spectral impulse. Relationship between the Fourier series and the Fourier transform.4. Continuous-time systems The characteristics of a linear time-invariant (non-parametric) system (frequency response, hodograf). System transfer function, zero-pole plot. Ideal transfer circuit. Frequency filters. Non-linear systems. Superheterodyne.5. Sampling of continuous-time signals Ideal sampling of continuous-time signal and its reconstruction. Sampling theorem. Amplitude quantization. A/D and D/A conversions. Aliasing. Sampling of bandpass signals.6. Discrete-time signals Discrete time axis. Basic discrete signals. Signal theorems. Discrete linear, periodic and circular convolutions. Using FFT for convolution calculation.7. Fourier transform of discrete-time signals. The discrete Fourier series and the discrete Fourier transform. The fast Fourier transform (FFT). Decimation-in-Time (DIT) and Decimation-in-Frequency (DIF) algorithms, FFT algorithm properties.8. Z transform and its properties Definition of the Z transform and its properties. The inverse Z transform and its calculation. The relationship between the Z transform and the discrete Fourier transform.9. Modulation signals in base-band and transition-band Communication system and its properties, modulation and transmission rates, spectrum of communication channel. Amplitude, frequency, and phase analog modulations and their spectra. Digital modulations.10. Stochastic variables and processes and their properties Continuous and discrete time variables. Definition of stochastic processes with continuous- and discrete-time and their representations. Cumulative distribution function, probability density function. Moments (mean, variance, standard deviation, etc.). Stationarity and ergodicity.11. Power spectral density and its calculation Power spectral density of continuous- and discrete-time stochastic processes. Periodogram, using FFT for its calculation. White noise. Processing of stochastic signal by linear system. Non-parametric and parametric models.12. Discrete-time systems Linear time-invariant discrete system, impulse response. System transfer function, frequency response, zero-pole plot. Systems of the type of IIR and FIR. Connection of LTI systems. Series, parallel and feedback connections of partial sections.13. Realization of LTI discrete system Design of LTI discrete system based on analog prototype. Structures of realization. Mason’s gain rule. Implementation of LTI system on microprocessor. Calculation of frequency response based on time responses.

Literatura

MITRA, S. K. Digital signal procesing. A computer-base approach. 1. vyd. New York: The McGraw-Hill Companies, 1998OPPENHEIM, A. V., WILLSKY, A. S. Signals and Systems. Englewood Cliffs: Prentice Hall, 1997SMÉKAL, Z.: Signals and Systems Analysis for joint teaching programme of BUT and VSB-TUO

Požadavky

The subject knowledge on the secondary school level especially of maths and physics is required. Furthermore, a general knowledge of programming and computer skills are important. Emphasis is placed on the knowledge of complex numbers and their application.

Garant

prof. Ing. Zdeněk Smékal, CSc.

Vyučující

Ing. Jiří Mekyska, Ph.D.prof. Ing. Zdeněk Smékal, CSc.