Theory of Signal Processing

Historical development, current situation and development perspectives of the theory of signal. Use signals and signal systems in science and technology. Signals and their classification. Examples of signals and their spectra.
Deterministic signals. Spectral analysis of signals.
Harmonious process. Periodic waveforms. Performance ratios for periodic waveforms
(Parseval's theorem). Non-periodic waveforms. Energy ratios for non-periodic
curves (Rayleigh theorem). Properties of signals and spectra (additivity,
superposition, convolution). Elementary functions and their transformation (unit
jump, the unit impulse). Discrete Fourier transformation. Fast Fourier
transformation.
Sampling signals. Principles of sampling. Shannon-
Kotělnikovova (sampling) theorem. Spectrum of sampled signal.
Stochastic signals. Stochastic properties of signals.
Probability of occurrence of the phenomenon (the phenomenon of probability, statistical definition
probability, geometrical definition of probability). Random variables
(Partition function, numerical characteristics of random variables, some types of
distribution of random variables). Systems of random variables. Functions of random
variables. Random processes. Statistics random process. Stationary Random
processes. Ergodic random processes. Autokovarianční function. Autocorrelation
function. The mutual correlation function.
Mathematical methods of signal processing. Fourier analysis
signal (Fourier series, Fourier integral, Fourier transform).
Laplace transformation. Wagner-Laplace transformation. Bilinear
transformation. Z-transform. Hilbert transformation. Walsh transformation.
Haar transformation. Window transformation. Wavelet transform.
Linear signal transmission system. Transfer factor. Pulse
characteristics. Step response. Linear distortion. Nonlinear
distortion.