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Deterministic and stochastic signals in geophysics. Linear filtration, z-transformation, prediction filters.
Autocorrelation and power spectral density of random signals, parametric and nonparametric methods.
Multichannel data, polarization analysis.
Last update: T_KG (02.05.2013)
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The lecture provides basic techniques for analysis, filtration, modeling and prediction of signals and their applications to geophysical temporal and spatial data. Last update: T_KG (02.05.2013)
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Podmínkou udělení zápočtu je aktivní účast na cvičeních. Povaha kontroly studia předmětu vylučuje opravné termíny zápočtu. Získání zápočtu je podmínkou pro konání zkoušky. Last update: Gallovič František, prof. RNDr., Ph.D. (06.10.2017)
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Last update: T_KG (16.11.2011)
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Lecture + exercises Last update: T_KG (11.04.2008)
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Zkouška je ústní, požadavky odpovídají sylabu v rozsahu prezentovaném na přednášce. Last update: Gallovič František, prof. RNDr., Ph.D. (06.10.2017)
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Classification of geophysical data
Deterministic and stochastic processes, stationary random process, mean and autocorrelation, spectrum and power spectral density, ergodicity. Linear filters Linearity, time invariance, causality, stability, impulse response, transfer function, ideal filter, convolution in the frequency domain, filter with zero and linear phase, low pass-, band pass- and high pass-filters, Butterworth filter, filtration of a random process. Discrete signals Sampling, Nyquist frequency, relation between continuous and discrete Fourier transform, alias. Z-transform and digital filtering, convolution and deconvolution, minimum phase, dipole with minimum phase, bilinear transformation, spectral factorization and Töplitz approach. Wiener filter, Yule-Walker normal equations, optimal filtering, linear prediction. Nonparametric power spectral density estimates Data tapering. Sample spectrum, correlograms, periodograms, multitaper approach. Trade-off between estimation variance and resolution. Parametric power spectral density estimates Definition of Autoregressive (AR) and Moving Average (MA) random process, AR power spectral density estimation, relation of AR parametry and autocorrelation function, relation to linear prediction filter. Estimates of the AR parameters, model order selection. Pseudo power-spectral density Minimum variance (MV) spectral estimation, relationship between MV and AR spectral estimator. Eigenanalysis-based frequency estimation, eigenanalysis of autocorrelation matrix for sinusoids in white noise, signal and noise subspace frequency estimators, order selection. Multichannel and vector data Spectral estimates, polarization analysis. Last update: T_KG (02.05.2013)
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