Syllabus
* 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.
Annotation
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.