Auxiliary results from linear algebra: matrices, eigenvalues, reduction to diagonal form, singular value decomposition, method of least squares. Multiple linear regression and correlation. Empirical orthogonal functions (EOF). Objective analysis: polynomial fitting, objective interpolation. Time series, spatial fields: a) deterministic theory: linear systems, Fourier transform, discrete sampling, aliasing, digital filters; b) stochastic theory in frequency domain as well as in the domain of wave numbers: linear systems with stochastic input, power spectra and cross-spectra of stationary stochastic processes, linear model with noise; d) wavelets.
Exercises will comprise the implementation of various methods on computer. These will be used to analyze real or artificial (computer generated) data.
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- Bendat, S. J., Piersol, G. A. 2000: Random Data Analysis and Measurement Procedures. John Wiley & Sons, Inc., New York, 594 pp.
- Jenkins, G. M., Watts, D. G. 1968: Spectral Analysis and its applications. Holden-Day, San Francisco, 525 pp.
- Papoulis, A. 1977: Signal Analysis. McGraw-Hill, Auckland, 431 pp.
- Papoulis, A. 1984: Probability, Random Variables, and Stochastic Processes. McGrew-Hill, Auckland, 576 pp.
- Press, H. W., Teukolsky, A. S., Vetterling, T. W., Flannery, P. B. 2001: Numerical Recipes in Fortran 77, Cambridge University Press, Cambridge, 974 pp.
- von Storch, H., Zwiers, W. F. 2003: Statistical Analysis in Climate Research, Cambridge University Press, Cambridge, 484 pp.
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