Enable students for application of basic tools in spectral analyses, especially dealing with geophysical time-series.
Types of data. Fourier series and its complex form. Fourier integral. Inverse Fourier transformation. Power density spectrum, Autocorrelation function and its link to the power spectrum. Properties of physical systems with respect to the frequency. Dirac delta function, properties and applications. Dirac's comb and its Fourier pair. Digital filtering, convolution integral, ideal low-pass filter. Filtering discrete data. Trend. Sampling and aliasing. Sampling theorem. Data samples of finite length.
After completing the course on Introduction to Spectral Analyses students are able to:
- identify time series appropriate to be analyzed by harmonic or by spectral analyses,
- analyse data by Fourier series expansion,
- compute amplitude and phase spectra for periodic and transient data,
- define amplitude and phase spectra, and the power density spectra,
- compare physical systems according to their frequency response,
- define Dirac's delta function and its basic properties,
- perform time domain filtering with ideal filters,
- argue for the choice of the sampling interval for analyzed time-series.
- Attending lectures, study of literature and lecture notes,
- Derivation of the equations and case study.
- Lectures, discussions,
- Derivation of the equations,
- Solving problems.
METHODS OF MONITORING AND VERIFICATION:
Regularly attending lectures, problem solved. Colloquium and oral exam.
TERMS FOR RECEIVING THE SIGNATURE:
Solved task and a short report, attendance of lectures.