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Introduction to Spectral Analysis

Code: 66357
ECTS: 3.0
Lecturers in charge: prof. dr. sc. Marijan Herak
Lecturers: prof. dr. sc. Marijan Herak - Exercises
Take exam: Studomat

1. komponenta

Lecture typeTotal
Lectures 30
Exercises 15
* Load is given in academic hour (1 academic hour = 45 minutes)
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 analysed 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 analysed time-series.
  1. Bath, M. Spectral analysis in geophysics, Elsevier, Amsterdam, 1974.
  2. Bracewell, R. N: The Fourier transform and its applications, McGraw-Hill, New York, 1983.
  3. Papoulis, A: The Fourier integral and its applications, McGraw-Hill, New York, 1962.
Prerequisit for:
Examination :
Passed : Mathematical Methods in Physics 2
5. semester
Mandatory course - Regular study - Geophysics
Consultations schedule: