Load:

1. komponenta
Lecture type  Total 
Lectures 
30 
Exercises 
15 
* Load is given in academic hour (1 academic hour = 45 minutes)

Description:

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. Diracs comb and its Fourier pair. Digital filtering, convolution integral, ideal lowpass filter. Filtering discrete data. Trend. Sampling and aliasing. Sampling theorem. Data samples of finite length.
LEARNING OUTCOMES:
After completing the course on Introduction to Spectral Analyses students are able to:
identify timeseries 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 phasespectra, and the power density spectra,
compare physical systems according to their frequency response,
define Dirac's deltafunction and its basic properties,
perform timedomain filtering with ideal filters,
argue for the choice of the sampling interval for analysed timeseries.

Literature:

 Bath, M. Spectral analysis in geophysics, Elsevier, Amsterdam, 1974.
 Bracewell, R. N: The Fourier transform and its applications, McGrawHill, New York, 1983.
 Papoulis, A: The Fourier integral and its applications, McGrawHill, New York, 1962.

Prerequisit for:

Enrollment
:
Attended
:
Mathematical Methods in Physics 2
