Bi6446 Spectral Analysis of Time Series

Faculty of Science
Autumn 2010 - only for the accreditation
Extent and Intensity
3/0/0. 3 credit(s) (plus extra credits for completion). Type of Completion: zk (examination).
Teacher(s)
prof. Ing. Jiří Holčík, CSc. (lecturer)
Guaranteed by
prof. RNDr. Ladislav Dušek, Ph.D.
RECETOX – Faculty of Science
Contact Person: prof. Ing. Jiří Holčík, CSc.
Prerequisites (in Czech)
Bi5440 Signals & Linear Systems
Course Enrolment Limitations
The course is also offered to the students of the fields other than those the course is directly associated with.
fields of study / plans the course is directly associated with
Course objectives
At the end of the course, students should be able to: - know fundamental theoretical and methodological principles of methods of time series spectral analysis with emphasis to biological data processing - explain consequences and relationships between characteristics of real processes and data and applied methods and algorithms; - apply different practical approaches to data processing to obtain required analytic results; - design of modified algorithms to process data of given particular characteristics
Syllabus
  • 1. Basic terms, definitions – continuous and discrete signals, spectrum, energy, power, power spectral density, autocorrelation function, ... 2. Signals multiplication by windows and its influence to signal spectral characteristics. Estimates of autocorrelation function for complete and incomplete signal. Properties, consequences. 3. DFT – FFT, fast algorithms for a general number of samples. Properties, implementation. 4. Spectral analysis algorithms for regularly and irregularly sampled signals. 5. Nonparametric methods based on DFT algorithm – periodogram, Bartlett, Welch, and Blackman-Tukey methods. 6. Parametric methods for estimation of frequency spectrum – linear system model, AR, ARMA, and MA models. 7. Levinson-Durbin algorithm, properties, consequences of its application. Spectral estimation with maximum entropy. 8. Burg method. Unconstrained Least-Squares Method for AR model parameters. 9. Properties of methods for AR models, their comparison. Selection of AR-model order. 10. ARMA and MA models for power spectrum estimation 11. Sequential estimation methods 12. Eigenanalysis algorithms for spectrum estimation – Pisarenko harmonic decomposition method 13. Prony methods
Literature
  • IEEE Signal Processing Letters
  • Handbook for Digital Signal Processing. (S.K.Mitra, J.F.Kaiser, eds.), New York, John Wiley & Sons 1993.
  • Proakis, J.G. et al.: Advanced Digital Signal Processing. New York, Macmillan Publ. Comp. 1992.
  • IEEE Trans. on Signal Processing
  • Oppenheim, A.V., Schafer, R.W.: Digital Signal Processing. London, Prentice Hall 1975.
  • Kay, S.M., Marple, S.L.: Spectrum Analysis - A Modern Perspective. Proc. IEEE, roč.69, č.11, Nov. 1981, s.1380-1418.
Teaching methods
Lectures supported by Power Point presentations. Understanding of principles, methods and algorithms is emphasized. Students are continuously encouraged to be in an interaction with a lecturer.
Assessment methods
oral examination
Language of instruction
Czech
Further comments (probably available only in Czech)
The course is taught annually.
Information on course enrolment limitations: základy metod zpracování signálů a spektrální analýzy
The course is also listed under the following terms Autumn 2008, Autumn 2009, Autumn 2010, Autumn 2011, Autumn 2011 - acreditation, Spring 2013, Spring 2014, Spring 2015, Spring 2016, Spring 2017, spring 2018, Spring 2019, Spring 2020, Spring 2021, autumn 2021, Spring 2022.