Objectives and outcomes
The course deals with classical and modern algorithms for computer spectral analysis of time and space signals. Moreover, students learn about the applications of spectral analysis in telecommunications, computer engineering, biomedicine, economics. Candidates understand the concept of spectral analysis and signal spectrum. They analyse several non-parametric methods of spectral analysis based on periodograms, filter banks, and apply them to solve problems from different fields. They analyse and apply certain parametric methods of spectral analysis. Candidates make decisions about the choice of a certain algorithm and the determination of parameters. They apply spectral analysis methods to various areas to solve problems.
Lectures
Definition and overview of the spectral estimation problem. Time-invariant random signals. Fourier transforms for spectrum determination. Application of wavelets and filter banks. Methods based on periodograms and correlograms. Advanced methods based on periodograms. Properties of periodograms. Analysis of window functions to determine the periodogram. Spectrograms. Parametric methods of spectral analysis. ARMA (autoregressive moving average) processes. AR signals – Yule – Walker method, and the Levinson – Durbin algorithm, least squares algorithm. MA signals. ARMA signals. Spectral analysis of time series. Spectral analysis of spatial signals. Application of spectral analysis in telecommunications, biomedicine, economy.
Researchwork
Application of software packages GNU Octave, Matlab to spectral analysis of selected signals. Application of spectral analysis in given situations. Studying scientific journals and other literature through research work, students independently broaden the knowledge acquired in lectures. Working with professors, they are trained to write scientific papers.