Theory of Signals

The course is devoted to fundamentals of theory and applications of continuous and digital signal processing. The aim of the discipline is to give students understanding of application of signal processing methods in physical and biomedical electronics and strong background in using signal analysis, especially biomedical signals. The classification and parameters of signals, linear stationary digital systems are considered. The focus of the discipline is given to processing and analysis of discrete signals in linear stationary systems. We consider the representation of signals in a Hilbert space, the concept of generalized signal decomposition and energy preserving transforms. We study the theoretical basis and practical application of classical and new methods for analysis of deterministic and random signals: spectral analysis, time-frequency analysis, wavelet transform, correlation and statistical analysis, modulation, filtration and pattern recognition of signals.
Syllabus:

• Introduction.
• Types and parameters of signals.
• Introduction to discrete signal processing systems.
• Mathematical foundations of signal processing and analysis.
• Spectral analysis and time-frequency analysis.
• Wavelet analysis of signals.
• Frequency-dependent signal processing.
• Modulation and manipulation of signals.
• Statistical signal analysis.
• Fundamentals of pattern recognition.