Signal Analysis

The course provides an in-depth look into signal theory and signal processing. Initially, it defines the concept of a signal through a brief historical overview of the development of the field of signal processing, and explains its significance in electrical engineering and science in general. Students are introduced to representations of signals with mathematical models and various types of signals. Special attention is given to the usefulness of representing signals with other signals, representation methods, and quality criteria, including examples of basis functions used for this purpose. The course then focuses on the frequency analysis of periodic and deterministic non-periodic signals and explains the basic principles of processing random signals, including stationary random signals and their deterministic characteristics. Furthermore, the course discusses the correlation and convolution of signals, the definitions of both concepts on different types of signals, and their properties. Practical aspects of the course include the use of correlation and convolution in signal processing, signal similarity estimation, spectrum estimation with time filtering, the use of convolution in linear stationary systems, and the detection of periodic components in noisy signals. In the final part of the lectures, the course focuses on presenting basic procedures for obtaining digital signals and their properties, including the frequency representation of digital signals and discrete correlation and convolution. 

The aim of this course is to familiarize students with different types of signals and to present different approaches to signal description and processing. Students develop an understanding of the concepts used for signal representation and get acquainted with signal analysis techniques based on correlation and convolution. The course provides the theoretical basis for many practical problems in the fields of imaging technologies, speech technologies, pattern recognition, artificial intelligence and machine learning. 

Lectures, Interactive teaching, Practical assignements.