Continuous Signals and Systems

Continuous time linear casual time invariant systems (LTI, system equation).

Basic continuous time electric signals: selected types and operations. Representation and analysis of continuous signals using Fourier series, Fourier transform (frequency and power spectrum) and Laplace transform.

Definition, properties and limitations of a linear circuit. Topological circuit description, describing a circuit using matrix equations. Using different methods to analyse the circuit (branch current method, window current method and intersection potential method). Power source transformation theorem.

Classical analysis of circuits using differential equations, interpretation, convolution. Steady state analysis (pointers, system function, power). Single input circuits (Thevenin equivalent, maximum power transmission theorem, resonance). Dual-input circuits: reciprocity theorem, modelling circuit as a quadripole and determining different quadripole parameters, Bode diagram.

Spectral analysis (using spectrum to analyse circuits), using Laplace to analyse circuits.

The objective of the course is to familiarize students with basics of time continuous linear circuits and systems including the relationship of signal representation domain and type of system analysis. 

Basic understanding of linear circuits and systems. Understanding of the relationship between continuous time signal representations and linear system analysis. Recognition of a system type according to types of their components. Recognition and understanding of selected phenomena in linear systems in terms of communications.

Lectures provide theoretical backgrounds and basic reasoning supported by illustrative examples. Tutorials adds more examples and focus on improvement of analytical skills of students. Both methods are supported by a web based linear system simulator allowing hands-on learning and voluntary student’s work at home. It covers analyzable examples of linear systems in terms of system response. Signal representations on different domains are supported by web based Jupyter Python system.