Subject description
The course introduces the basic categorization and properties of continuous-time signals and the mathematical tools for their frequency analysis – Fourier series and transform. Signal conditioning with linear time-invariant (LTI) systems introduced. Various ways of describing the LTI systems are shown: differential equation, impulse response, frequency response and system function (Laplace transform of impulse response). The basic methods for such systems synthesis are also shown.
Sampling and reconstruction are introduced, which are used to convert continuous-time signals into discrete-time signals and back. The requirements and implications of both conversions are considered. Mathematical tools for frequency analysis of time-continuous signals are adapted for the purpose of time-discrete signals. The basic structures and properties of discrete-time LTI systems are shown, and basic tools for their analysis and synthesis are given. Practical implementation of a discrete-time system is demonstrated.
The subject is taught in programs
Objectives and competences
To introduce the fundamentals of signal processing, including the basics of continuous-time signal processing by linear circuits as well as digital processing of discrete signals.
The acquired knowledge in this field enable proper selection of computer aided tools for signal analysis and processing.
Teaching and learning methods
Lectures, tutorial, homeworks.
Expected study results
After successful completion of the course, students should be able to:
- classify signals with respect to their main characteristics,
- explain the term signal spectrum and its significance with regard to signal processing,
- calculate frequency spectra of simple periodic and aperiodic signals
- establish the system function of linear circuits and the location of poles and zeroes,
- explain the influence of system function pole location on circuit (system) stability,
- justify the lowest permissible sampling frequency for perfect reconstruction of a frequency limited signal,
- calculate the frequency response of a discrete system.
Basic sources and literature
- F. Mihelič, Signali, Založba FE in FRI, Ljubljana, 2014
- S. Tomažič, S. Leonardis: Zvezni in diskretni signali, Založba FE in FRI, Ljubljana 1998
- S. Tomažič, S. Leonardis: Diskretni signali in sistemi, Založba FE in FRI, Ljubljana 2017
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University of Ljubljana, Faculty of Electrical Engineering Tržaška cesta 25, 1000 Ljubljana