Digital Signal Processing

Subject description

Fundamentals of digital signals (signals, phasors, the building blocks for digital signal processing, signal classification, time and frequency space). Sampling (sampling theorem, effects of sampling in time and frequency domain). Discrete-time systems (linear time- invariant discrete systems, causality, differential equations and discrete linear systems, impulse response , the discrete – time systems structure, implementation) . Frequency analysis of discrete – time signals. Discrete Fourier transform (Fast Fourier transform algorithms, fast discrete filtering using FFT). Z-transform (Z transform and inverse Z transform , application in digital signal processing , rational Z transform, time behaviour and roots of rational Z transform) . Analysis and synthesis of discrete time systems in frequency domain (transfer function of the system, analysis of systems with rational Z transfer function, stability, frequency response). Digital filter design (finite response filters, the infinite response filters). Quantized signal (analog-to- digital conversion, quantisers, quantization error, quantization and digital filtering). Digital sound and image processing. Transformations of multidimensional signals. Compression of sound, image and video signals.

The subject is taught in programs

Objectives and competences

Learning about the basic tools for digital signal processing. Understanding the processes and consequences of capture, analysis and signal processing in discrete – digital form and their reconstruction back to the analog domain. Competence for the selection of a suitable method of digital signal acquisition, understanding the implications of digitalisation and understanding the basic signal analysis in time and frequency domain. The ability to use basic systems for digital filtering and signal enhancement. Understanding digital signal processing as a building block of complex digital communication devices. Knowing the basic procedures for digital recording, processing and compression of sound and images.

Teaching and learning methods

Lectures with DSP theory and practically oriented lab assignments encouraging teamwork.

Expected study results

After successful completion of the course, students should be able to:

Possess fundamental understanding of complex signal representation.
Understand the practical aspects of sampling and reconstruction.
Select a suitable sampling rate for a given signal processing problem.
Understand the use and applications of Discrete Fourier transform
Convert between time and frequency domain representations of signals and systems.
Be capable of application of transform methods to the analysis of digital linear time-invariant systems
Design and analyse digital filters of a given specification.

Basic sources and literature

Tasič, J. F., Uvod v postopke digitalne obdelave signalov, Založba FE in FRI, 2002.
Manolakis, Ingle, Applied Digital Signal Processing, Cambridge University Press, 2011
Bose, T., Digital signal and image processing, John Wiley and Sons, 2004.