# Digital Signal Processing

## Subject description

Fundamentals of time-discrete signals (signals, 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). Random signal generators (uniform distribution, Gaussian white noise). Signal quantisation (analogue-to- digital conversion, quantizers, and quantization errors).

## Objectives and competences

To know 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 digitalization 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.

## 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:

• analyze time discrete signals,
• analyze linear and timeinvariant discrete time systems,
• use discrete Fourier transform in the analysis and processing of signals,
• design a digital FIR filters,
• design a digital IIR filters,

design real-time digital signal processing systems.

## Basic sources and literature

1. Sašo Tomažič, Savo Leonardis, Diskretni signali in sistemi Založba FE in FRI, 2004.

2. John G. Proakis, Dimitris K. Manolakis, Digital Signal Processing (4th Edition) Prentice Hall; 4 edition, 2006

## Stay up to date

University of Ljubljana, Faculty of Electrical Engineering Tržaška cesta 25, 1000 Ljubljana