# Discrete Signals and Systems

## Subject description

Sampling, spectrum of naturally sampled signal, reconstruction of continuous-time signal, sampling theorem, frequency aliasing.

Classification and properties of discrete signals(periodic, aperiodic, random signals)

Spectral analysis of discrete signals: discrete time Fourier transform TDFT, discrete Fourier transform DFT.

Discrete linear time invariant systems (LTI):

Characterization of LTI systems: difference equation, impulse response, frequency response, system function, z-transform.

Location of poles and zeroes: stability, phase shift, linear phase systems.

Discrete filters: block scheme, signal flow graph, structures, digital filter specifications.

FIR filter design: windowing, frequency transformations, equiripple filter design.

IIR filter design: invariant impulse response method, bilinear transformation.

Multirate systems: decimation, interpolation.

Effects of digital implementation: quantisation noise, effects of coefficient quantisation.

## Objectives and competences

Basic properties of discrete signals.

Relations between discrete and continuous-time signals due to sampling and reconstruction.

Spectral analysis of analogue signals using DFT

Advantages and drawbacks of FIR filters

Advantages and drawbacks of IIR filters

Significance of proper structure selection for fixed point implementations

## Teaching and learning methods

Lectures, tutorial, homework

## Expected study results

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

– describe the main differences between continuous and discrete signals,

– compute the approximate  spectrum of an analogue signal by using DFT,

– determine a suitable sampling frequency and the required antialiasing filter for the acquisition of an analogue signal,

– compare the main features of FIR and IIR, discrete systems,

– compute the coefficients of a digital FIR filter  using the windowing method, and the coefficients of a digital IIR filter using the bilinear transformation method,

– select filter type and structure suitable for microcontroller  implementation for a given problem,

– estimate the impact of signal quantisation on the output noise power.

## Basic sources and literature

1. S. Tomažič, S. Leonardis: Diskretni signali in sistemi,  Založba FE in FRI, Ljubljana, 2004
2. S. K. Mitra, Digital signal processing: a computer based approach, fourth edition, McGraw-Hill, 2011

## Stay up to date

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