# DIGITAL SYSTEMS AND COMMUNICATIONS (UNIT 1)

## Learning outcomes of the course unit

1- Knowledge and understanding

Goal of the course is to provide the students with the basics of the analysis of discrete-time signals, the design of digital signal processing systems and digital filtering.

2- Applying knowledge and understanding

Students learn how to analyze and design simple linear systems (digital filters) being aware of the capabilities an practical limitations of digital signal processing techniques.

## Prerequisites

"Signal theory" (suggested)

## Course contents summary

- Discrete-time signals and systems.

Basic signals and elementary transformations. Sampling of continuous- time signals: sampling theorem, Nyquist condition, aliasing and anti-aliasing filtering. Representation of discrete-time signals in the frequency domain: the Fourier Transform of a sequence and its properties. Discrete- time systems and their properties: linear, time invariant, memoryless, stable, causal systems. Linear time-invariant systems (LTI) and the discrete convolution. Difference equations. Analysis of LTI systems in the frequency domain: the discrete-time complex exponential, the frequency response.

- The z-Transform.

Definition and properties. Inversion of the z-Transform. Theorems and properties of the z-Transform. Transfer function of a LTI system. Rational transfer functions. Finite impulse response (FIR) systems and infinite impulse response (IIR) systems. Stability of discrete systems.

- The Discrete Fourier Transform (DFT).

Definition, properties and use of the DFT. Circular convolution and relationship with linear convolution. Relationship with the Fourier Transform. Efficient computation of the DFT: the Fast Fourier Transform (FFT).

- Digital processing of analog signals.

Simulation of analog systems. Design of IIR digital filters. Design of FIR filters.

## Course contents

- Discrete-time signals and systems.

Basic signals and elementary transformations. Sampling of continuous-

time signals: sampling theorem, Nyquist condition, aliasing and anti-aliasing filtering. Representation of discrete-time signals in the frequency domain: the Fourier Transform of a sequence and its properties. Discrete- time systems and their properties: linear, time invariant, memoryless, stable, causal systems. Linear time-invariant systems (LTI) and the discrete convolution. Difference equations. Analysis of LTI systems in the frequency domain: the discrete-time complex exponential, the frequency response.

- The z-Transform.

Definition and properties. Inversion of the z-Transform. Theorems and properties of the z-Transform. Transfer function of a LTI system. Rational transfer functions. Finite impulse response (FIR) systems and infinite impulse response (IIR) systems. Stability of discrete systems.

- The Discrete Fourier Transform (DFT).

Definition, properties and use of the DFT. Circular convolution and relationship with linear convolution. Relationship with the Fourier Transform. Efficient computation of the DFT: the Fast Fourier Transform (FFT).

- Digital processing of analog signals.

Simulation of analog systems. Design of IIR digital filters. Design of FIR filters.

## Recommended readings

- A.V. Oppenheim, R. W. Schafer , “Discrete-Time Signal Processing”, 3rd Edition, Prentice Hall Signal Processing (2009), ISBN: 0131988425

- M. H. Hayes, "Digital Signal Processing" (Schaum's Outline Series) McGraw-Hill Education (1998 o 1999), ISBN: 0070273898

- D. G. Manolakis, V. K. Ingle, "Applied Digital Signal Processing: Theory and Practice", (1st edition), Cambridge University Press (2011), ISBN-10: 0521110025 ISBN-13: 978-0521110020

- A. V. Oppenheim, R. W. Schafer, "Elaborazione numerica dei segnali", (13^ ed.) Franco Angeli (2001), ISBN: 8820430061

- M. Laddomada, M. Mondin, "Elaborazione numerica dei segnali", Addison Wesley Longman Italia, (2007), ISBN: 887192438X

- A. V. Oppenheim, R. W. Schafer, "Digital Signal Processing", Prentice Hall, (1975), ISBN: 0132146355

- M. Luise, G. M. Vitetta, "Teoria dei segnali", (3^ ed.), McGraw-Hill (2009), ISBN: 9788838665837

## Teaching methods

Classroom lessons and exercise sessions.

## Assessment methods and criteria

- The first session foresees two intermediate written exams, the first after half of the unit, the second at its end. A sufficient mark in the intermediate exams allows to take an optional oral exam. The unit final mark is computed as the average of the two written exams and, if taken, of the oral exam.

- The next sessions foresee a written and an oral exam. The unit final mark is computed as the average of the written and the oral exams.

- In either case, the exam final mark is computed as the weighted average of the first (2/3 of the mark) and the second unit (1/3 of the mark) marks.

## Other informations

Information to students and various documents are provided through the platform:

elly.dii.unipr.it