Digital Signal Processing with Matlab Examples, Volume 1: Signals and Data, Filtering, Non-stationary Signals, Modulation

653 Pages·2017·26.76 MB·English

Signals and Communication Technology
Jose Maria Giron-Sierra
Digital Signal
Processing with
Matlab Examples,
Volume 1
Signals and Data, Filtering, Non-
stationary Signals, Modulation
Signals and Communication Technology
More information about this series at http://www.springer.com/series/4748
Jose Maria Giron-Sierra
Digital Signal Processing
with Matlab Examples,
Volume 1
Signals and Data, Filtering, Non-stationary
Signals, Modulation
123
Jose Maria Giron-Sierra
SystemsEngineeringandAutomaticControl
Universidad Complutense deMadrid
Madrid
Spain
ISSN 1860-4862 ISSN 1860-4870 (electronic)
Signals andCommunication Technology
ISBN978-981-10-2533-4 ISBN978-981-10-2534-1 (eBook)
DOI 10.1007/978-981-10-2534-1
LibraryofCongressControlNumber:2016951678
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To Our Lady and to my parents
Preface
In our contemporary world, the digital processing of signals and data is certainly
very important. Most people are now using it, as it is involved in mobile com-
munications, TV and radio, GPS, medical instruments, transportation and traffic,
andalongetcetera.Also,mostbranchesoftechnicaldevelopmentandresearchare
intrinsically connected to signals and data processing.
Thisbookisthefirstofatrilogy.Ourdesireistoprovideaconciseandrelatively
complete exposition of signal processing topics, and a guide for personal practical
exploration based on MATLAB programs. It has been said by many experts on
learning that readings could be forgotten, but experiments leave a mark in our
minds and help to gain significant insights.
ThebooksincludeMATLABprogramstoillustrateeachofthemainstepsofthe
theory.Thecodehasbeenembeddedinthetext;withthepurposeofshowinghow
to put into practice the ideas and methods being proposed.
Itseemsopportune tosaysomewordsontheauthor’sexperience inthefieldof
signal and data processing. Since 30 years ago I belong to the Faculty of Physics,
UniversityComplutenseofMadrid,Spain.Myresearchconcernsautomaticcontrol
androbotics, with applications inautonomous vehicles,maritimedrones, chemical
processes, satellites, and others. During the research a variety of sensors has been
used, for the measurement of gases, pH, forces, light, magnetic fields, evoked
humanpotentials,etc.Morecomplexsensors,likeGPSorcameras,havealsobeen
employed. Currently I teach Biomedical Digital Signal Processing, and Digital
Signal Processing for New Technologies.
The motivation for elaborating this book is related to our interaction with stu-
dents and young researchers. Our teaching includes theory classes and laboratory
exercises. It was noticed in laboratory that the use of MATLAB and its Signal
ProcessingToolboxhasnoticeableinitialdifficultiesforthestudents,iftheyhadto
startfromscratch.Therefore,webegantoprovidethemsomesimpleprogramsthat
give them initial success, and graphical results. A good start encourages the stu-
dents for further study steps, and helps to develop a more ambitious teaching.
This book is divided into three parts. The first part introduces periodic and
non-periodicsignals.Thesecondpartisdevotedtofiltering, whichisanimportant
vii
viii Preface
and most usual application. The third part contemplates topics that could be con-
sideredasadvanced;onetriestoanalyze,withseveralpurposes,whathappenswith
signals and data from real life, like for example fatigue of structures, earthquakes,
electro-encephalograms, animal songs, etc. Therefore, the third part focuses on
non-stationarysignals.Thelastchapterisdevotedtomodulation,whichimpliesthe
intentional use of non-stationary signals, and so this chapter belongs to the third
part.
The book has two appendices. The first appendix is devoted to the Fourier
transform,othertransforms,andsamplingfundamentals.Thesecondcontainslong
programs, which are put here in order to make the chapters more readable.
Concerning the MATLAB programs, the programming style is purposively
simpleandillustrative.Wetriedtoavoidcodingwaysthatcouldbemoreoptimized
but may result in obscuring the ideas behind. The programs work in the diverse
MATLABversions,withperhapssomepossiblechangesforsomefunctions(inthis
case, MATLAB itself suggests appropriate changes).
There are traditional books that could be used for consultation. The chapters
includereferencestothesebooksandpertinentscientificpapers.Mostofthepapers
areavailablefromInternet.Bytheway,wehavetoshowourgratitudetothepublic
information available from Internet, from web sites, academic institutions, ency-
clopedia,etc.AllchaptershaveafinalsectionwithsomeconvenientInternetlinks.
The reader is invited to typeset the programs included in the book, for it would
helpforcatchingcodingdetails.Anyway,allprogramsareavailablefromthebook
web page: www.dacya.ucm.es/giron/SPBook1/Programs.
Please, send feedback and suggestions for further improvements and support.
Acknowledgments: Thanks to my university, my colleagues and my students.
I have to mention in particular the help I received, along friendly discussions on
some signal processing topics, from Juan F. Jimenez and Segundo Esteban, two
members of my department. Since this book required a lot of time taken from
nights, weekends and holidays, I have to sincerely express my gratitude to my
family.
Madrid, Spain Jose Maria Giron-Sierra
Contents
Part I Signals and Data
1 Periodic Signals. .... .... ..... .... .... .... .... .... ..... .... 3
1.1 Introduction ... .... ..... .... .... .... .... .... ..... .... 3
1.2 Signal Representation..... .... .... .... .... .... ..... .... 3
1.3 Generation of Periodic Signals.. .... .... .... .... ..... .... 5
1.3.1 Sinusoidal .. ..... .... .... .... .... .... ..... .... 5
1.3.2 Square. .... ..... .... .... .... .... .... ..... .... 7
1.3.3 Sawtooth... ..... .... .... .... .... .... ..... .... 8
1.4 Hearing the Signals . ..... .... .... .... .... .... ..... .... 10
1.5 Operations with Signals ... .... .... .... .... .... ..... .... 11
1.5.1 Adding Signals ... .... .... .... .... .... ..... .... 11
1.5.2 Multiplication .... .... .... .... .... .... ..... .... 12
1.6 Harmonics. Fourier.. ..... .... .... .... .... .... ..... .... 13
1.6.1 Odd Signals. ..... .... .... .... .... .... ..... .... 14
1.6.2 Even Signals..... .... .... .... .... .... ..... .... 16
1.6.3 Half Wave Symmetry .. .... .... .... .... ..... .... 18
1.6.4 Pulse Train . ..... .... .... .... .... .... ..... .... 19
1.7 Sampling Frequency. ..... .... .... .... .... .... ..... .... 22
1.8 Suggested Experiments and Exercises. .... .... .... ..... .... 25
1.9 Resources. .... .... ..... .... .... .... .... .... ..... .... 26
1.9.1 MATLAB .. ..... .... .... .... .... .... ..... .... 26
1.9.2 Web Sites .. ..... .... .... .... .... .... ..... .... 28
References.. .... .... .... ..... .... .... .... .... .... ..... .... 28
2 Statistical Aspects ... .... ..... .... .... .... .... .... ..... .... 29
2.1 Introduction ... .... ..... .... .... .... .... .... ..... .... 29
2.2 Random Signals and Probability Density Distributions..... .... 30
2.2.1 Basic Concepts ... .... .... .... .... .... ..... .... 30
2.2.2 Random Signal with Uniform PD. .... .... ..... .... 31
ix
x Contents
2.2.3 Random Signal with Normal (Gaussian) PDF..... .... 33
2.2.4 Random Signal with Log-Normal PDF. .... ..... .... 36
2.3 Expectations and Moments. .... .... .... .... .... ..... .... 38
2.3.1 Expected Values, and Moments... .... .... ..... .... 39
2.3.2 Mean, Variance, Etc.... .... .... .... .... ..... .... 39
2.3.3 Transforms . ..... .... .... .... .... .... ..... .... 41
2.3.4 White Noise ..... .... .... .... .... .... ..... .... 42
2.4 Power Spectra.. .... ..... .... .... .... .... .... ..... .... 42
2.4.1 Basic Concept.... .... .... .... .... .... ..... .... 43
2.4.2 Example of Power Spectral Density of a Random
Variable.... ..... .... .... .... .... .... ..... .... 43
2.4.3 Detecting a Sinusoidal Signal Buried in Noise .... .... 44
2.4.4 Hearing Random Signals.... .... .... .... ..... .... 46
2.5 More Types of PDFs ..... .... .... .... .... .... ..... .... 47
2.5.1 Distributions Related with the Gamma Function... .... 47
2.5.2 Weibull and Rayleigh PDFs . .... .... .... ..... .... 53
2.5.3 Multivariate Gaussian PDFs . .... .... .... ..... .... 55
2.5.4 Discrete Distributions .. .... .... .... .... ..... .... 57
2.6 Distribution Estimation.... .... .... .... .... .... ..... .... 60
2.6.1 Probability Plots .. .... .... .... .... .... ..... .... 60
2.6.2 Histogram .. ..... .... .... .... .... .... ..... .... 61
2.6.3 Likelihood.. ..... .... .... .... .... .... ..... .... 63
2.6.4 The Method of Moments.... .... .... .... ..... .... 65
2.6.5 Mixture of Gaussians... .... .... .... .... ..... .... 67
2.6.6 Kernel Methods... .... .... .... .... .... ..... .... 69
2.7 Monte Carlo Methods..... .... .... .... .... .... ..... .... 72
2.7.1 Monte Carlo Integration .... .... .... .... ..... .... 72
2.7.2 Generation of Random Data with a Desired PDF .. .... 80
2.8 Central Limit .. .... ..... .... .... .... .... .... ..... .... 87
2.9 Bayes’ Rule ... .... ..... .... .... .... .... .... ..... .... 89
2.9.1 Conditional Probability . .... .... .... .... ..... .... 90
2.9.2 Bayes’ Rule. ..... .... .... .... .... .... ..... .... 91
2.9.3 Bayesian Networks. Graphical Models . .... ..... .... 94
2.10 Markov Process .... ..... .... .... .... .... .... ..... .... 96
2.10.1 Markov Chain.... .... .... .... .... .... ..... .... 97
2.10.2 Markov Chain Monte Carlo (MCMC).. .... ..... .... 99
2.10.3 Hidden Markov Chain (HMM) ... .... .... ..... .... 103
2.11 MATLAB Tools for Distributions ... .... .... .... ..... .... 106
2.12 Resources. .... .... ..... .... .... .... .... .... ..... .... 108
2.12.1 MATLAB .. ..... .... .... .... .... .... ..... .... 108
2.12.2 Web Sites .. ..... .... .... .... .... .... ..... .... 109
References.. .... .... .... ..... .... .... .... .... .... ..... .... 110