Digital Signal Processing-A Primer With MATLAB®

339 Pages·2020·28.717 MB·\339

by  Samir I. Abood (Author)

Digital Signal Processing
A Primer With MATLAB®

Digital Signal Processing
A Primer With MATLAB®
Samir I. Abood
MATLAB® is a trademark of The MathWorks, Inc. and is used with permission. The MathWorks does not warrant the accuracy
of the text or exercises in this book. This book’s use or discussion of MATLAB® software or related products does not constitute
endorsement or sponsorship by The MathWorks of a particular pedagogical approach or particular use of the MATLAB® software.
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Dedicated to
My great parents, who never stop giving of themselves in countless ways,
My beloved brothers and sisters;
My dearest wife, who offered me unconditional love
with the light of hope and support;
My beloved kids: Daniah, and Mustafa, whom I can't force myself to stop loving;
To all my family, the symbol of love and giving.

Contents
Preface............................................................................................................................................ xiii
Acknowledgments............................................................................................................................xv
Author ............................................................................................................................................xvii
Chapter 1 Continuous and Discrete Signals .................................................................................1
1.1 Continuous Signals............................................................................................1
1.1.1 Generation of Continuous Signals in MATLAB .................................1
1.1.2 Operations on Signals and Sequences..................................................2
1.2 Discrete-Time Signals .......................................................................................5
1.2.1 Complex Sequences..............................................................................5
1.3 Signals and Systems ..........................................................................................6
1.4 Classification of Signals and Systems...............................................................6
1.4.1 Continuous-Time and Discrete-Time Signals ......................................6
1.4.2 Analog and Digital Signals ..................................................................6
1.4.3 Deterministic and Random Signals......................................................6
1.4.4 Periodic and Nonperiodic Signals........................................................7
1.4.5 Power and Energy Signals....................................................................7
1.4.5.1 What Is Digital Signal Processing?......................................7
1.4.5.2 Why DSP?.............................................................................7
1.4.5.3 Applications (DSP)...............................................................7
1.5 Introduction to MATLAB in DSP.....................................................................8
1.5.1 MATLAB Windows.............................................................................8
1.5.2 Basic Commands in MATLAB............................................................9
1.6 Some Fundamental Sequences........................................................................11
1.6.1 Impulse Response in MATLAB ........................................................ 11
1.6.2 Signal Duration .................................................................................. 12
1.7 Generation of Discrete Signals in MATLAB.................................................. 12
Problems.....................................................................................................................17
Chapter 2 Signals Properties....................................................................................................... 19
2.1 Periodic and Aperiodic Sequences..................................................................19
2.2 Even and Odd Parts of a Signal (Symmetric Sequences).................................20
2.3 Signal Manipulations.......................................................................................23
2.3.1 Transformations of the Independent Variable....................................23
2.3.1.1 Shifting...............................................................................23
2.3.1.2 Reversal ..............................................................................23
2.3.1.3 Time-Scaling ......................................................................23
2.3.1.4 Addition, Multiplication, and Scaling ................................24
2.3.1.5 Addition..............................................................................24
2.3.1.6 Multiplication......................................................................24
2.3.1.7 Scaling................................................................................24
2.3.1.8 Signal Decomposition.........................................................24
2.4 Discrete-Time Systems....................................................................................25
2.4.1 System Properties...............................................................................25
2.4.1.1 Memoryless System............................................................25
2.4.1.2 Additivity............................................................................26
vii
viii Contents
2.4.1.3 Homogeneity.......................................................................26
2.4.1.4 Stability...............................................................................26
2.5 Linear Time-Invariant Causal Systems (LTI).................................................27
2.5.1 Linearity.............................................................................................27
2.5.2 Time-Invariance ................................................................................. 31
2.5.3 Causality............................................................................................. 32
2.6 Definitions .......................................................................................................36
2.6.1 Continuous-Time System ...................................................................36
2.6.2 Discrete-Time System ........................................................................37
2.6.2.1 Delay Operator....................................................................38
2.6.2.2 Convolution Property..........................................................38
2.6.2.3 Impulse Function................................................................38
2.6.2.4 Impulse Response...............................................................38
2.6.2.5 Frequency Response...........................................................38
2.7 System Output .................................................................................................39
2.7.1 Causality.............................................................................................39
2.7.2 Stability..............................................................................................39
2.7.3 Invertibility.........................................................................................40
2.7.4 Memory..............................................................................................40
Problems.....................................................................................................................42
Chapter 3 Convolution ................................................................................................................ 47
3.1 Linear Convolution..........................................................................................47
3.2 Convolution Properties .................................................................................... 47
3.2.1 Commutative Property ....................................................................... 47
3.2.2 Associative Property ..........................................................................48
3.2.3 Distributive Property..........................................................................48
3.3 Types of Convolutions.....................................................................................48
3.3.1 Equations Method ..............................................................................49
3.3.1.1 Convolution of Two Sequences in MATLAB..................... 53
3.3.2 Graphical Method ..............................................................................54
3.3.3 Tabular Method .................................................................................. 55
Problems.....................................................................................................................60
Chapter 4 Difference Equations..................................................................................................65
4.1 Difference Equations and Impulse Responses................................................65
4.2 System Representation Using Its Impulse Response.......................................66
4.3 The Methods That One May Use to Solve the Difference Equations ............. 67
4.4 The Classical Approach...................................................................................68
Problems.....................................................................................................................72
Chapter 5 Discrete-Time Fourier Series (DTFS)........................................................................ 75
5.1 DTFS Coefficients of Periodic Discrete Signals ............................................. 75
5.2 Parseval’s Relation...........................................................................................77
5.3 Discreet Fourier Series....................................................................................79
Problems.....................................................................................................................83
Contents ix
Chapter 6 Discrete-Time Fourier Transform (DTFT) ................................................................85
6.1 Frequency Response........................................................................................85
6.2 DTFT for Any Discrete Signal........................................................................87
6.3 Inverse DTFT..................................................................................................88
6.4 Interconnection of Systems .............................................................................89
6.5 DTFT Properties ............................................................................................. 91
6.6 Applications of DTFT ..................................................................................... 91
6.7 LSI Systems and Difference Equations...........................................................91
6.8 Solving Difference Equations Using DTFT....................................................93
6.9 Frequency Response in MATLAB................................................................ 102
Problems...................................................................................................................106
Chapter 7 Discrete Fourier Transform (DFT) .......................................................................... 109
7.1 Method of Decimation-in-Frequency............................................................109
7.2 Method of Decimation-in-Time..................................................................... 112
7.3 Properties of Discrete Fourier Transform ..................................................... 117
7.4 Discrete Fourier Transform of a Sequence in MATLAB ............................. 122
7.5 Linear Convolution Using the DFT...............................................................123
7.6 Generation of Inverse Discrete Fourier Transform in MATLAB.................124
Problems...................................................................................................................125
Chapter 8 Fast Fourier Transform (FFT).................................................................................. 129
8.1 Fast Fourier Transform Definition................................................................. 129
8.1.1 Decimation-in-Time FFT .................................................................1 29
8.1.2 Decimation-in-Frequency FFT ........................................................1 29
8.2 Finding the FFT of Different Signals in MATLAB...................................... 134
8.3 Power Spectral Density Using Square Magnitude and Autocorrelation ....... 135
8.3.1 Equivalence of FFT and N-phase Sequence Component
Transformation.................................................................................136
Problems...................................................................................................................140
Chapter 9 Z-Transform.............................................................................................................. 143
9.1 Z-Transform Representation.......................................................................... 143
9.2 Region of Convergence (ROC)...................................................................... 144
9.3 Properties of the z-transform ......................................................................... 147
9.4 Inverse z-transform........................................................................................151
9.4.1 Partial Fraction Expansion and a Look-up Table.............................151
9.4.2 Power Series.....................................................................................154
9.4.3 Contour Integration..........................................................................154
Problems...................................................................................................................163
Chapter 10 Z-Transform Applications in DSP............................................................................165
10.1 Evaluation of LTI System Response Using Z-Transform..............................165
10.2 Digital System Implementation from Its Function........................................165
10.3 Pole-Zero Diagrams for a Function in the z-Domain....................................172
10.4 Frequency Response Using z-Transform ....................................................... 172
Problems................................................................................................................... 174