Signals and systems laboratory with MATLAB

559 Pages·2011·4.65 MB·English

by  Palamides

Signals and
Systems
Laboratory
with
MATLAB®
TThhiiss ppaaggee iinntteennttiioonnaallllyy lleefftt bbllaannkk
Alex Palamides
Anastasia Veloni
Boca Raton London New York
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To Zoe
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TThhiiss ppaaggee iinntteennttiioonnaallllyy lleefftt bbllaannkk
Contents
Preface.......................................................................................................................................... xiii
Authors....................................................................................................................................... xvii
1. Introduction to MATLAB.....................................................................................................1
1.1 What Is MATLAB?.......................................................................................................1
1.2 Working Environment.................................................................................................1
1.3 Getting Started..............................................................................................................2
1.3.1 Simple Arithmetic Operations.......................................................................3
1.3.2 Comments........................................................................................................3
1.3.3 The Variable ans..............................................................................................3
1.3.4 Priority of Operations.....................................................................................3
1.3.5 Constants..........................................................................................................4
1.3.6 Built-In Functions............................................................................................5
1.3.7 Variables...........................................................................................................6
1.3.8 Format...............................................................................................................7
1.3.9 Help in MATLAB............................................................................................7
1.4 Memory Management.................................................................................................8
1.4.1 Commandssave-load-exit-quit.........................................................9
1.4.2 The Command clear..................................................................................10
1.5 Commandsdiary and clc.....................................................................................10
1.6 Vectors.........................................................................................................................11
1.6.1 Row Vectors...................................................................................................11
1.6.2 Commandslength=size..........................................................................11
1.6.3 Addition=Subtraction...................................................................................12
1.6.4 Multiplication, Division, and Power..........................................................13
1.6.5 Column Vectors.............................................................................................14
1.6.6 Dot Product of Two Vectors........................................................................14
1.6.7 Useful Commands........................................................................................15
1.7 Matrices........................................................................................................................16
1.7.1 Matrix Concatenation...................................................................................17
1.7.2 WorkingwithMatrices................................................................................17
1.7.3 Addition=Subtraction...................................................................................19
1.7.4 Multiplication of Matrices............................................................................19
1.7.4.1 The DotProductas aSpecial Case of Matrix
Multiplication.................................................................................21
1.7.5 Power of a Matrix.........................................................................................21
1.7.6 Inverse of a Matrix........................................................................................22
1.7.7 Determinant of a Matrix..............................................................................22
1.7.8 Divisionof Matrices......................................................................................23
1.7.9 Transpose of aMatrix...................................................................................24
1.7.10 Special Forms of Matrices............................................................................25
1.7.11 Useful Commands........................................................................................26
1.8 Plotting with MATLAB.............................................................................................27
1.8.1 Plotting in Two Dimensions........................................................................27
v
vi Contents
1.8.2 The Fig File.....................................................................................................29
1.8.3 The Command linspace...........................................................................29
1.8.4 Plotting SeveralFunctions in OneFigure..................................................30
1.8.5 Formatting a Figure......................................................................................32
1.8.6 Plotting in Different Figures........................................................................34
1.8.7 Commandsfor Plotting................................................................................36
1.8.8 Plotting Discrete-Time Functions................................................................38
1.8.9 Graph in Polar Coordinates.........................................................................39
1.8.10 Piecewise Functions......................................................................................39
1.8.11 Plotting in ThreeDimensions......................................................................40
1.8.11.1 PlottingCurves in ThreeDimensions........................................41
1.8.11.2 PlottingSurfaces in ThreeDimensions......................................41
1.9 Complex Numbers.....................................................................................................43
1.9.1 Useful Commands........................................................................................43
1.9.2 Forms of ComplexNumbers.......................................................................44
1.9.3 Operations with Complex Numbers..........................................................45
1.9.4 Graph ofComplex Numbers.......................................................................46
1.10 M-Files.........................................................................................................................48
1.10.1 Scripts..............................................................................................................48
1.10.2 Functions........................................................................................................51
1.11 Input=Output Commands........................................................................................54
1.12 File Management........................................................................................................55
1.13 Logical=Relational Operators...................................................................................57
1.14 Control Flow...............................................................................................................58
1.15 SymbolicVariables.....................................................................................................62
1.15.1 Differentiation of a Function.......................................................................62
1.15.2 Integration of a Function.............................................................................63
1.15.3 Summationof a Function............................................................................63
1.15.4 RationalForm................................................................................................64
1.15.5 Solving AlgebraicEquations.......................................................................64
1.15.6 Solving DifferentialEquations....................................................................65
1.15.7 The Command subs....................................................................................66
1.16 Polynomials.................................................................................................................66
1.17 (Pseudo)Random Numbers......................................................................................68
1.18 Solved Problems.........................................................................................................69
1.19 HomeworkProblems.................................................................................................75
2. Signals....................................................................................................................................77
2.1 Categorization by the Variable Type......................................................................77
2.1.1 Continuous-Time Signals.............................................................................77
2.1.2 Discrete-Time Signals...................................................................................78
2.1.3 Digital Signals................................................................................................79
2.2 Basic Continuous-TimeSignals................................................................................81
2.2.1 SinusoidalSignals.........................................................................................81
2.2.2 Exponential Signals.......................................................................................82
2.2.3 Complex Exponential Signals......................................................................83
2.2.4 Unit Step Function........................................................................................84
2.2.5 Unit Impulse or Dirac Delta Function.......................................................89
Contents vii
2.2.6 Ramp Function..............................................................................................93
2.2.7 RectangularPulse Function.........................................................................96
2.3 Discrete-Time Signals................................................................................................99
2.3.1 Unit Impulse Sequence...............................................................................100
2.3.2 Unit Step Sequence.....................................................................................102
2.3.3 Real Exponential Sequence........................................................................104
2.3.4 Complex Exponential Sequence................................................................105
2.3.5 SinusoidalSequence...................................................................................109
2.4 Properties of Signals................................................................................................111
2.4.1 Periodic Signals...........................................................................................111
2.4.1.1 Sum of PeriodicContinuous-TimeSignals..............................112
2.4.1.2 Construction of PeriodicSignals...............................................114
2.4.2 Causal Signals..............................................................................................118
2.4.3 Even and Odd Signals................................................................................119
2.4.4 Energy and Power Signals.........................................................................121
2.4.5 Deterministic and StochasticSignals........................................................124
2.5 Transformations of the Time Variable for Continuous-TimeSignals..............126
2.5.1 Time Reversalor Reflection.......................................................................126
2.5.2 Time Scaling.................................................................................................127
2.5.3 Time Shifting................................................................................................129
2.6 Transformations of the Time Variable for Discrete-Time Signals.....................132
2.7 Solved Problems.......................................................................................................135
2.8 HomeworkProblems...............................................................................................145
3. Systems................................................................................................................................147
3.1 Systems Classification..............................................................................................147
3.1.1 Classification according to the Number of Inputs and Outputs.........147
3.1.2 Continuous-Time and Discrete-Time Signals.........................................151
3.1.3 Deterministic and StochasticSystems......................................................151
3.2 Properties of Systems...............................................................................................151
3.2.1 Causal and NoncausalSystems................................................................151
3.2.2 Static (Memoryless) and Dynamic(with Memory) Systems................152
3.2.3 Linear and Nonlinear Systems..................................................................155
3.2.4 Time-Invariant andTime-VariantSystems.............................................158
3.2.5 Invertibleand Non-InvertibleSystems....................................................165
3.2.5.1 Construction of the Inverse System..........................................166
3.2.6 Stable and Unstable Systems.....................................................................167
3.3 Solved Problems.......................................................................................................168
3.4 HomeworkProblems...............................................................................................176
4. Time DomainSystemAnalysis......................................................................................179
4.1 Impulse Response.....................................................................................................179
4.2 Continuous-Time Convolution..............................................................................179
4.2.1 Computation of Convolution....................................................................180
4.2.2 The Command conv..................................................................................186
4.2.3 Deconvolution.............................................................................................188
4.2.4 Continuous-Time Convolution Examples...............................................189
4.3 Convolution Properties...........................................................................................199