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1 CHAPTER ONE SIGNAL REPRESENTATION
1.1 EXAMPLES OF CONTINUOUS SIGNALS
1.2 THE CONTINUOUS SIGNAL
1.3 PERIODIC AND NONPERIODIC SIGNALS
1.4 GENERAL FORM OF SINUSOIDAL SIGNALS
1.5 ENERGY AND POWER SIGNALS
1.6 THE SHIFTING OPERATION
1.7 THE REFLECTION OPERATION
1.8 EVEN AND ODD FUNCTIONS
1.9 TIME SCALING
1.10 THE UNIT STEP SIGNAL
1.11 THE SIGNUM SIGNAL
1.12 THE RAMP SIGNAL
1.13 THE SAMPLING SIGNAL
1.14 THE IMPULSE SIGNAL
1.15 SOME INSIGHTS: SIGNALS IN THE REAL WORLD
1.15.1 The Step Signal
1.15.2 The Impulse Signal
1.15.3 The Sinusoidal Signal
1.15.4 The Ramp Signal
1.15.5 Other Signals
1.16 END OF CHAPTER EXAMPLES
1.17 END OF CHAPTER PROBLEMS
2 CHAPTER TWO CONTINUOUS SYSTEMS
2.1 DEFINITION OF A SYSTEM
2.2 INPUT AND OUTPUT
2.3 LINEAR CONTINUOUS SYSTEM
2.4 TIME-INVARIANT SYSTEMS
2.5 SYSTEMS WITH MEMORY
2.6 CAUSAL SYSTEMS
2.7 THE INVERSE OF A SYSTEM
2.8 STABLE SYSTEMS
2.9 CONVOLUTION
2.10 SIMPLE BLOCK DIAGRAMS
2.11 GRAPHICAL CONVOLUTION
2.12 DIFFERENTIAL EQUATIONS AND PHYSICAL SYSTEMS
2.13 HOMOGENEOUS DIFFERENTIAL EQUATIONS AND THEIR SOLUTIONS
2.13.1 Case When Roots Are All Distinct
2.13.2 Case When Two Roots Are Real And Equal
2.13.3 Case When Two Roots Are Complex
2.14 NONHOMOGENEOUS DIFFERENTIAL EQUATIONS AND THEIR SOLUTIONS
2.14.1 How Do We Find The Particular Solution?
2.15 THE STABILITY OF LINEAR SYSTEMS: THE CHARACTERISTIC EQUATION
2.16 BLOCK DIAGRAM REPRESENTATION OF LINEAR SYSTEMS
2.16.1 Integrator
2.16.3 Subtractor
2.16.4 Multiplier
2.17 FROM BLOCK DIAGRAMS TO DIFFERENTIAL EQUATIONS
2.18 FROM DIFFERENTIAL EQUATIONS TO BLOCK DIAGRAMS
2.19 THE IMPULSE RESPONSE
2.20 SOME INSIGHTS: CALCULATING y(t)
2.20.1 How Can We Find These Eigen-Values
2.20.2 Stability And Eigen-Values
2.21 END OF CHAPTER EXAMPLES
2.22 END OF CHAPTER PROBLEMS
3 CHAPTER THREE FOURIER SERIES
3.1 REVIEW OF COMPLEX NUMBERS
3.1.1 Definition
3.1.3 Subtraction
3.1.4 Multiplication
3.1.5 Division
3.1.6 From Rectangular To Polar
3.1.7 From Polar To Rectangular
3.2 ORTHOGONAL FUNCTIONS
3.3 PERIODIC SIGNALS
3.4 CONDITIONS FOR WRITING A SIGNAL AS A FOURIER SERIES SUM
3.5 BASIS FUNCTIONS
3.6 THE MAGNITUDE AND THE PHASE SPECTRA
3.7 FOURIER SERIES AND THE SIN-COS NOTATION
3.8 FOURIER SERIES APPROXIMATION AND THE RESULTING ERROR
3.9 THE THEOREM OF PARSEVAL
3.10 SYSTEMS WITH PERIODIC INPUTS
3.11 A FORMULA FOR FINDING y(t) WHEN x(t) IS PERIODIC: THE STEADY STATE RESPONSE
3.12 SOME INSIGHTS: WHY FOURIER SERIES?
3.12.1 No Exact Sinusoidal Form For x(t)
3.12.2 The Frequency Components
3.13 END OF CHAPTER EXAMPLES
3.14 END OF CHAPTER PROBLEMS
4 CHAPTER FOUR FOURIER TRANSFORM AND LINEAR SYSTEMS
4.1 DEFINITION
4.2 INTRODUCTION
4.3 THE FOURIER TRANSFORM PAIRS
4.4 ENERGY OF NONPERIODIC SIGNALS
4.5 THE ENERGY SPECTRAL DENSITY OF A LINEAR SYSTEM
4.6 SOME INSIGHTS: NOTES AND A USEFUL FORMULA
4.7 END OF CHAPTER EXAMPLES
5 CHAPTER FIVE LAPLACE TRANSFORM AND LINEAR SYSTEMS
5.1 DEFINITION
5.2 THE BILATERAL LAPLACE TRANSFORM
5.3 THE UNILATERAL LAPLACE TRANSFORM
5.4 THE INVERSE LAPLACE TRANSFORM
5.5 BLOCK DIAGRAMS USING THE LAPLACE TRANSFORM
5.5.1 Parallel Systems
5.5.2 Series Systems
5.6 REPRESENTATION OF TRANSFER FUNCTIONS AS BLOCK DIAGRAMS
5.7 PROCEDURE FOR DRAWING THE BLOCK DIAGRAM FROM THE TRANSFER FUNCTION
5.8 SOLVING LTI SYSTEMS USING THE LAPLACE TRANSFORM
5.9 SOLVING DIFFERENTIAL EQUATIONS USING THE LAPLACE TRANSFORM
5.10 THE FINAL VALUE THEOREM
5.11 THE INITIAL VALUE THEOREM
5.12 SOME INSIGHTS: POLES AND ZEROS
5.12.1 The Poles Of The System
5.12.2 The Zeros Of The System
5.12.3 The Stability Of The System
5.13 END OF CHAPTER EXAMPLES
5.14 END OF CHAPTER PROBLEMS
6 CHAPTER SIX STATE-SPACE AND LINEAR SYSTEMS
6.1 INTRODUCTION
6.2 A REVIEW ON MATRIX ALGEBRA
6.2.1 Definition, General Terms, And Notations
6.2.2 The Identity Matrix
6.2.4 Subtracting Two Matrices
6.2.5 Multiplying A Matrix By A Constant
6.2.6 Determinant Of A Two-By-Two Matrix
6.2.7 Transpose Of A Matrix
6.2.8 Inverse Of A Matrix
6.2.9 Matrix Multiplication
6.2.10 Diagonal Form Of A Matrix
6.2.11 Exponent Of A Matrix
6.2.12 A Special Matrix
6.2.13 Observation
6.2.14 Eigen-Values Of A Matrix
6.2.15 Eigen-Vectors Of A Matrix
6.3 GENERAL REPRESENTATION OF SYSTEMS IN STATE-SPACE
6.4 GENERAL SOLUTION OF THE STATE-SPACE EQUATIONS USING THE LAPLACE TRANSFORM
6.5 GENERAL SOLUTION OF THE STATE-SPACE EQUATIONS IN REAL TIME
6.6 WAYS OF EVALUATING eAt
6.6.1 First Method: A Is Diagonal
6.6.2 Second Method: A Is Of The Form
6.6.3 Third Method: Numerical Evaluation, A Of Any Form
6.6.4 Forth Method: The Cayley-Hamilton Approach
6.6.5 Fifth Method: The Inverse Laplace Method
6.6.6 Sixth Method: Using The General Form Of =eAt And Its Properties
6.7 SOME INSIGHTS: POLES AND STABILITY
6.8 END OF CHAPTER EXAMPLES
6.9 END OF CHAPTER PROBLEMS
CHAPTER 7 BLOCK DIAGRAMS
7.1 INTRODUCTION
7.2 BASIC BLOCK DIAGRAM COMPONENTS
7.2.1 The Ideal Integrator
7.2.3 The Subtractor
7.2.4 The Multiplier
7.3 BLOCK DIAGRAMS AS INTERCONNECTED SUBSYSTEMS
7.3.1 The General Transfer Function Representation
7.3.2 The Parallel Representation
7.3.3 The Series Representation
7.3.4 The Basic Feedback Representation
7.4 THE CONTROLLABLE CANONICAL FORM (CCF) BLOCK DIAGRAMS WITH BASIC BLOCKS
7.5 THE OBSERVABLE CANONICAL FORM (OCF) BLOCK DIAGRAMS WITH BASIC BLOCKS
7.6 THE DIAGONAL FORM (DF) BLOCK DIAGRAMS WITH BASIC BLOCKS
7.6.1 Distinct Roots Case
7.6.2 Repeated Roots Case
7.7 THE PARALLEL BLOCK DIAGRAMS WITH SUBSYSTEMS
7.7.1 Distinct Roots Case
7.7.2 Repeated Roots Case
7.8 THE SERIES BLOCK DIAGRAMS WITH SUBSYSTEMS
7.8.1 Distinct Real Roots Case
7.8.2 Mixed Complex And Real Roots Case
7.9 BLOCK DIAGRAM REDUCTION RULES
7.9.1 Using The Reduction Rules
7.9.2 Using Mason¿s Rule
7.10 END OF CHAPTER EXAMPLES
7.10.1 From Block Diagrams With Basic Block Components To Transfer Functions
7.10.2 From Block Diagrams With Interconnected Subsystems To Transfer Functions
7.11 END OF CHAPTER PROBLEMS
8 CHAPTER EIGHT: ANALOGUE FILTER DESIGN
8.1 INTROUDCTION
8.2 ANALOGUE FILTER SPECIFICATIONS
8.3 BUTTERWORTH FILTER APPROXIMATION
8.4 CHEBYSHEV FILTERS
8.4.1 Type I Chebyshev Approximation
8.4.2 Inverse Chebyshev Filter (Type II Chebyshev Filters)
8.5 ELLIPTIC FILTER APPROXIMATION
8.6 BESSEL FILTERS
8.7 ANALOGUE FREQUENCY TRANSFORMATION
8.8 ANALOGUE FILTER DESIGN USING MATLAB
8.8.1 Order Estimation Functions
8.8.2 Analogue Prototype Design Functions
8.8.3 Complete Classical IIR Filter Design
8.8.4 Analogue Frequency Transformation
8.9 HOW DO WE FIND THE CUT-OFF FREQUENCY ANALYTICALLY?
8.10 LMITATIONS
8.11 COMPARISON BETWEEN ANALOGUE FILTER TYPES
8.12 IMPLEMENTATION OF ANALOGUE FILTERS
8.13 SOME INSIGHTS: FILTERS WITH HIGH GAIN VERSUS FILTERS WITH LOW GAIN AND THE RELATION BETWEEN THE TIME CONSTANT AND THE CUT-OFF FREQUENCY FOR FIRST ORDER CIRCUITS AND THE SERIES RLC CIRCUIT
8.14 END OF CHAPTER EXAMPLES
8.15 END OF CHAPTER PROBLEMS
9 CHAPTER NINE INTRODUCTION TO NONLINEAR SYSTEMS
9.1 INTRODUCTION
9.2 LINEAR AND NONLINEAR DIFFERENTIAL EQUATIONS
9.3 THE PROCESS OF LINEARIZATION
9.3.1 Linearization Of A Nonlinear System Given By A Differential Equation
9.3.2 Linearization When f(z) Is A Function Of The State Vector Only
9.3.3 Linearization When f(z) Is A Function Of The State Vector And The Input x(t)
9.4 SOME INSIGHTS: THE MEANING OF LINEAR AND NONLINEAR
9.5 END OF CHAPTER EXAMPLES
9.6 END OF CHAPTER PROBLEMS
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Library of Congress Subject Headings for this publication:

Signal processing -- Mathematics.
System analysis.
MATLAB.