Systems and Signal Processing with MATLAB®: Two Volume Set, 3rd Edition

Cover
Volume 01
Cover
Half Page
Title Page
Copyright Page
Dedication
Table of Contents
Preface
About the Author
Acknowledgment
Chapter 1 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
Chapter 2 Continuous Systems
2.1 Definition of a System
2.2 Input and Output
2.3 Linear Continuous System
2.4 Time-Invariant System
2.5 Systems Without 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 the 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 Continuous Systems: The Characteristic Equation
2.16 Block Diagram Representation of Linear Systems
2.16.1 Integrator
2.16.2 Adder
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 Eigenvalues?
2.20.2 Stability and Eigenvalues
2.21 End-of-Chapter Examples
2.22 End-of-Chapter Problems
Chapter 3 Fourier Series
3.1 Review of Complex Numbers
3.1.1 Definition
3.1.2 Addition
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 Insight: Why the Fourier Series
3.12.1 No Exact Sinusoidal Representation for x(t)
3.12.2 The Frequency Components
3.13 End-of-Chapter Examples
3.14 End-of-Chapter Problems
Chapter 4 The 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
4.8 End-of-Chapter Problems
Chapter 5 The 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
Chapter 6 State-Space and Linear Systems
6.1 Introduction
6.2 A Review of Matrix Algebra
6.2.1 Definition, General Terms, and Notations
6.2.2 The Identity Matrix
6.2.3 Adding Two Matrices
6.2.4 Subtracting Two Matrices
6.2.5 Multiplying a Matrix by a Constant
6.2.6 Determinant of a 2 × 2 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 Eigenvalues of a Matrix
6.2.15 Eigenvectors of a Matrix
6.3 General Representation of Systems in State Space
6.4 General Solution of 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 a Diagonal Matrix
6.6.2 Second Method: A Is of the Form
6.6.3 Third Method: Numerical Evaluation, A of Any Form
6.6.4 Fourth Method: The Cayley–Hamilton Approach
6.6.5 Fifth Method: The Inverse Laplace Method
6.6.6 Sixth Method: Using the General Form of Φ(t) = eAt and Its Properties
6.7 Some Insights: Poles and Stability
6.8 End-of-Chapter Examples
6.9 End-of-Chapter Problems
Index
Volume 02
Cover
Half Title
Title Page
Copyright Page
Dedication
Table of Contents
Preface
About the Author
Acknowledgment
Chapter 1 Signal Representation
1.1 Introduction
1.2 Why Do We Discretize Continuous Systems?
1.3 Periodic and Nonperiodic Discrete Signals
1.4 Unit Step Discrete Signal
1.5 Impulse Discrete Signal
1.6 Ramp Discrete Signal
1.7 Real Exponential Discrete Signal
1.8 Sinusoidal Discrete Signal
1.9 Exponentially Modulated Sinusoidal Signal
1.10 Complex Periodic Discrete Signal
1.11 Shifting Operation
1.12 Representing a Discrete Signal Using Impulses
1.13 Reflection Operation
1.14 Time Scaling
1.15 Amplitude Scaling
1.16 Even and Odd Discrete Signal
1.17 Does a Discrete Signal Have a Time Constant?
1.18 Basic Operations on Discrete Signals
1.18.1 Modulation
1.18.2 Addition and Subtraction
1.18.3 Scalar Multiplication
1.18.4 Combined Operations
1.19 Energy and Power Discrete Signals
1.20 Bounded and Unbounded Discrete Signals
1.21 Some Insights: Signals in the Real World
1.21.1 Step Signal
1.21.2 Impulse Signal
1.21.3 Sinusoidal Signal
1.21.4 Ramp Signal
1.21.5 Other Signals
1.22 End-of-Chapter Examples
1.23 End-of-Chapter Problems
Chapter 2 Discrete System
2.1 Definition of a System
2.2 Input and Output
2.3 Linear Discrete Systems
2.4 Time Invariance and Discrete Signals
2.5 Systems with Memory
2.6 Causal Systems
2.7 Inverse of a System
2.8 Stable System
2.9 Convolution
2.10 Difference Equations of Physical Systems
2.11 Homogeneous Difference Equation and Its Solution
2.11.1 Case When Roots Are All Distinct
2.11.2 Case When Two Roots Are Real and Equal
2.11.3 Case When Two Roots Are Complex
2.12 Nonhomogeneous Difference Equations and Their Solutions
2.12.1 How Do We find the Particular Solution?
2.13 Stability of Linear Discrete Systems: The Characteristic Equation
2.13.1 Stability Depending on the Values of the Poles
2.13.2 Stability from the Jury Test
2.14 Block Diagram Representation of Linear Discrete Systems
2.14.1 Delay Element
2.14.2 Summing/Subtracting Junction
2.14.3 Multiplier
2.15 From the Block Diagram to the Difference Equation
2.16 From the Difference Equation to the Block Diagram: A Formal Procedure
2.17 Impulse Response
2.18 Correlation
2.18.1 Cross-Correlation
2.18.2 Auto-Correlation
2.19 Some Insights
2.19.1 How Can We Find These Eigenvalues?
2.19.2 Stability and Eigenvalues
2.20 End-of-Chapter Examples
2.21 End-of-Chapter Problems
Chapter 3 Fourier Series and the Fourier Transform of Discrete Signals
3.1 Introduction
3.2 Review of Complex Numbers
3.2.1 Definition
3.2.2 Addition
3.2.3 Subtraction
3.2.4 Multiplication
3.2.5 Division
3.2.6 From Rectangular to Polar
3.2.7 From Polar to Rectangular
3.3 Fourier Series of Discrete Periodic Signals
3.4 Discrete System with Periodic Inputs: The Steady-State Response
3.4.1 General Form for yss (n)
3.5 Frequency Response of Discrete Systems
3.5.1 Properties of the Frequency Response
3.5.1.1 Periodicity Property
3.5.1.2 Symmetry Property
3.6 Fourier Transform of Discrete Signals
3.7 Convergence Conditions
3.8 Properties of the Fourier Transform of Discrete Signals
3.8.1 Periodicity Property
3.8.2 Linearity Property
3.8.3 Discrete-Time-Shifting Property
3.8.4 Frequency-Shifting Property
3.8.5 Reflection Property
3.8.6 Convolution Property
3.9 Parsevals Relation and Energy Calculations
3.10 Numerical Evaluation of the Fourier Transform of Discrete Signals
3.11 Some Insights: Why Is This Fourier Transform?
3.11.1 Ease in Analysis and Design
3.11.2 Sinusoidal Analysis
3.12 End-of-Chapter Examples
3.13 End-of-Chapter Problems
Chapter 4 z-Transform and Discrete Systems
4.1 Introduction
4.2 Bilateral z-Transform
4.3 Unilateral z-Transform
4.4 Convergence Considerations
4.5 Inverse z-Transform
4.5.1 Partial Fraction Expansion
4.5.2 Long Division
4.6 Properties of the z-Transform
4.6.1 Linearity Property
4.6.2 Shifting Property
4.6.3 Multiplication by e−an
4.6.4 Convolution
4.7 Representation of Transfer Functions as Block Diagrams
4.8 x(n), h(n), y(n), and the z-Transform
4.9 Solving Difference Equation Using the z-Transform
4.10 Convergence Revisited
4.11 Final-Value Theorem
4.12 Initial-Value Theorem
4.13 Some Insights: Poles and Zeroes
4.13.1 Poles of the System
4.13.2 Zeros of the System
4.13.3 Stability of the System
4.14 End-of-Chapter Examples
4.15 End-of-Chapter Problems
Chapter 5 Discrete Fourier Transform and Discrete Systems
5.1 Introduction
5.2 Discrete Fourier Transform and the Finite-Duration Discrete Signals
5.3 Properties of the DFT
5.3.1 How Does the Defining Equation Work?
5.3.2 DFT Symmetry
5.3.3 DFT Linearity
5.3.4 Magnitude of the DFT
5.3.5 What Does k in x(k), the DFT, Mean?
5.4 Relation the DFT Has with the Fourier Transform of Discrete Signals, the z-Transform, and the Continuous Fourier Transform
5.4.1 DFT and the Fourier Transform of x(n)
5.4.2 DFT and the z-Transform of x(n)
5.4.3 DFT and the Continuous Fourier Transform of x(t)
5.5 Numerical Computation of the DFT
5.6 Fast Fourier Transform: A Faster Way of Computing the DFT
5.7 Applications of the DFT
5.7.1 Circular Convolution
5.7.2 Linear Convolution
5.7.3 Approximation to the Continuous Fourier Transform
5.7.4 Approximation to the Coefficients of the Fourier Series and the Average Power of the Periodic Signal x(t)
5.7.5 Total Energy in the Signal x(n) and x(t)
5.7.6 Block Filtering
5.7.7 Correlation
5.8 Some Insights
5.8.1 DFT is the Same as the fft
5.8.2 DFT Points Are the Samples of the Fourier Transform of x(n)
5.8.3 How Can We Be Certain that Most of the Frequency Contents of x(t) Are in the DFT?
5.8.4 Is the Circular Convolution the Same as the Linear Convolution?
5.8.5. Is |X(w)| ≊ |X(k)|?
5.8.6 Frequency Leakage and the DFT
5.9 End-of-Chapter Examples
5.10 End-of-Chapter Problems
Chapter 6 State-Space and Discrete Systems
6.1 Introduction
6.2 Review on Matrix Algebra
6.2.1 Definition, General Terms, and Notations
6.2.2 Identity Matrix
6.2.3 Adding Two Matrices
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 Inverse of a Matrix
6.2.8 Matrix Multiplication
6.2.9 Eigenvalues of a Matrix
6.2.10 Diagonal Form of a Matrix
6.2.11 Eigenvectors of a Matrix
6.3 General Representation of Systems in State Space
6.3.1 Recursive Systems
6.3.2 Nonrecursive Systems
6.3.3 From the Block Diagram to State Space
6.3.4 From the Transfer Function H(z) to State Space
6.4 Solution of the State-Space Equations in the z-Domain
6.5 General Solution of the State Equation in Real Time
6.6 Properties of An and Its Evaluation
6.7 Transformations for State-Space Representations
6.8 Some Insights: Poles and Stability
6.9 End-of-Chapter Examples
6.10. End-of-Chapter Problems
Index