Discrete Systems and Digital Signal Processing with MATLAB, 2nd Edition

Discrete Systems and Digital Signal Processing with MATLAB, 2nd Edition

by Taan S. ElAli
Released April 2016
Publisher(s): CRC Press
ISBN: 9781000755688

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Book description

"Discrete linear systems and digital signal processing have been treated for years in separate publications. ElAli has skillfully combined these two subjects into a single and very useful volume. � Useful for electrical and computer engineering students and working professionals� a nice addition to the shelves of academic and public libraries. "Sum

Table of contents

  1. Cover
  2. Half Title
  3. Title Page
  4. Copyright Page
  5. Dedication
  6. Table of Contents
  7. Preface
  8. Acknowledgments
  9. Author
  10. 1. Signal Representation
    1. 1.1 Introduction
    2. 1.2 Why Do We Discretize Continuous Systems?
    3. 1.3 Periodic and Nonperiodic Discrete Signals
    4. 1.4 Unit Step Discrete Signal
    5. 1.5 Impulse Discrete Signal
    6. 1.6 Ramp Discrete Signal
    7. 1.7 Real Exponential Discrete Signal
    8. 1.8 Sinusoidal Discrete Signal
    9. 1.9 Exponentially Modulated Sinusoidal Signal
    10. 1.10 Complex Periodic Discrete Signal
    11. 1.11 Shifting Operation
    12. 1.12 Representing a Discrete Signal Using Impulses
    13. 1.13 Reflection Operation
    14. 1.14 Time Scaling
    15. 1.15 Amplitude Scaling
    16. 1.16 Even and Odd Discrete Signal
    17. 1.17 Does a Discrete Signal Have a Time Constant?
    18. 1.18 Basic Operations on Discrete Signals
      1. 1.18.1 Modulation
      2. 1.18.2 Addition and Subtraction
      3. 1.18.3 Scalar Multiplication
      4. 1.18.4 Combined Operations
    19. 1.19 Energy and Power Discrete Signals
    20. 1.20 Bounded and Unbounded Discrete Signals
    21. 1.21 Some Insights: Signals in the Real World
      1. 1.21.1 Step Signal
      2. 1.21.2 Impulse Signal
      3. 1.21.3 Sinusoidal Signal
      4. 1.21.4 Ramp Signal
      5. 1.21.5 Other Signals
    22. End of Chapter Examples
    23. End of Chapter Problems
  11. 2. Discrete System
    1. 2.1 Definition of a System
    2. 2.2 Input and Output
    3. 2.3 Linear Discrete Systems
    4. 2.4 Time Invariance and Discrete Signals
    5. 2.5 Systems with Memory
    6. 2.6 Causal Systems
    7. 2.7 Inverse of a System
    8. 2.8 Stable System
    9. 2.9 Convolution
    10. 2.10 Difference Equations of Physical Systems
    11. 2.11 Homogeneous Difference Equation and Its Solution
      1. 2.11.1 Case When Roots Are All Distinct
      2. 2.11.2 Case When Two Roots Are Real and Equal
      3. 2.11.3 Case When Two Roots Are Complex
    12. 2.12 Nonhomogeneous Difference Equations and Their Solutions
      1. 2.12.1 How Do We Find the Particular Solution?
    13. 2.13 Stability of Linear Discrete Systems: The Characteristic Equation
      1. 2.13.1 Stability Depending on the Values of the Poles
      2. 2.13.2 Stability from the Jury Test
    14. 2.14 Block Diagram Representation of Linear Discrete Systems
      1. 2.14.1 Delay Element
      2. 2.14.2 Summing/Subtracting Junction
      3. 2.14.3 Multiplier
    15. 2.15 From the Block Diagram to the Difference Equation
    16. 2.16 From the Difference Equation to the Block Diagram: A Formal Procedure
    17. 2.17 Impulse Response
    18. 2.18 Correlation
      1. 2.18.1 Cross-Correlation
      2. 2.18.2 Auto-Correlation
    19. 2.19 Some Insights
      1. 2.19.1 How Can We Find These Eigenvalues?
      2. 2.19.2 Stability and Eigenvalues
    20. End of Chapter Examples
    21. End of Chapter Problems
  12. 3. Fourier Series and the Fourier Transform of Discrete Signals
    1. 3.1 Introduction
    2. 3.2 Review of Complex Numbers
      1. 3.2.1 Definition
      2. 3.2.2 Addition
      3. 3.2.3 Subtraction
      4. 3.2.4 Multiplication
      5. 3.2.5 Division
      6. 3.2.6 From Rectangular to Polar
      7. 3.2.7 From Polar to Rectangular
    3. 3.3 Fourier Series of Discrete Periodic Signals
    4. 3.4 Discrete System with Periodic Inputs: The Steady-State Response
      1. 3.4.1 General Form for yss(n)
    5. 3.5 Frequency Response of Discrete Systems
      1. 3.5.1 Properties of the Frequency Response
        1. 3.5.1.1 Periodicity Property
        2. 3.5.1.2 Symmetry Property
    6. 3.6 Fourier Transform of Discrete Signals
    7. 3.7 Convergence Conditions
    8. 3.8 Properties of the Fourier Transform of Discrete Signals
      1. 3.8.1 Periodicity Property
      2. 3.8.2 Linearity Property
      3. 3.8.3 Discrete-Time Shifting Property
      4. 3.8.4 Frequency Shifting Property
      5. 3.8.5 Reflection Property
      6. 3.8.6 Convolution Property
    9. 3.9 Parseval’s Relation and Energy Calculations
    10. 3.10 Numerical Evaluation of the Fourier Transform of Discrete Signals
    11. 3.11 Some Insights: Why Is This Fourier Transform?
      1. 3.11.1 Ease in Analysis and Design
      2. 3.11.2 Sinusoidal Analysis
    12. End of Chapter Examples
    13. End of Chapter Problems
  13. 4. z-Transform and Discrete Systems
    1. 4.1 Introduction
    2. 4.2 Bilateral z-Transform
    3. 4.3 Unilateral z-Transform
    4. 4.4 Convergence Considerations
    5. 4.5 Inverse z-Transform
      1. 4.5.1 Partial Fraction Expansion
      2. 4.5.2 Long Division
    6. 4.6 Properties of the z-Transform
      1. 4.6.1 Linearity Property
      2. 4.6.2 Shifting Property
      3. 4.6.3 Multiplication by e−an
      4. 4.6.4 Convolution
    7. 4.7 Representation of Transfer Functions as Block Diagrams
    8. 4.8 x(n), h(n), y(n), and the z-Transform
    9. 4.9 Solving Difference Equation Using the z-Transform
    10. 4.10 Convergence Revisited
    11. 4.11 Final-Value Theorem
    12. 4.12 Initial-Value Theorem
    13. 4.13 Some Insights: Poles and Zeroes
      1. 4.13.1 Poles of the System
      2. 4.13.2 Zeros of the System
      3. 4.13.3 Stability of the System
    14. End of Chapter Exercises
    15. End of Chapter Problems
  14. 5. State-Space and Discrete Systems
    1. 5.1 Introduction
    2. 5.2 Review on Matrix Algebra
      1. 5.2.1 Definition, General Terms, and Notations
      2. 5.2.2 Identity Matrix
      3. 5.2.3 Adding Two Matrices
      4. 5.2.4 Subtracting Two Matrices
      5. 5.2.5 Multiplying a Matrix by a Constant
      6. 5.2.6 Determinant of a Two-by-Two Matrix
      7. 5.2.7 Transpose of a Matrix
      8. 5.2.8 Inverse of a Matrix
      9. 5.2.9 Matrix Multiplication
      10. 5.2.10 Eigenvalues of a Matrix
      11. 5.2.11 Diagonal Form of a Matrix
      12. 5.2.12 Eigenvectors of a Matrix
    3. 5.3 General Representation of Systems in State Space
      1. 5.3.1 Recursive Systems
      2. 5.3.2 Nonrecursive Systems
      3. 5.3.3 From the Block Diagram to State Space
      4. 5.3.4 From the Transfer Function H(z) to State Space
    4. 5.4 Solution of the State-Space Equations in the z-Domain
    5. 5.5 General Solution of the State Equation in Real Time
    6. 5.6 Properties of An and Its Evaluation
    7. 5.7 Transformations for State-Space Representations
    8. 5.8 Some Insights: Poles and Stability
    9. End of Chapter Examples
    10. End of Chapter Problems
  15. 6. Block Diagrams and Review of Discrete System Representations
    1. 6.1 Introduction
    2. 6.2 Basic Block Diagram Components
      1. 6.2.1 Ideal Delay
      2. 6.2.2 Adder
      3. 6.2.3 Subtractor
      4. 6.2.4 Multiplier
    3. 6.3 Block Diagrams as Interconnected Subsystems
      1. 6.3.1 General Transfer Function Representation
      2. 6.3.2 Parallel Representation
      3. 6.3.3 Series Representation
      4. 6.3.4 Basic Feedback Representation
    4. 6.4 Controllable Canonical Form Block Diagrams with Basic Blocks
    5. 6.5 Observable Canonical Form Block Diagrams with Basic Blocks
    6. 6.6 Diagonal Form Block Diagrams with Basic Blocks
      1. 6.6.1 Distinct Roots Case
      2. 6.6.2 Repeated Roots Case
    7. 6.7 Parallel Block Diagrams with Subsystems
      1. 6.7.1 Distinct Roots Case
      2. 6.7.2 Repeated Roots Case
    8. 6.8 Series Block Diagrams with Subsystems
      1. 6.8.1 Distinct Real Roots Case
      2. 6.8.2 Mixed Complex and Real Roots Case
    9. 6.9 Block Diagram Reduction Rules
      1. 6.9.1 Using the Reduction Rules
      2. 6.9.2 Using Mason’s Rule
    10. End of Chapter Examples
    11. End of Chapter Problems
  16. 7. Discrete Fourier Transform and Discrete Systems
    1. 7.1 Introduction
    2. 7.2 Discrete Fourier Transform and the Finite-Duration Discrete Signals
    3. 7.3 Properties of the DFT
      1. 7.3.1 How Does the Defining Equation Work?
      2. 7.3.2 DFT Symmetry
      3. 7.3.3 DFT Linearity
      4. 7.3.4 Magnitude of the DFT
      5. 7.3.5 What Does k in X(k), the DFT, Mean?
    4. 7.4 Relation the DFT Has with the Fourier Transform of Discrete Signals, the z-Transform, and the Continuous Fourier Transform
      1. 7.4.1 DFT and the Fourier Transform of x(n)
      2. 7.4.2 DFT and the z-Transform of x(n)
      3. 7.4.3 DFT and the Continuous Fourier Transform of x(t)
    5. 7.5 Numerical Computation of the DFT
    6. 7.6 Fast Fourier Transform: A Faster Way of Computing the DFT
    7. 7.7 Applications of the DFT
      1. 7.7.1 Circular Convolution
      2. 7.7.2 Linear Convolution
      3. 7.7.3 Approximation to the Continuous Fourier Transform
      4. 7.7.4 Approximation to the Coefficients of the Fourier Series and the Average Power of the Periodic Signal x(t)
      5. 7.7.5 Total Energy in the Signal x(n) and x(t)
      6. 7.7.6 Block Filtering
      7. 7.7.7 Correlation
    8. 7.8 Some Insights
      1. 7.8.1 DFT Is the Same as the fft
      2. 7.8.2 DFT Points Are the Samples of the Fourier Transform of x(n)
      3. 7.8.3 How Can We Be Certain That Most of the Frequency Contents of x(t) Are in the DFT?
      4. 7.8.4 Is the Circular Convolution the Same as the Linear Convolution?
      5. 7.8.5 Is |X(w)| ≅ |X(k)|?
      6. 7.8.6 Frequency Leakage and the DFT
    9. End of Chapter Exercises
    10. End of Chapter Problems
  17. 8. Sampling and Transformations
    1. 8.1 Need for Converting a Continuous Signal to a Discrete Signal
    2. 8.2 From the Continuous Signal to Its Binary Code Representation
    3. 8.3 From the Binary Code to the Continuous Signal
    4. 8.4 Sampling Operation
      1. 8.4.1 Ambiguity in Real-Time Domain
      2. 8.4.2 Ambiguity in the Frequency Domain
      3. 8.4.3 Sampling Theorem
      4. 8.4.4 Filtering before Sampling
      5. 8.4.5 Sampling and Recovery of the Continuous Signal
    5. 8.5 How Do We Discretize the Derivative Operation?
    6. 8.6 Discretization of the State-Space Representation
    7. 8.7 Bilinear Transformation and the Relationship between the Laplace-Domain and the z-Domain Representations
    8. 8.8 Other Transformation Methods
      1. 8.8.1 Impulse Invariance Method
      2. 8.8.2 Step Invariance Method
      3. 8.8.3 Forward Difference Method
      4. 8.8.4 Backward Difference Method
      5. 8.8.5 Bilinear Transformation
    9. 8.9 Some Insights
      1. 8.9.1 Choice of the Sampling Interval Ts
      2. 8.9.2 Effect of Choosing Ts on the Dynamics of the System
      3. 8.9.3 Does Sampling Introduce Additional Zeros to the Transfer Function H(z)?
    10. End of Chapter Examples
    11. End of Chapter Problems
  18. 9. Infinite Impulse Response Filter Design
    1. 9.1 Introduction
    2. 9.2 Design Process
      1. 9.2.1 Design Based on the Impulse Invariance Method
      2. 9.2.2 Design Based on the Bilinear Transform Method
    3. 9.3 IIR Filter Design Using MATLAB®
      1. 9.3.1 From the Analogue Prototype to the IIR Digital Filter
      2. 9.3.2 Direct Design
    4. 9.4 Some Insights
      1. 9.4.1 Difficulty in Designing IIR Digital Filters in the z-Domain
      2. 9.4.2 Using the Impulse Invariance Method
      3. 9.4.3 Choice of the Sampling Interval Ts
    5. End of Chapter Examples
    6. End of Chapter Problems
  19. 10. Finite Impulse Response Digital Filters
    1. 10.1 Introduction
      1. 10.1.1 What Is an FIR Digital Filter?
      2. 10.1.2 Motivating Example
    2. 10.2 FIR Filter Design
      1. 10.2.1 Stability of FIR Filters
      2. 10.2.2 Linear Phase of FIR Filters
    3. 10.3 Design Based on the Fourier Series: The Windowing Method
      1. 10.3.1 Ideal Lowpass FIR Filter Design
      2. 10.3.2 Other Ideal Digital FIR Filters
      3. 10.3.3 Windows Used in the Design of the Digital FIR Filter
      4. 10.3.4 Which Window Does Give the Optimal h(n)?
      5. 10.3.5 Design of a Digital FIR Differentiator
      6. 10.3.6 Design of Comb FIR Filters
      7. 10.3.7 Design of a Digital Shifter: The Hilbert Transform Filter
    4. 10.4 From IIR to FIR Digital Filters: An Approximation
    5. 10.5 Frequency Sampling and FIR Filter Design
    6. 10.6 FIR Digital Design Using MATLAB®
      1. 10.6.1 Design Using Windows
      2. 10.6.2 Design Using Least-Squared Error
      3. 10.6.3 Design Using the Equiripple Linear Phase
      4. 10.6.4 How to Obtain the Frequency Response
    7. 10.7 Some Insights
      1. 10.7.1 Comparison with IIR Filters
      2. 10.7.2 Different Methods Used in the FIR Filter Design
    8. End of the Chapter Examples
    9. End of Chapter Problems
  20. Bibliography

Product information

  • Title: Discrete Systems and Digital Signal Processing with MATLAB, 2nd Edition
  • Author(s): Taan S. ElAli
  • Release date: April 2016
  • Publisher(s): CRC Press
  • ISBN: 9781000755688