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Signals and Systems

Book Description

Drawing on the author's 25+ years of teaching experience, Signals and Systems: A MATLAB Integrated Approach presents a novel and comprehensive approach to understanding signals and systems theory. Many texts use MATLAB as a computational tool, but Alkin's text employs MATLAB both computationally and pedagogically to provide interactive, visual rein

Table of Contents

  1. Preliminaries
  2. Dedication
  3. Preface
    1. Organization of the Material
    2. To the Instructor
    3. Supplementary Materials
    4. Acknowledgments
  4. Chapter 1 Signal Representation and Modeling
    1. Chapter Objectives
    2. 1.1 Introduction
    3. 1.2 Mathematical Modeling of Signals
    4. 1.3 Continuous-Time Signals
      1. 1.3.1 Signal operations
        1. Arithmetic operations
        2. Time shifting
        3. Time scaling
        4. Time reversal
        5. Integration and differentiation
      2. 1.3.2 Basic building blocks for continuous-time signals
        1. Unit-impulse function
        2. Unit-step function
        3. Unit-pulse function
        4. Unit-ramp function
        5. Unit-triangle function
        6. Sinusoidal signals
      3. 1.3.3 Impulse decomposition for continuous-time signals
      4. 1.3.4 Signal classifications
        1. Real vs. complex signals
        2. Periodic vs. non-periodic signals
        3. Deterministic vs. random signals
      5. 1.3.5 Energy and power definitions
        1. Energy of a signal
        2. Time averaging operator
        3. Power of a signal
        4. Energy signals vs. power signals
        5. RMS value of a signal
      6. 1.3.6 Symmetry properties
        1. Even and odd symmetry
        2. Decomposition into even and odd components
        3. Symmetry properties for complex signals
        4. Decomposition of complex signals
      7. 1.3.7 Graphical representation of sinusoidal signals using phasors
    5. 1.4 Discrete-Time Signals
      1. 1.4.1 Signal operations
        1. Arithmetic operations
        2. Time shifting
        3. Time scaling
        4. Time reversal
      2. 1.4.2 Basic building blocks for discrete-time signals
        1. Unit-impulse function
        2. Unit-step function
        3. Unit-ramp function
        4. Sinusoidal signals
      3. 1.4.3 Impulse decomposition for discrete-time signals
      4. 1.4.4 Signal classifications
        1. Real vs. complex signals
        2. Periodic vs. non-periodic signals
        3. Periodicity of discrete-time sinusoidal signals
        4. Deterministic vs. random signals
      5. 1.4.5 Energy and power definitions
        1. Energy of a signal
        2. Time averaging operator
        3. Power of a signal
        4. Energy signals vs. power signals
      6. 1.4.6 Symmetry properties
        1. Even and odd symmetry
        2. Decomposition into even and odd components
        3. Symmetry properties for complex signals
        4. Decomposition of complex signals
    6. 1.5 Further Reading
    7. MATLAB Exercises
    8. Problems
    9. MATLAB Problems
    10. MATLAB Projects
      1. Figure 1.1
      2. Figure 1.2
      3. Figure 1.3
      4. Figure 1.4
      5. Figure 1.5
      6. Figure 1.6
      7. Figure 1.7
      8. Figure 1.8
      9. Figure 1.9
      10. Figure 1.10
      11. Figure 1.11
      12. Figure 1.12
      13. Figure 1.13
      14. Figure 1.14
      15. Figure 1.15
      16. Figure 1.16
      17. Figure 1.17
      18. Figure 1.18
      19. Figure 1.19
      20. Figure 1.20
      21. Figure 1.21
      22. Figure 1.22
      23. Figure 1.23
      24. Figure 1.24
      25. Figure 1.25
      26. Figure 1.26
      27. Figure 1.27
      28. Figure 1.28
      29. Figure 1.29
      30. Figure 1.30
      31. Figure 1.31
      32. Figure 1.32
      33. Figure 1.33
      34. Figure 1.34
      35. Figure 1.35
      36. Figure 1.36
      37. Figure 1.37
      38. Figure 1.38
      39. Figure 1.39
      40. Figure 1.40
      41. Figure 1.41
      42. Figure 1.42
      43. Figure 1.43
      44. Figure 1.44
      45. Figure 1.45
      46. Figure 1.46
      47. Figure 1.47
      48. Figure 1.48
      49. Figure 1.49
      50. Figure 1.50
      51. Figure 1.51
      52. Figure 1.52
      53. Figure 1.53
      54. Figure 1.54
      55. Figure 1.55
      56. Figure 1.56
      57. Figure 1.57
      58. Figure 1.58
      59. Figure 1.59
      60. Figure 1.60
      61. Figure 1.61
      62. Figure 1.62
      63. Figure 1.63
      64. Figure 1.64
      65. Figure 1.65
      66. Figure 1.66
      67. Figure 1.67
      68. Figure 1.68
      69. Figure 1.69
      70. Figure 1.70
      71. Figure 1.71
      72. Figure 1.72
      73. Figure 1.73
      74. Figure 1.74
      75. Figure 1.75
      76. Figure 1.76
      77. Figure 1.77
      78. Figure 1.78
      79. Figure 1.79
      80. Figure 1.80
      81. Figure 1.81
      82. Figure 1.82
      83. Figure 1.83
      84. Figure 1.84
      85. Figure 1.85
      86. Figure 1.86
      87. Figure 1.87
      88. Figure 1.88
      89. Figure 1.89
      90. Figure 1.90
      91. Figure 1.91
      92. Figure 1.92
      93. Figure 1.93
      94. Figure P. 1.2
      95. Figure P. 1.4
      96. Figure P. 1.10
      97. Figure P. 1.12
      98. Figure P. 1.13
      99. Figure P. 1.23
      100. Figure P. 1.25
      101. Figure P. 1.33
      102. Figure P. 1.39
      103. Figure P. 1.51
  5. Chapter 2 Analyzing Continuous-Time Systems in the Time Domain
    1. Chapter Objectives
    2. 2.1 Introduction
    3. 2.2 Linearity and Time Invariance
      1. 2.2.1 Linearity in continuous-time systems
      2. 2.2.2 Time invariance in continuous-time systems
      3. 2.2.3 CTLTI systems
    4. 2.3 Differential Equations for Continuous-Time Systems
    5. 2.4 Constant-Coefficient Ordinary Differential Equations
    6. 2.5 Solving Differential Equations
      1. 2.5.1 Solution of the first-order differential equation
      2. 2.5.2 Solution of the general differential equation
      3. 2.5.3 Finding the natural response of a continuous-time system
      4. 2.5.4 Finding the forced response of a continuous-time system
    7. 2.6 Block Diagram Representation of Continuous-Time Systems
      1. Imposing initial conditions
    8. 2.7 Impulse Response and Convolution
      1. 2.7.1 Finding impulse response of a CTLTI system
      2. 2.7.2 Convolution operation for CTLTI systems
    9. 2.8 Causality in Continuous-Time Systems
      1. Can a non-causal system be realized?
    10. 2.9 Stability in Continuous-Time Systems
      1. Why is stability important for a CTLTI system?
    11. 2.10 Approximate Numerical Solution of a Differential Equation
    12. 2.11 Further Reading
    13. MATLAB Exercises
    14. Problems
    15. MATLAB Problems
    16. MATLAB Projects
      1. Figure 2.1
      2. Figure 2.2
      3. Figure 2.3
      4. Figure 2.4
      5. Figure 2.5
      6. Figure 2.6
      7. Figure 2.7
      8. Figure 2.8
      9. Figure 2.9
      10. Figure 2.10
      11. Figure 2.11
      12. Figure 2.12
      13. Figure 2.13
      14. Figure 2.14
      15. Figure 2.15
      16. Figure 2.16
      17. Figure 2.17
      18. Figure 2.18
      19. Figure 2.19
      20. Figure 2.20
      21. Figure 2.21
      22. Figure 2.22
      23. Figure 2.23
      24. Figure 2.24
      25. Figure 2.25
      26. Figure 2.26
      27. Figure 2.27
      28. Figure 2.28
      29. Figure 2.29
      30. Figure 2.30
      31. Figure 2.31
      32. Figure 2.32
      33. Figure 2.33
      34. Figure 2.34
      35. Figure 2.35
      36. Figure 2.36
      37. Figure 2.37
      38. Figure 2.38
      39. Figure 2.39
      40. Figure 2.40
      41. Figure 2.41
      42. Figure 2.42
      43. Figure 2.43
      44. Figure 2.44
      45. Figure 2.45
      46. Figure 2.46
      47. Figure 2.47
      48. Figure 2.48
      49. Figure 2.49
      50. Figure 2.50
      51. Figure 2.51
      52. Figure 2.52
      53. Figure 2.53
      54. Figure P. 2.2
      55. Figure P. 2.4
      56. Figure P. 2.5
      57. Figure P. 2.12
      58. Figure P. 2.17
      59. Figure P. 2.18
      60. Figure P. 2.19
      61. Figure P. 2.20
      62. Figure P. 2.23
      63. Figure P. 2.24
      64. Figure P. 2.30
      65. Figure P. 2.36
      66. Figure P. 2.37
      1. Table 2.1
  6. Chapter 3 Analyzing Discrete-Time Systems in the Time Domain
    1. Chapter Objectives
    2. 3.1 Introduction
    3. 3.2 Linearity and Time Invariance
      1. 3.2.1 Linearity in discrete-time systems
      2. 3.2.2 Time invariance in discrete-time systems
      3. 3.2.3 DTLTI systems
    4. 3.3 Difference Equations for Discrete-Time Systems
    5. 3.4 Constant-Coefficient Linear Difference Equations
    6. 3.5 Solving Difference Equations
      1. 3.5.1 Finding the natural response of a discrete-time system
      2. 3.5.2 Finding the forced response of a discrete-time system
    7. 3.6 Block Diagram Representation of Discrete-Time Systems
      1. Imposing initial conditions
    8. 3.7 Impulse Response and Convolution
      1. 3.7.1 Finding impulse response of a DTLTI system
      2. 3.7.2 Convolution operation for DTLTI systems
    9. 3.8 Causality in Discrete-Time Systems
    10. 3.9 Stability in Discrete-Time Systems
      1. Why is stability important for a DTLTI system?
    11. 3.10 Further Reading
    12. MATLAB Exercises
    13. Problems
    14. MATLAB Problems
    15. MATLAB Projects
      1. Figure 3.1
      2. Figure 3.2
      3. Figure 3.3
      4. Figure 3.4
      5. Figure 3.5
      6. Figure 3.6
      7. Figure 3.7
      8. Figure 3.8
      9. Figure 3.9
      10. Figure 3.10
      11. Figure 3.11
      12. Figure 3.12
      13. Figure 3.13
      14. Figure 3.14
      15. Figure 3.15
      16. Figure 3.16
      17. Figure 3.17
      18. Figure 3.18
      19. Figure 3.19
      20. Figure 3.20
      21. Figure 3.21
      22. Figure 3.22
      23. Figure 3.23
      24. Figure 3.24
      25. Figure 3.25
      26. Figure 3.26
      27. Figure 3.27
      28. Figure 3.28
      29. Figure 3.29
      30. Figure 3.30
      31. Figure 3.31
      32. Figure 3.32
      33. Figure 3.33
      34. Figure 3.34
      35. Figure 3.35
      36. Figure P. 3.3
      37. Figure P. 3.19
      38. Figure P. 3.20
      39. Figure P. 3.21
      40. Figure P. 3.22
      41. Figure P. 3.32
      42. Figure P. 3.35
      1. Table 3.1
  7. Chapter 4 Fourier Analysis for Continuous-Time Signals and Systems
    1. Chapter Objectives
    2. 4.1 Introduction
    3. 4.2 Analysis of Periodic Continuous-Time Signals
      1. 4.2.1 Approximating a periodic signal with trigonometric functions
      2. 4.2.2 Trigonometric Fourier series (TFS)
      3. 4.2.3 Exponential Fourier series (EFS)
        1. Single-tone signals
        2. The general case
      4. 4.2.4 Compact Fourier series (CFS)
      5. 4.2.5 Existence of Fourier series
      6. 4.2.6 Gibbs phenomenon
      7. 4.2.7 Properties of Fourier series
        1. Linearity
        2. Symmetry of Fourier series
        3. Fourier series for even and odd signals
        4. Time shifting
    4. 4.3 Analysis of Non-Periodic Continuous-Time Signals
      1. 4.3.1 Fourier transform
      2. 4.3.2 Existence of Fourier transform
      3. 4.3.3 Developing further insight
      4. 4.3.4 Fourier transforms of some signals
      5. 4.3.5 Properties of the Fourier transform
        1. Linearity
        2. Duality
        3. Symmetry of the Fourier Transform
        4. Transforms of even and odd signals
        5. Time shifting
        6. Frequency shifting
        7. Modulation property
        8. Time and frequency scaling
        9. Differentiation in the time domain
        10. Differentiation in the frequency domain
        11. Convolution property
        12. Multiplication of two signals
        13. Integration
      6. 4.3.6 Applying Fourier transform to periodic signals
    5. 4.4 Energy and Power in the Frequency Domain
      1. 4.4.1 Parseval’s theorem
      2. 4.4.2 Energy and power spectral density
      3. 4.4.3 Autocorrelation
        1. Properties of the autocorrelation function
    6. 4.5 System Function Concept
      1. Obtaining the system function from the differential equation
    7. 4.6 CTLTI Systems with Periodic Input Signals
      1. 4.6.1 Response of a CTLTI system to complex exponential signal
      2. 4.6.2 Response of a CTLTI system to sinusoidal signal
      3. 4.6.3 Response of a CTLTI system to periodic input signal
    8. 4.7 CTLTI Systems with Non-Periodic Input Signals
    9. 4.8 Further Reading
    10. MATLAB Exercises
    11. Problems
    12. MATLAB Problems
    13. MATLAB Projects
      1. Figure 4.1
      2. Figure 4.2
      3. Figure 4.3
      4. Figure 4.4
      5. Figure 4.5
      6. Figure 4.6
      7. Figure 4.7
      8. Figure 4.8
      9. Figure 4.9
      10. Figure 4.10
      11. Figure 4.11
      12. Figure 4.12
      13. Figure 4.13
      14. Figure 4.14
      15. Figure 4.15
      16. Figure 4.16
      17. Figure 4.17
      18. Figure 4.18
      19. Figure 4.19
      20. Figure 4.20
      21. Figure 4.21
      22. Figure 4.22
      23. Figure 4.23
      24. Figure 4.24
      25. Figure 4.25
      26. Figure 4.26
      27. Figure 4.27
      28. Figure 4.28
      29. Figure 4.29
      30. Figure 4.30
      31. Figure 4.31
      32. Figure 4.32
      33. Figure 4.33
      34. Figure 4.34
      35. Figure 4.35
      36. Figure 4.36
      37. Figure 4.37
      38. Figure 4.38
      39. Figure 4.39
      40. Figure 4.40
      41. Figure 4.41
      42. Figure 4.42
      43. Figure 4.43
      44. Figure 4.44
      45. Figure 4.45
      46. Figure 4.46
      47. Figure 4.47
      48. Figure 4.48
      49. Figure 4.49
      50. Figure 4.50
      51. Figure 4.51
      52. Figure 4.52
      53. Figure 4.53
      54. Figure 4.54
      55. Figure 4.55
      56. Figure 4.56
      57. Figure 4.57
      58. Figure 4.58
      59. Figure 4.59
      60. Figure 4.60
      61. Figure 4.61
      62. Figure 4.62
      63. Figure 4.63
      64. Figure 4.64
      65. Figure 4.65
      66. Figure 4.66
      67. Figure 4.67
      68. Figure 4.68
      69. Figure 4.69
      70. Figure 4.70
      71. Figure 4.71
      72. Figure 4.72
      73. Figure 4.73
      74. Figure 4.74
      75. Figure 4.75
      76. Figure 4.76
      77. Figure 4.77
      78. Figure 4.78
      79. Figure 4.79
      80. Figure 4.80
      81. Figure 4.81
      82. Figure 4.82
      83. Figure 4.83
      84. Figure 4.84
      85. Figure 4.85
      86. Figure 4.86
      87. Figure 4.87
      88. Figure 4.88
      89. Figure 4.89
      90. Figure 4.90
      91. Figure 4.91
      92. Figure 4.92
      93. Figure 4.93
      94. Figure 4.94
      95. Figure 4.95
      96. Figure 4.96
      97. Figure 4.97
      98. Figure 4.98
      99. Figure 4.99
      100. Figure P. 4.2
      101. Figure P. 4.5
      102. Figure P. 4.7
      103. Figure P. 4.8
      104. Figure P. 4.11
      105. Figure. P.4.14
      106. Figure P. 4.19
      107. Figure. P.4.20
      108. Figure. P.4.23
      109. Figure. P.4.31
      110. Figure. P.4.34
      111. Figure P. 4.47
      112. Figure P. 4.48
      1. Table 4.1
      2. Table 4.2
      3. Table 4.3
      4. Table 4.4
      5. Table 4.5
      6. Table 4.6
  8. Chapter 5 Fourier Analysis for Discrete-Time Signals and Systems
    1. Chapter Objectives
    2. 5.1 Introduction
    3. 5.2 Analysis of Periodic Discrete-Time Signals
      1. 5.2.1 Discrete-Time Fourier Series (DTFS)
        1. Finding DTFS coefficients
      2. 5.2.2 Properties of the DTFS
        1. Periodicity
        2. Linearity
        3. Time shifting
        4. Symmetry of DTFS coefficients
        5. Polar form of DTFS coefficients
        6. DTFS spectra of even and odd signals
        7. Periodic convolution
    4. 5.3 Analysis of Non-Periodic Discrete-Time Signals
      1. 5.3.1 Discrete-time Fourier transform (DTFT)
      2. 5.3.2 Developing further insight
      3. 5.3.3 Existence of the DTFT
      4. 5.3.4 DTFT of some signals
      5. 5.3.5 Properties of the DTFT
        1. Periodicity
        2. Linearity
        3. Time shifting
        4. Time reversal
        5. Conjugation property
        6. Symmetry of the DTFT
        7. Cartesian and polar forms of the transform
        8. Transforms of even and odd signals
        9. Frequency shifting
        10. Modulation property
        11. Differentiation in the frequency domain
        12. Convolution property
        13. Multiplication of two signals
      6. 5.3.6 Applying DTFT to periodic signals
    5. 5.4 Energy and Power in the Frequency Domain
      1. 5.4.1 Parseval’s theorem
      2. 5.4.2 Energy and power spectral density
        1. Energy or power in a frequency range
      3. 5.4.3 Autocorrelation
        1. Properties of the autocorrelation function
    6. 5.5 System Function Concept
      1. Obtaining the system function from the difference equation
    7. 5.6 DTLTI Systems with Periodic Input Signals
      1. 5.6.1 Response of a DTLTI system to complex exponential signal
      2. 5.6.2 Response of a DTLTI system to sinusoidal signal
      3. 5.6.3 Response of a DTLTI system to periodic input signal
    8. 5.7 DTLTI Systems with Non-Periodic Input Signals
    9. 5.8 Discrete Fourier Transform
      1. 5.8.1 Relationship of the DFT to the DTFT
      2. 5.8.2 Zero padding
      3. 5.8.3 Properties of the DFT
        1. Linearity
        2. Time shifting
        3. Time reversal
        4. Conjugation property
        5. Symmetry of the DFT
        6. Frequency shifting
        7. Circular convolution
      4. 5.8.4 Using the DFT to approximate the EFS coefficients
      5. 5.8.5 Using the DFT to approximate the continuous Fourier transform
    10. 5.9 Further Reading
    11. MATLAB Exercises
    12. Problems
    13. MATLAB Problems
    14. MATLAB Projects
      1. Figure 5.1
      2. Figure 5.2
      3. Figure 5.3
      4. Figure 5.4
      5. Figure 5.5
      6. Figure 5.6
      7. Figure 5.7
      8. Figure 5.8
      9. Figure 5.9
      10. Figure 5.10
      11. Figure 5.11
      12. Figure 5.12
      13. Figure 5.13
      14. Figure 5.14
      15. Figure 5.15
      16. Figure 5.16
      17. Figure 5.17
      18. Figure 5.18
      19. Figure 5.19
      20. Figure 5.20
      21. Figure 5.21
      22. Figure 5.22
      23. Figure 5.23
      24. Figure 5.24
      25. Figure 5.25
      26. Figure 5.26
      27. Figure 5.27
      28. Figure 5.28
      29. Figure 5.29
      30. Figure 5.30
      31. Figure 5.31
      32. Figure 5.32
      33. Figure 5.33
      34. Figure 5.34
      35. Figure 5.35
      36. Figure 5.36
      37. Figure 5.37
      38. Figure 5.38
      39. Figure 5.39
      40. Figure 5.40
      41. Figure 5.41
      42. Figure 5.42
      43. Figure 5.43
      44. Figure 5.44
      45. Figure 5.45
      46. Figure 5.46
      47. Figure 5.47
      48. Figure 5.48
      49. Figure 5.49
      50. Figure 5.50
      51. Figure 5.51
      52. Figure 5.52
      53. Figure 5.53
      54. Figure 5.54
      55. Figure 5.55
      56. Figure 5.56
      57. Figure 5.57
      58. Figure P.5.3
      59. Figure P.5.4
      60. Figure P.5.8
      61. Figure P.5.9
      62. Figure P.5.37
      63. Figure P.5.45
      1. Table 5.1
      2. Table 5.2
      3. Table 5.3
      4. Table 5.4
      5. Table 5.5
      6. Table 5.6
  9. Chapter 6 Sampling and Reconstruction
    1. Chapter Objectives
    2. 6.1 Introduction
    3. 6.2 Sampling of a Continuous-Time Signal
      1. 6.2.1 Nyquist sampling criterion
      2. 6.2.2 DTFT of sampled signal
      3. 6.2.3 Sampling of sinusoidal signals
      4. 6.2.4 Practical issues in sampling
        1. Natural sampling
        2. Zero-order hold sampling
    4. 6.3 Reconstruction of a Signal from Its Sampled Version
    5. 6.4 Resampling Discrete-Time Signals
      1. 6.4.1 Reducing the sampling rate by an integer factor
      2. 6.4.2 Increasing the sampling rate by an integer factor
    6. 6.5 Further Reading
    7. MATLAB Exercises
    8. Problems
    9. MATLAB Problems
    10. MATLAB Projects
      1. Figure 6.1
      2. Figure 6.2
      3. Figure 6.3
      4. Figure 6.4
      5. Figure 6.5
      6. Figure 6.6
      7. Figure 6.7
      8. Figure 6.8
      9. Figure 6.9
      10. Figure 6.10
      11. Figure 6.11
      12. Figure 6.12
      13. Figure 6.13
      14. Figure 6.14
      15. Figure 6.15
      16. Figure 6.16
      17. Figure 6.17
      18. Figure 6.18
      19. Figure 6.19
      20. Figure 6.20
      21. Figure 6.21
      22. Figure 6.22
      23. Figure 6.23
      24. Figure 6.24
      25. Figure 6.25
      26. Figure 6.26
      27. Figure 6.27
      28. Figure 6.28
      29. Figure 6.29
      30. Figure 6.30
      31. Figure 6.31
      32. Figure 6.32
      33. Figure 6.33
      34. Figure 6.34
      35. Figure 6.35
      36. Figure 6.36
      37. Figure 6.37
      38. Figure 6.38
      39. Figure 6.39
      40. Figure 6.40
      41. Figure 6.41
      42. Figure 6.42
      43. Figure 6.43
      44. Figure 6.44
      45. Figure 6.45
      46. Figure 6.46
      47. Figure 6.47
      48. Figure 6.48
      49. Figure 6.49
      50. Figure 6.50
      51. Figure 6.51
      52. Figure 6.52
      53. Figure 6.53
      54. Figure 6.54
      55. Figure 6.55
      56. Figure 6.56
      57. Figure 6.57
      58. Figure P. 6.1
      59. Figure P. 6.2
      60. Figure P. 6.14
      61. Figure P. 6.15
      62. Figure P. 6.19
      1. Table 6.1
  10. Chapter 7 Laplace Transform for Continuous-Time Signals and Systems
    1. Chapter Objectives
    2. 7.1 Introduction
    3. 7.2 Characteristics of the Region of Convergence
    4. 7.3 Properties of the Laplace Transform
      1. 7.3.1 Linearity
      2. 7.3.2 Time shifting
      3. 7.3.3 Shifting in the s-domain
      4. 7.3.4 Scaling in time and s-domain
      5. 7.3.5 Differentiation in the time domain
      6. 7.3.6 Differentiation in the s-domain
      7. 7.3.7 Convolution property
      8. 7.3.8 Integration property
    5. 7.4 Inverse Laplace Transform
      1. 7.4.1 Partial fraction expansion with simple poles
      2. 7.4.2 Partial fraction expansion with multiple poles
    6. 7.5 Using the Laplace Transform with CTLTI Systems
      1. 7.5.1 Relating the system function to the differential equation
        1. System function, linearity, and initial conditions
        2. Characteristic polynomial vs. the denominator of the system function
      2. 7.5.2 Response of a CTLTI system to a complex exponential signal
      3. 7.5.3 Response of a CTLTI system to an exponentially damped sinusoid
      4. 7.5.4 Pole-zero plot for a system function
      5. 7.5.5 Graphical interpretation of the pole-zero plot
      6. 7.5.6 System function and causality
      7. 7.5.7 System function and stability
      8. 7.5.8 Allpass systems
      9. 7.5.9 Inverse systems
      10. 7.5.10 Bode plots
        1. Zero at the origin
        2. Pole at the origin
        3. Single real zero
        4. Single real pole
        5. Conjugate pair of poles
        6. Analysis of the second-order system
    7. 7.6. Simulation Structures for CTLTI Systems
      1. 7.6.1 Direct-form implementation
      2. 7.6.2 Cascade and parallel forms
    8. 7.7 Unilateral Laplace Transform
      1. 7.7.1 Time shifting
      2. 7.7.2 Differentiation in time
      3. 7.7.3 Initial and final value theorems
    9. 7.5 Further Reading
    10. MATLAB Exercises
    11. Problems
    12. MATLAB Problems
    13. MATLAB Projects
      1. Figure 7.1
      2. Figure 7.2
      3. Figure 7.3
      4. Figure 7.4
      5. Figure 7.5
      6. Figure 7.6
      7. Figure 7.7
      8. Figure 7.8
      9. Figure 7.9
      10. Figure 7.10
      11. Figure 7.11
      12. Figure 7.12
      13. Figure 7.13
      14. Figure 7.14
      15. Figure 7.15
      16. Figure 7.16
      17. Figure 7.17
      18. Figure 7.18
      19. Figure 7.19
      20. Figure 7.20
      21. Figure 7.21
      22. Figure 7.22
      23. Figure 7.23
      24. Figure 7.24
      25. Figure 7.25
      26. Figure 7.26
      27. Figure 7.27
      28. Figure 7.28
      29. Figure 7.29
      30. Figure 7.30
      31. Figure 7.31
      32. Figure 7.32
      33. Figure 7.33
      34. Figure 7.34
      35. Figure 7.35
      36. Figure 7.36
      37. Figure 7.37
      38. Figure 7.38
      39. Figure 7.39
      40. Figure 7.40
      41. Figure 7.41
      42. Figure 7.42
      43. Figure 7.43
      44. Figure 7.44
      45. Figure 7.45
      46. Figure 7.46
      47. Figure 7.47
      48. Figure 7.48
      49. Figure 7.49
      50. Figure 7.50
      51. Figure 7.51
      52. Figure 7.52
      53. Figure 7.53
      54. Figure 7.54
      55. Figure 7.55
      56. Figure 7.56
      57. Figure 7.57
      58. Figure 7.58
      59. Figure 7.59
      60. Figure 7.60
      61. Figure 7.61
      62. Figure 7.62
      63. Figure 7.63
      64. Figure 7.64
      65. Figure 7.65
      66. Figure 7.66
      67. Figure 7.67
      68. Figure 7.68
      69. Figure 7.69
      70. Figure 7.70
      71. Figure 7.71
      72. Figure 7.72
      73. Figure 7.73
      74. Figure 7.74
      75. Figure 7.75
      76. Figure 7.76
      77. Figure 7.77
      78. Figure 7.78
      79. Figure 7.79
      80. Figure 7.80
      81. Figure P. 7.3
      82. Figure P. 7.13
      83. Figure P. 7.14
      84. Figure P. 7.15
      85. Figure P. 7.34
      86. Figure P. 7.48
      87. Figure P. 7.49
  11. Chapter 8 z-Transform for Discrete-Time Signals and Systems
    1. Chapter Objectives
    2. 8.1 Introduction
    3. 8.2 Characteristics of the Region of Convergence
    4. 8.3 Properties of the z-Transform
      1. 8.3.1 Linearity
      2. 8.3.2 Time shifting
      3. 8.3.3 Time reversal
      4. 8.3.4 Multiplication by an exponential signal
      5. 8.3.5 Differentiation in the z-domain
      6. 8.3.6 Convolution property
      7. 8.3.7 Initial value
      8. 8.3.8 Correlation property
      9. 8.3.9 Summation property
    5. 8.4 Inverse z-Transform
      1. 8.4.1 Inversion integral
      2. 8.4.2 Partial fraction expansion
      3. 8.4.3 Long division
    6. 8.5 Using the z-Transform with DTLTI Systems
      1. 8.5.1 Relating the system function to the difference equation
      2. 8.5.2 Response of a DTLTI system to complex exponential signal
      3. 8.5.3 Response of a DTLTI system to exponentially damped sinusoid
      4. 8.5.4 Graphical interpretation of the pole-zero plot
      5. 8.5.5 System function and causality
      6. 8.5.6 System function and stability
      7. 8.5.7 Allpass systems
      8. 8.5.8 Inverse systems
    7. 8.6 Implementation Structures for DTLTI Systems
      1. 8.6.1 Direct-form implementations
      2. 8.6.2 Cascade and parallel forms
    8. 8.7 Unilateral z-Transform
    9. 8.8 Further Reading
    10. MATLAB Exercises
    11. Problems
    12. MATLAB Problems
    13. MATLAB Project
      1. Figure 8.1
      2. Figure 8.2
      3. Figure 8.3
      4. Figure 8.4
      5. Figure 8.5
      6. Figure 8.6
      7. Figure 8.7
      8. Figure 8.8
      9. Figure 8.9
      10. Figure 8.10
      11. Figure 8.11
      12. Figure 8.12
      13. Figure 8.13
      14. Figure 8.14
      15. Figure 8.15
      16. Figure 8.16
      17. Figure 8.17
      18. Figure 8.18
      19. Figure 8.19
      20. Figure 8.20
      21. Figure 8.21
      22. Figure 8.22
      23. Figure 8.23
      24. Figure 8.24
      25. Figure 8.25
      26. Figure 8.26
      27. Figure 8.27
      28. Figure 8.28
      29. Figure 8.29
      30. Figure 8.30
      31. Figure 8.31
      32. Figure 8.32
      33. Figure 8.33
      34. Figure 8.34
      35. Figure 8.35
      36. Figure 8.36
      37. Figure 8.37
      38. Figure 8.38
      39. Figure 8.39
      40. Figure 8.40
      41. Figure 8.41
      42. Figure 8.42
      43. Figure 8.43
      44. Figure 8.44
      45. Figure 8.45
      46. Figure 8.46
      47. Figure 8.47
      48. Figure 8.48
      49. Figure 8.49
      50. Figure 8.50
      51. Figure 8.51
      52. Figure 8.52
      53. Figure 8.53
      54. Figure 8.54
      55. Figure 8.55
      56. Figure 8.56
      57. Figure 8.57
      58. Figure 8.58
      59. Figure 8.59
      60. Figure 8.60
      61. Figure 8.61
      62. Figure P. 8.3
      63. Figure P. 8.33
      64. Figure P. 8.56
  12. Chapter 9 State-Space Analysis of Systems
    1. Chapter Objectives
    2. 9.1 Introduction
    3. 9.2 State-Space Modeling of Continuous-Time Systems
      1. 9.2.1 State-space models for CTLTI systems
      2. 9.2.2 Obtaining state-space model from physical description
      3. 9.2.3 Obtaining state-space model from differential equation
      4. 9.2.4 Obtaining state-space model from system function
      5. 9.2.5 Alternative state-space models
      6. 9.2.6 CTLTI systems with multiple inputs and/or outputs
      7. 9.2.7 Solution of state-space model
      8. 9.2.8 Computation of the state transition matrix
      9. 9.2.9 Obtaining system function from state-space model
    4. 9.3 State-Space Modeling of Discrete-Time Systems
      1. 9.3.1 State-space models for DTLTI systems
      2. 9.3.2 Obtaining state-space model from difference equation
      3. 9.3.3 Obtaining state-space model from system function
      4. 9.3.4 Solution of state-space model
      5. 9.3.5 Obtaining system function from state-space model
    5. 9.4 Discretization of Continuous-Time State-Space Model
    6. 9.5 Further Reading
    7. MATLAB Exercises
    8. Problems
    9. MATLAB Problems
      1. Figure 9.1
      2. Figure 9.2
      3. Figure 9.3
      4. Figure 9.4
      5. Figure 9.5
      6. Figure 9.6
      7. Figure 9.7
      8. Figure 9.8
      9. Figure 9.9
      10. Figure 9.10
      11. Figure 9.11
      12. Figure 9.12
      13. Figure 9.13
      14. Figure 9.14
      15. Figure 9.15
      16. Figure 9.16
      17. Figure 9.17
      18. Figure 9.18
      19. Figure P. 9.3
      20. Figure P. 9.4
  13. Chapter 10 Analysis and Design of Filters
    1. Chapter Objectives
    2. 10.1 Introduction
    3. 10.2 Distortionless Transmission
    4. 10.3 Ideal Filters
    5. 10.4 Design of Analog Filters
      1. 10.4.1 Butterworth lowpass filters
        1. Obtaining N and ωc for the Butterworth lowpass filter
      2. 10.4.2 Chebyshev lowpass filters
        1. Chebyshev polynomials
        2. Poles for the Chebyshev lowpass filter
        3. Obtaining N and ε for the Chebyshev lowpass filter
      3. 10.4.3 Inverse Chebyshev lowpass filters
        1. Poles and zeros of the inverse Chebyshev filter
        2. Obtaining N and ε for the inverse Chebyshev lowpass filter
      4. 10.4.4 Analog filter transformations
        1. Lowpass to highpass transformation
        2. Lowpass to bandpass transformation
        3. Lowpass to band-reject transformation
    6. 10.5 Design of Digital Filters
      1. 10.5.1 Design of IIR filters
        1. Analog to discrete-time conversion
        2. Impulse invariance
        3. Bilinear transformation
        4. Obtaining analog prototype specifications
      2. 10.5.2 Design of FIR filters
        1. Conditions for linear phase
        2. Fourier series design of FIR filters
        3. Filter types other than lowpass
        4. Parks-McClellan technique for FIR filter design
    7. 10.6 Further Reading
    8. MATLAB Exercises
    9. Problems
    10. MATLAB Problems
    11. MATLAB Projects
      1. Figure 10.1
      2. Figure 10.2
      3. Figure 10.3
      4. Figure 10.4
      5. Figure 10.5
      6. Figure 10.6
      7. Figure 10.7
      8. Figure 10.8
      9. Figure 10.9
      10. Figure 10.10
      11. Figure 10.11
      12. Figure 10.12
      13. Figure 10.13
      14. Figure 10.14
      15. Figure 10.15
      16. Figure 10.16
      17. Figure 10.17
      18. Figure 10.18
      19. Figure 10.19
      20. Figure 10.20
      21. Figure 10.21
      22. Figure 10.22
      23. Figure 10.23
      24. Figure 10.24
      25. Figure 10.25
      26. Figure 10.26
      27. Figure 10.27
      28. Figure 10.28
      29. Figure 10.29
      30. Figure 10.30
      31. Figure 10.31
      32. Figure 10.32
      33. Figure 10.33
      34. Figure 10.34
      35. Figure 10.35
      36. Figure 10.36
      37. Figure 10.37
      38. Figure 10.38
      39. Figure 10.39
      40. Figure 10.40
      41. Figure 10.41
      42. Figure 10.42
      43. Figure 10.43
      44. Figure 10.44
      45. Figure 10.45
      46. Figure 10.46
      47. Figure 10.47
      48. Figure 10.48
      49. Figure 10.49
      50. Figure 10.50
      51. Figure 10.51
      52. Figure 10.52
      53. Figure 10.53
      54. Figure 10.54
      55. Figure 10.55
      56. Figure P. 10.3
      57. Figure P. 10.4
      58. Figure P. 10.19
      59. Figure P. 10.32
      60. Figure P. 10.37
  14. Chapter 11 Amplitude Modulation
    1. Chapter Objectives
    2. 11.1 Introduction
    3. 11.2 The Need for Modulation
    4. 11.3 Types of Modulation
    5. 11.4 Amplitude Modulation
      1. 11.4.1 Frequency spectrum of the AM signal
      2. 11.4.2 Power balance and modulation efficiency
      3. 11.4.3 Generation of AM signals
        1. Switching modulator
        2. Square-law modulator
      4. 11.4.4 Demodulation of AM signals
        1. Envelope detector
        2. Coherent demodulation
    6. 11.5 Double-Sideband Suppressed Carrier Modulation
      1. 11.5.1 Frequency spectrum of the DSB-SC signal
    7. 11.6 Single-Sideband Modulation
    8. 11.7 Further Reading
    9. MATLAB Exercises
    10. Problems
    11. MATLAB Problems
    12. MATLAB Projects
      1. Figure 11.1
      2. Figure 11.2
      3. Figure 11.3
      4. Figure 11.4
      5. Figure 11.5
      6. Figure 11.6
      7. Figure 11.7
      8. Figure 11.8
      9. Figure 11.9
      10. Figure 11.10
      11. Figure 11.11
      12. Figure 11.12
      13. Figure 11.13
      14. Figure 11.14
      15. Figure 11.15
      16. Figure 11.16
      17. Figure 11.17
      18. Figure 11.18
      19. Figure 11.19
      20. Figure 11.20
      21. Figure 11.21
      22. Figure 11.22
      23. Figure 11.23
      24. Figure 11.24
      25. Figure 11.25
      26. Figure 11.26
      27. Figure 11.27
      28. Figure 11.28
      29. Figure 11.29
      30. Figure 11.30
      31. Figure 11.31
      32. Figure 11.32
      33. Figure 11.33
      34. Figure 11.34
      35. Figure 11.35
      36. Figure 11.36
      37. Figure 11.37
      38. Figure 11.38
      39. Figure 11.39
      40. Figure 11.40
      41. Figure P. 11.7
      42. Figure P. 11.9
      43. Figure P. 11.12
      44. Figure P. 11.15
      45. Figure P. 11.16
      46. Figure P. 11.21
      1. Table 11.1
  15. Appendix A Complex Numbers and Euler’s Formula
    1. A.1 Introduction
    2. A.2 Arithmetic with Complex Numbers
      1. A.2.1 Addition and subtraction
      2. A.2.2 Multiplication and division
    3. A.3 Euler’s Formula
      1. Figure A.1
      2. Figure A.2
      3. Figure A.3
  16. Appendix B Mathematical Relations
    1. B.1 Trigonometric Identities
    2. B.2 Indefinite Integrals
    3. B.3 Laplace Transform Pairs
    4. B.4 z-Transform Pairs
  17. Appendix C Closed Forms for Sums of Geometric Series
    1. C.1 Infinite-Length Geometric Series
    2. C.2 Finite-Length Geometric Series
    3. C.3 Finite-Length Geometric Series (Alternative Form)
  18. Appendix D Orthogonality of Basis Functions
    1. D.1 Orthogonality for Trigonometric Fourier Series
    2. D.2 Orthogonality for Exponential Fourier Series
    3. D.3 Orthogonality for Discrete-Time Fourier Series
  19. Appendix E Partial Fraction Expansion
    1. E.1 Partial Fraction Expansion for Continuous-Time Signals and Systems
    2. E.2 Partial Fraction Expansion for Discrete-Time Signals and Systems
  20. Appendix F Review of Matrix Algebra
    1. Matrix
    2. Vector
    3. Square matrix
    4. Diagonal matrix
    5. Identity matrix
    6. Equality of two matrices
    7. Trace of a square matrix
    8. Transpose of a matrix
    9. Determinant of a square matrix
    10. Minors of a square square matrix
    11. Cofactors of a square square matrix
    12. Adjoint of a square square matrix
    13. Scaling a matrix
    14. Addition of two matrices
    15. Scalar product of two vectors
    16. Multiplication of two matrices
    17. Inversion of a matrix
    18. Eigenvalues and eigenvectors