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LINEAR SYSTEMS AND SIGNALS

LINEAR SYSTEMS AND SIGNALS

Author: B. P. Lathi and R. A. Green
Category: engineering
Pages: 1010 | Year: 2017
Tags: 3rd, and, lathi, linear, signals, systems

📖 Book Chapters & Sections

  1. LINEAR SYSTEMS AND SIGNALS (Cover)
  2. (c) (Half title)
  3. [B.2 SINUSOIDS (B.2 SINUSOIDS)](/engineering/linear-systems-and-signals/003_b-2-sinusoids/)
  4. [B.3 SKETCHING SIGNALS (B.3 SKETCHING SIGNALS)](/engineering/linear-systems-and-signals/004_b-3-sketching-signals/)
  5. EXAMPLE B.7 Using Cramer’s Rule to Solve a System of Equations (B.4 CRAMER’S RULE)
  6. [B.5 PARTIAL FRACTION EXPANSION (B.5 PARTIAL FRACTION EXPANSION)](/engineering/linear-systems-and-signals/006_b-5-partial-fraction-expansion/)
  7. [B.6-1 Some Definitions and Properties (B.6 VECTORS AND MATRICES)](/engineering/linear-systems-and-signals/007_b-6-vectors-and-matrices/)
  8. [B.7 MATLAB: ELEMENTARY OPERATIONS (B.7 MATLAB - ELEMENTARY OPERATIONS)](/engineering/linear-systems-and-signals/008_b-7-matlab-elementary-operations/)
  9. [B.8-4 Taylor and Maclaurin Series (B.8 APPENDIX - USEFUL MATHEMATICAL FORMULAS)](/engineering/linear-systems-and-signals/009_b-8-appendix-useful-mathematical-formulas/)
  10. [REFERENCES (REFERENCES)](/engineering/linear-systems-and-signals/010_references/)
  11. - (d) Express w1 + w2 in standard rectangular form. (PROBLEMS)
  12. [SIGNALS AND SYSTEMS (1 SIGNALS AND SYSTEMS)](/engineering/linear-systems-and-signals/012_1-signals-and-systems/)
  13. [1.1 SIZE OF A SIGNAL (1.1 SIZE OF A SIGNAL)](/engineering/linear-systems-and-signals/013_1-1-size-of-a-signal/)
  14. [1.2 SOME USEFUL SIGNAL OPERATIONS (1.2 SOME USEFUL SIGNAL OPERATIONS)](/engineering/linear-systems-and-signals/014_1-2-some-useful-signal-operations/)
  15. [1.3 CLASSIFICATION OF SIGNALS (1.3 CLASSIFICATION OF SIGNALS)](/engineering/linear-systems-and-signals/015_1-3-classification-of-signals/)
  16. [1.4 SOME USEFUL SIGNAL MODELS (1.4 SOME USEFUL SIGNAL MODELS)](/engineering/linear-systems-and-signals/016_1-4-some-useful-signal-models/)
  17. [1.5 EVEN AND ODD FUNCTIONS (1.5 EVEN AND ODD FUNCTIONS)](/engineering/linear-systems-and-signals/017_1-5-even-and-odd-functions/)
  18. [1.6 SYSTEMS (1.6 SYSTEMS)](/engineering/linear-systems-and-signals/018_1-6-systems/)
  19. [1.7 CLASSIFICATION OF SYSTEMS (1.7 CLASSIFICATION OF SYSTEMS)](/engineering/linear-systems-and-signals/019_1-7-classification-of-systems/)
  20. [1.8 SYSTEM MODEL: INPUT–OUTPUT DESCRIPTION (1.8 SYSTEM MODEL - INPUT–OUTPUT DESCRIPTION)](/engineering/linear-systems-and-signals/020_1-8-system-model-input-output-description/)
  21. [1.9 INTERNAL AND EXTERNAL DESCRIPTIONS OF A SYSTEM (1.9 INTERNAL AND EXTERNAL DESCRIPTIONS OF A SYSTEM)](/engineering/linear-systems-and-signals/021_1-9-internal-and-external-descriptions-of-a-system/)
  22. [1.10 INTERNAL DESCRIPTION: THE STATE-SPACE DESCRIPTION (1.10 INTERNAL DESCRIPTION - THE STATE-SPACE DESCRIPTION)](/engineering/linear-systems-and-signals/022_1-10-internal-description-the-state-space-description/)
  23. [1.11 MATLAB: WORKING WITH FUNCTIONS (1.11 MATLAB - WORKING WITH FUNCTIONS)](/engineering/linear-systems-and-signals/023_1-11-matlab-working-with-functions/)
  24. [1.12 SUMMARY (1.12 SUMMARY)](/engineering/linear-systems-and-signals/024_1-12-summary/)
  25. [REFERENCES (REFERENCES)](/engineering/linear-systems-and-signals/025_references/)
  26. [TIME-DOMAIN ANALYSIS OF CONTINUOUS-TIME SYSTEMS (PROBLEMS)](/engineering/linear-systems-and-signals/026_problems/)
  27. 154 CHAPTER 2 TIME-DOMAIN ANALYSIS OF CONTINUOUS-TIME SYSTEMS (2 TIME-DOMAIN ANALYSIS OF CONTINUOUS-TIME SYSTEMS)
  28. (a) (2.2 SYSTEM RESPONSE TO INTERNAL CONDITIONS - THE ZERO-INPUT RESPONSE)
  29. EXAMPLE 2.5 Impulse Response via Impulse Matching (2.3 THE UNIT IMPULSE RESPONSE h(t))
  30. [2.4-1 The Convolution Integral (2.4 SYSTEM RESPONSE TO EXTERNAL INPUT - THE ZERO-STATE RESPONSE)](/engineering/linear-systems-and-signals/030_2-4-system-response-to-external-input-the-zero-state-response/)
  31. [2.5 SYSTEM STABILITY (2.5 SYSTEM STABILITY)](/engineering/linear-systems-and-signals/031_2-5-system-stability/)
  32. [2.6 INTUITIVE INSIGHTS INTO SYSTEM BEHAVIOR (2.6 INTUITIVE INSIGHTS INTO SYSTEM BEHAVIOR)](/engineering/linear-systems-and-signals/032_2-6-intuitive-insights-into-system-behavior/)
  33. [2.7 MATLAB: M-FILES (2.7 MATLAB - M-FILES)](/engineering/linear-systems-and-signals/033_2-7-matlab-m-files/)
  34. [2.8 APPENDIX: DETERMINING THE IMPULSE RESPONSE (2.8 APPENDIX - DETERMINING THE IMPULSE RESPONSE)](/engineering/linear-systems-and-signals/034_2-8-appendix-determining-the-impulse-response/)
  35. [2.9 SUMMARY (2.9 SUMMARY)](/engineering/linear-systems-and-signals/035_2-9-summary/)
  36. [REFERENCES (REFERENCES)](/engineering/linear-systems-and-signals/036_references/)
  37. [PROBLEMS (PROBLEMS)](/engineering/linear-systems-and-signals/037_problems/)
  38. [TIME-DOMAIN ANALYSIS OF DISCRETE-TIME SYSTEMS (3 TIME-DOMAIN ANALYSIS OF DISCRETE-TIME SYSTEMS)](/engineering/linear-systems-and-signals/038_3-time-domain-analysis-of-discrete-time-systems/)
  39. [3.1 INTRODUCTION (3.1 INTRODUCTION)](/engineering/linear-systems-and-signals/039_3-1-introduction/)
  40. [3.2 USEFUL SIGNAL OPERATIONS (3.2 USEFUL SIGNAL OPERATIONS)](/engineering/linear-systems-and-signals/040_3-2-useful-signal-operations/)
  41. [3.3 SOME USEFUL DISCRETE-TIME SIGNAL MODELS (3.3 SOME USEFUL DISCRETE-TIME SIGNAL MODELS)](/engineering/linear-systems-and-signals/041_3-3-some-useful-discrete-time-signal-models/)
  42. [3.4 EXAMPLES OF DISCRETE-TIME SYSTEMS (3.4 EXAMPLES OF DISCRETE-TIME SYSTEMS)](/engineering/linear-systems-and-signals/042_3-4-examples-of-discrete-time-systems/)
  43. [3.5 DISCRETE-TIME SYSTEM EQUATIONS (3.5 DISCRETE-TIME SYSTEM EQUATIONS)](/engineering/linear-systems-and-signals/043_3-5-discrete-time-system-equations/)
  44. [3.7 THE UNIT IMPULSE RESPONSE h[n] (3.6 SYSTEM RESPONSE TO INTERNAL CONDITIONS - THE ZERO-INPUT RESPONSE)](/engineering/linear-systems-and-signals/044_3-6-system-response-to-internal-conditions-the-zero-input-response/)
  45. EXAMPLE 3.17 Iterative Determination of the Impulse Response (3.7 THE UNIT IMPULSE RESPONSE h[n])
  46. [3.8 SYSTEM RESPONSE TO EXTERNAL INPUT: THE ZERO-STATE RESPONSE (3.8 SYSTEM RESPONSE TO EXTERNAL INPUT - THE ZERO-STATE RESPONSE)](/engineering/linear-systems-and-signals/046_3-8-system-response-to-external-input-the-zero-state-response/)
  47. [3.9 SYSTEM STABILITY (3.9 SYSTEM STABILITY)](/engineering/linear-systems-and-signals/047_3-9-system-stability/)
  48. [3.10 INTUITIVE INSIGHTS INTO SYSTEM BEHAVIOR (3.10 INTUITIVE INSIGHTS INTO SYSTEM BEHAVIOR)](/engineering/linear-systems-and-signals/048_3-10-intuitive-insights-into-system-behavior/)
  49. [3.11 MATLAB: DISCRETE-TIME SIGNALS AND SYSTEMS (3.11 MATLAB - DISCRETE-TIME SIGNALS AND SYSTEMS)](/engineering/linear-systems-and-signals/049_3-11-matlab-discrete-time-signals-and-systems/)
  50. [3.12 APPENDIX: IMPULSE RESPONSE FOR A SPECIAL CASE (3.12 APPENDIX - IMPULSE RESPONSE FOR A SPECIAL CASE)](/engineering/linear-systems-and-signals/050_3-12-appendix-impulse-response-for-a-special-case/)
  51. [3.13 SUMMARY (3.13 SUMMARY)](/engineering/linear-systems-and-signals/051_3-13-summary/)
  52. [CONTINUOUS-TIME SYSTEM ANALYSIS USING THE LAPLACE TRANSFORM (PROBLEMS)](/engineering/linear-systems-and-signals/052_problems/)
  53. (a) (4 CONTINUOUS-TIME SYSTEM ANALYSIS USING THE LAPLACE TRANSFORM)
  54. [4.2 SOME PROPERTIES OF THE LAPLACE TRANSFORM (4.2 SOME PROPERTIES OF THE LAPLACE TRANSFORM)](/engineering/linear-systems-and-signals/054_4-2-some-properties-of-the-laplace-transform/)
  55. [4.3 SOLUTION OF DIFFERENTIAL AND INTEGRO-DIFFERENTIAL EQUATIONS (4.3 SOLUTION OF DIFFERENTIAL AND INTEGRO-DIFFERENTIAL EQUATIONS)](/engineering/linear-systems-and-signals/055_4-3-solution-of-differential-and-integro-differential-equations/)
  56. 4.4 ANALYSIS OF ELECTRICAL NETWORKS: THE TRANSFORMED NETWORK (4.4 ANALYSIS OF ELECTRICAL NETWORKS - THE TRANSFORMED NETWORK)
  57. [4.5 BLOCK DIAGRAMS (4.5 BLOCK DIAGRAMS)](/engineering/linear-systems-and-signals/057_4-5-block-diagrams/)
  58. [4.6 SYSTEM REALIZATION (4.6 SYSTEM REALIZATION)](/engineering/linear-systems-and-signals/058_4-6-system-realization/)
  59. [4.7 APPLICATION TO FEEDBACK AND CONTROLS (4.7 APPLICATION TO FEEDBACK AND CONTROLS)](/engineering/linear-systems-and-signals/059_4-7-application-to-feedback-and-controls/)
  60. [4.8 FREQUENCY RESPONSE OF AN LTIC SYSTEM (4.8 FREQUENCY RESPONSE OF AN LTIC SYSTEM)](/engineering/linear-systems-and-signals/060_4-8-frequency-response-of-an-ltic-system/)
  61. [4.9 BODE PLOTS (4.9 BODE PLOTS)](/engineering/linear-systems-and-signals/061_4-9-bode-plots/)
  62. [4.10 FILTER DESIGN BY PLACEMENT OF POLES AND ZEROS OF H(s) (4.10 FILTER DESIGN BY PLACEMENT OF POLES AND ZEROS OF H(s))](/engineering/linear-systems-and-signals/062_4-10-filter-design-by-placement-of-poles-and-zeros-of-h-s/)
  63. [4.11 THE BILATERAL LAPLACE TRANSFORM (4.11 THE BILATERAL LAPLACE TRANSFORM)](/engineering/linear-systems-and-signals/063_4-11-the-bilateral-laplace-transform/)
  64. [4.12 MATLAB: CONTINUOUS-TIME FILTERS (4.12 MATLAB - CONTINUOUS-TIME FILTERS)](/engineering/linear-systems-and-signals/064_4-12-matlab-continuous-time-filters/)
  65. [4.13 SUMMARY (4.13 SUMMARY)](/engineering/linear-systems-and-signals/065_4-13-summary/)
  66. [DISCRETE-TIME SYSTEM ANALYSIS USING THE z-TRANSFORM (REFERENCES)](/engineering/linear-systems-and-signals/066_references/)
  67. 496 CHAPTER 5 DISCRETE-TIME SYSTEM ANALYSIS USING THE Z-TRANSFORM (5 DISCRETE-TIME SYSTEM ANALYSIS USING THE z-TRANSFORM)
  68. [5.2 SOME PROPERTIES OF THE z-TRANSFORM (5.2 SOME PROPERTIES OF THE z-TRANSFORM)](/engineering/linear-systems-and-signals/068_5-2-some-properties-of-the-z-transform/)
  69. (d) (5.3 z-TRANSFORM SOLUTION OF LINEAR DIFFERENCE EQUATIONS)
  70. [5.5 FREQUENCY RESPONSE OF DISCRETE-TIME SYSTEMS (5.5 FREQUENCY RESPONSE OF DISCRETE-TIME SYSTEMS)](/engineering/linear-systems-and-signals/070_5-5-frequency-response-of-discrete-time-systems/)
  71. [5.6 FREQUENCY RESPONSE FROM POLE-ZERO LOCATIONS (5.6 FREQUENCY RESPONSE FROM POLE-ZERO LOCATIONS)](/engineering/linear-systems-and-signals/071_5-6-frequency-response-from-pole-zero-locations/)
  72. [5.7 DIGITAL PROCESSING OF ANALOG SIGNALS (5.7 DIGITAL PROCESSING OF ANALOG SIGNALS)](/engineering/linear-systems-and-signals/072_5-7-digital-processing-of-analog-signals/)
  73. [5.8 THE BILATERAL z-TRANSFORM (5.8 THE BILATERAL z-TRANSFORM)](/engineering/linear-systems-and-signals/073_5-8-the-bilateral-z-transform/)
  74. [5.9 CONNECTING THE LAPLACE AND z-TRANSFORMS (5.9 CONNECTING THE LAPLACE AND z-TRANSFORMS)](/engineering/linear-systems-and-signals/074_5-9-connecting-the-laplace-and-z-transforms/)
  75. [5.10 MATLAB: DISCRETE-TIME IIR FILTERS (5.10 MATLAB - DISCRETE-TIME IIR FILTERS)](/engineering/linear-systems-and-signals/075_5-10-matlab-discrete-time-iir-filters/)
  76. [5.11 SUMMARY (5.11 SUMMARY)](/engineering/linear-systems-and-signals/076_5-11-summary/)
  77. $$ (REFERENCES)
  78. [CONTINUOUS-TIME SIGNAL ANALYSIS: THE FOURIER SERIES (6 CONTINUOUS-TIME SIGNAL ANALYSIS - THE FOURIER SERIES)](/engineering/linear-systems-and-signals/078_6-continuous-time-signal-analysis-the-fourier-series/)
  79. [6.1 PERIODIC SIGNAL REPRESENTATION BY TRIGONOMETRIC FOURIER SERIES (6.1 PERIODIC SIGNAL REPRESENTATION BY TRIGONOMETRIC FOURIER SERIES)](/engineering/linear-systems-and-signals/079_6-1-periodic-signal-representation-by-trigonometric-fourier-series/)
  80. [6.2 EXISTENCE AND CONVERGENCE OF THE FOURIER SERIES (6.2 EXISTENCE AND CONVERGENCE OF THE FOURIER SERIES)](/engineering/linear-systems-and-signals/080_6-2-existence-and-convergence-of-the-fourier-series/)
  81. EXAMPLE 6.6 Exponential Fourier Series of Periodic Exponential Wave (6.3 EXPONENTIAL FOURIER SERIES)
  82. [6.4 LTIC SYSTEM RESPONSE TO PERIODIC INPUTS (6.4 LTIC SYSTEM RESPONSE TO PERIODIC INPUTS)](/engineering/linear-systems-and-signals/082_6-4-ltic-system-response-to-periodic-inputs/)
  83. [6.5 GENERALIZED FOURIER SERIES: SIGNALS AS VECTORS (6.5 GENERALIZED FOURIER SERIES - SIGNALS AS VECTORS)](/engineering/linear-systems-and-signals/083_6-5-generalized-fourier-series-signals-as-vectors/)
  84. [6.6 NUMERICAL COMPUTATION OF Dn (6.6 NUMERICAL COMPUTATION OF D n)](/engineering/linear-systems-and-signals/084_6-6-numerical-computation-of-d_n/)
  85. [6.7 MATLAB: FOURIER SERIES APPLICATIONS (6.7 MATLAB - FOURIER SERIES APPLICATIONS)](/engineering/linear-systems-and-signals/085_6-7-matlab-fourier-series-applications/)
  86. [6.8 SUMMARY (6.8 SUMMARY)](/engineering/linear-systems-and-signals/086_6-8-summary/)
  87. [REFERENCES (REFERENCES)](/engineering/linear-systems-and-signals/087_references/)
  88. [CONTINUOUS-TIME SIGNAL ANALYSIS: THE FOURIER TRANSFORM (PROBLEMS)](/engineering/linear-systems-and-signals/088_problems/)
  89. 696 CHAPTER 7 CONTINUOUS-TIME SIGNAL ANALYSIS: THE FOURIER TRANSFORM (7 CONTINUOUS-TIME SIGNAL ANALYSIS - THE FOURIER TRANSFORM)
  90. [7.2-1 Connection Between the Fourier and Laplace Transforms (7.2 TRANSFORMS OF SOME USEFUL FUNCTIONS)](/engineering/linear-systems-and-signals/090_7-2-transforms-of-some-useful-functions/)
  91. 7.3 Some Properties of the Fourier Transform 701 (7.3 SOME PROPERTIES OF THE FOURIER TRANSFORM)
  92. [7.4 SIGNAL TRANSMISSION THROUGH LTIC SYSTEMS (7.4 SIGNAL TRANSMISSION THROUGH LTIC SYSTEMS)](/engineering/linear-systems-and-signals/092_7-4-signal-transmission-through-ltic-systems/)
  93. [7.5 IDEAL AND PRACTICAL FILTERS (7.5 IDEAL AND PRACTICAL FILTERS)](/engineering/linear-systems-and-signals/093_7-5-ideal-and-practical-filters/)
  94. [7.6 SIGNAL ENERGY (7.6 SIGNAL ENERGY)](/engineering/linear-systems-and-signals/094_7-6-signal-energy/)
  95. [7.7 APPLICATION TO COMMUNICATIONS: AMPLITUDE MODULATION (7.7 APPLICATION TO COMMUNICATIONS - AMPLITUDE MODULATION)](/engineering/linear-systems-and-signals/095_7-7-application-to-communications-amplitude-modulation/)
  96. [7.8 DATA TRUNCATION: WINDOW FUNCTIONS (7.8 DATA TRUNCATION - WINDOW FUNCTIONS)](/engineering/linear-systems-and-signals/096_7-8-data-truncation-window-functions/)
  97. [7.9 MATLAB: FOURIER TRANSFORM TOPICS (7.9 MATLAB - FOURIER TRANSFORM TOPICS)](/engineering/linear-systems-and-signals/097_7-9-matlab-fourier-transform-topics/)
  98. [7.10 SUMMARY (7.10 SUMMARY)](/engineering/linear-systems-and-signals/098_7-10-summary/)
  99. [REFERENCES (REFERENCES)](/engineering/linear-systems-and-signals/099_references/)
  100. [PROBLEMS (PROBLEMS)](/engineering/linear-systems-and-signals/100_problems/)
  101. [SAMPLING: THE BRIDGE FROM CONTINUOUS TO DISCRETE (8 SAMPLING - THE BRIDGE FROM CONTINUOUS TO DISCRETE)](/engineering/linear-systems-and-signals/101_8-sampling-the-bridge-from-continuous-to-discrete/)
  102. [8.1 THE SAMPLING THEOREM (8.1 THE SAMPLING THEOREM)](/engineering/linear-systems-and-signals/102_8-1-the-sampling-theorem/)
  103. [8.2 SIGNAL RECONSTRUCTION (8.2 SIGNAL RECONSTRUCTION)](/engineering/linear-systems-and-signals/103_8-2-signal-reconstruction/)
  104. [8.3 ANALOG-TO-DIGITAL (A/D) CONVERSION (8.3 ANALOG-TO-DIGITAL (A - D) CONVERSION)](/engineering/linear-systems-and-signals/104_8-3-analog-to-digital-a-d-conversion/)
  105. [8.4 DUAL OF TIME SAMPLING: SPECTRAL SAMPLING (8.4 DUAL OF TIME SAMPLING - SPECTRAL SAMPLING)](/engineering/linear-systems-and-signals/105_8-4-dual-of-time-sampling-spectral-sampling/)
  106. [8.5 NUMERICAL COMPUTATION OF THE FOURIER TRANSFORM: THE (8.5 NUMERICAL COMPUTATION OF THE FOURIER TRANSFORM - THE DISCRETE FOURIER TRANSFORM)](/engineering/linear-systems-and-signals/106_8-5-numerical-computation-of-the-fourier-transform-the-discrete-fourier-transform/)
  107. [8.6 THE FAST FOURIER TRANSFORM (FFT) (8.6 THE FAST FOURIER TRANSFORM (FFT))](/engineering/linear-systems-and-signals/107_8-6-the-fast-fourier-transform-fft/)
  108. [8.7 MATLAB: THE DISCRETE FOURIER TRANSFORM (8.7 MATLAB - THE DISCRETE FOURIER TRANSFORM)](/engineering/linear-systems-and-signals/108_8-7-matlab-the-discrete-fourier-transform/)
  109. [8.8 SUMMARY (8.8 SUMMARY)](/engineering/linear-systems-and-signals/109_8-8-summary/)
  110. [REFERENCES (REFERENCES)](/engineering/linear-systems-and-signals/110_references/)
  111. [FOURIER ANALYSIS OF DISCRETE-TIME SIGNALS (PROBLEMS)](/engineering/linear-systems-and-signals/111_problems/)
  112. 852 CHAPTER 9 FOURIER ANALYSIS OF DISCRETE-TIME SIGNALS (9 FOURIER ANALYSIS OF DISCRETE-TIME SIGNALS)
  113. 9.2 APERIODIC SIGNAL REPRESENTATION BY FOURIER INTEGRAL (9.2 APERIODIC SIGNAL REPRESENTATION BY FOURIER INTEGRAL)
  114. FREQUENCY-SHIFTING PROPERTY (9.3 PROPERTIES OF THE DTFT)
  115. [9.4 LTI DISCRETE-TIME SYSTEM ANALYSIS BY DTFT (9.4 LTI DISCRETE-TIME SYSTEM ANALYSIS BY DTFT)](/engineering/linear-systems-and-signals/115_9-4-lti-discrete-time-system-analysis-by-dtft/)
  116. [9.5 DTFT CONNECTION WITH THE CTFT (9.5 DTFT CONNECTION WITH THE CTFT)](/engineering/linear-systems-and-signals/116_9-5-dtft-connection-with-the-ctft/)
  117. [9.6 GENERALIZATION OF THE DTFT TO THE z-TRANSFORM (9.6 GENERALIZATION OF THE DTFT TO THE z-TRANSFORM)](/engineering/linear-systems-and-signals/117_9-6-generalization-of-the-dtft-to-the-z-transform/)
  118. [9.7-1 Computing the Discrete-Time Fourier Series (9.7 MATLAB - WORKING WITH THE DTFS AND THE DTFT)](/engineering/linear-systems-and-signals/118_9-7-matlab-working-with-the-dtfs-and-the-dtft/)
  119. [9.8 SUMMARY (9.8 SUMMARY)](/engineering/linear-systems-and-signals/119_9-8-summary/)
  120. [REFERENCE (REFERENCE)](/engineering/linear-systems-and-signals/120_reference/)
  121. $$ (PROBLEMS)
  122. [STATE-SPACE ANALYSIS (10 STATE-SPACE ANALYSIS)](/engineering/linear-systems-and-signals/122_10-state-space-analysis/)
  123. 910 CHAPTER 10 STATE-SPACE ANALYSIS (10.1 MATHEMATICAL PRELIMINARIES)
  124. [10.2 INTRODUCTION TO STATE SPACE (10.2 INTRODUCTION TO STATE SPACE)](/engineering/linear-systems-and-signals/124_10-2-introduction-to-state-space/)
  125. [10.3 A SYSTEMATIC PROCEDURE TO DETERMINE STATE EQUATIONS (10.3 A SYSTEMATIC PROCEDURE TO DETERMINE STATE EQUATIONS)](/engineering/linear-systems-and-signals/125_10-3-a-systematic-procedure-to-determine-state-equations/)
  126. [10.4 SOLUTION OF STATE EQUATIONS (10.4 SOLUTION OF STATE EQUATIONS)](/engineering/linear-systems-and-signals/126_10-4-solution-of-state-equations/)
  127. [10.5 LINEAR TRANSFORMATION OF A STATE VECTOR (10.5 LINEAR TRANSFORMATION OF A STATE VECTOR)](/engineering/linear-systems-and-signals/127_10-5-linear-transformation-of-a-state-vector/)
  128. [10.6 CONTROLLABILITY AND OBSERVABILITY (10.6 CONTROLLABILITY AND OBSERVABILITY)](/engineering/linear-systems-and-signals/128_10-6-controllability-and-observability/)
  129. [10.7 STATE-SPACE ANALYSIS OF DISCRETE-TIME SYSTEMS (10.7 STATE-SPACE ANALYSIS OF DISCRETE-TIME SYSTEMS)](/engineering/linear-systems-and-signals/129_10-7-state-space-analysis-of-discrete-time-systems/)
  130. [10.8 MATLAB: TOOLBOXES AND STATE-SPACE ANALYSIS (10.8 MATLAB - TOOLBOXES AND STATE-SPACE ANALYSIS)](/engineering/linear-systems-and-signals/130_10-8-matlab-toolboxes-and-state-space-analysis/)
  131. [10.9 SUMMARY (10.9 SUMMARY)](/engineering/linear-systems-and-signals/131_10-9-summary/)
  132. $$ (REFERENCES)
  133. [INDEX (INDEX)](/engineering/linear-systems-and-signals/133_index/)

📋 Original Table of Contents

  • Cover (p. 1)
  • Half title (p. 3)
  • Series page (p. 4)
  • Title page (p. 5)
  • Copyright page (p. 6)
  • CONTENTS (p. 7)
  • PREFACE (p. 17)
  • B BACKGROUND (p. 21)
    • B.1 COMPLEX NUMBERS (p. 21)
      • B.1-1 A Historical Note (p. 21)
      • B.1-2 Algebra of Complex Numbers (p. 25)
    • B.2 SINUSOIDS (p. 36)
      • B.2-1 Addition of Sinusoids (p. 38)
      • B.2-2 Sinusoids in Terms of Exponentials (p. 40)
    • B.3 SKETCHING SIGNALS (p. 40)
      • B.3-1 Monotonic Exponentials (p. 40)
      • B.3-2 The Exponentially Varying Sinusoid (p. 42)
    • B.4 CRAMER’S RULE (p. 43)
    • B.5 PARTIAL FRACTION EXPANSION (p. 45)
      • B.5-1 Method of Clearing Fractions (p. 46)
      • B.5-2 The Heaviside “Cover-Up” Method (p. 47)
      • B.5-3 Repeated Factors of Q(x) (p. 51)
      • B.5-4 A Combination of Heaviside “Cover-Up” and Clearing Fractions (p. 52)
      • B.5-5 Improper F(x) with m = n (p. 54)
      • B.5-6 Modified Partial Fractions (p. 55)
    • B.6 VECTORS AND MATRICES (p. 56)
      • B.6-1 Some Definitions and Properties (p. 57)
      • B.6-2 Matrix Algebra (p. 58)
    • B.7 MATLAB: ELEMENTARY OPERATIONS (p. 62)
      • B.7-1 MATLAB Overview (p. 62)
      • B.7-2 Calculator Operations (p. 63)
      • B.7-3 Vector Operations (p. 65)
      • B.7-4 Simple Plotting (p. 66)
      • B.7-5 Element-by-Element Operations (p. 68)
      • B.7-6 Matrix Operations (p. 69)
      • B.7-7 Partial Fraction Expansions (p. 73)
    • B.8 APPENDIX: USEFUL MATHEMATICAL FORMULAS (p. 74)
      • B.8-1 Some Useful Constants (p. 74)
      • B.8-2 Complex Numbers (p. 74)
      • B.8-3 Sums (p. 74)
      • B.8-4 Taylor and Maclaurin Series (p. 75)
      • B.8-5 Power Series (p. 75)
      • B.8-6 Trigonometric Identities (p. 75)
      • B.8-7 Common Derivative Formulas (p. 76)
      • B.8-8 Indefinite Integrals (p. 77)
      • B.8-9 L’Hôpital’s Rule (p. 78)
      • B.8-10 Solution of Quadratic and Cubic Equations (p. 78)
    • REFERENCES (p. 78)
    • PROBLEMS (p. 79)
  • 1 SIGNALS AND SYSTEMS (p. 84)
    • 1.1 SIZE OF A SIGNAL (p. 84)
      • 1.1-1 Signal Energy (p. 85)
      • 1.1-2 Signal Power (p. 85)
    • 1.2 SOME USEFUL SIGNAL OPERATIONS (p. 91)
      • 1.2-1 Time Shifting (p. 91)
      • 1.2-2 Time Scaling (p. 93)
      • 1.2-3 Time Reversal (p. 96)
      • 1.2-4 Combined Operations (p. 97)
    • 1.3 CLASSIFICATION OF SIGNALS (p. 98)
      • 1.3-1 Continuous-Time and Discrete-Time Signals (p. 98)
      • 1.3-2 Analog and Digital Signals (p. 98)
      • 1.3-3 Periodic and Aperiodic Signals (p. 99)
      • 1.3-4 Energy and Power Signals (p. 102)
      • 1.3-5 Deterministic and Random Signals (p. 102)
    • 1.4 SOME USEFUL SIGNAL MODELS (p. 102)
      • 1.4-1 The Unit Step Function u(t) (p. 103)
      • 1.4-2 The Unit Impulse Function δ(t) (p. 106)
      • 1.4-3 The Exponential Function e^{st} (p. 109)
    • 1.5 EVEN AND ODD FUNCTIONS (p. 112)
      • 1.5-1 Some Properties of Even and Odd Functions (p. 112)
      • 1.5-2 Even and Odd Components of a Signal (p. 113)
    • 1.6 SYSTEMS (p. 115)
    • 1.7 CLASSIFICATION OF SYSTEMS (p. 117)
      • 1.7-1 Linear and Nonlinear Systems (p. 117)
      • 1.7-2 Time-Invariant and Time-Varying Systems (p. 122)
      • 1.7-3 Instantaneous and Dynamic Systems (p. 123)
      • 1.7-4 Causal and Noncausal Systems (p. 124)
      • 1.7-5 Continuous-Time and Discrete-Time Systems (p. 127)
      • 1.7-6 Analog and Digital Systems (p. 129)
      • 1.7-7 Invertible and Noninvertible Systems (p. 129)
      • 1.7-8 Stable and Unstable Systems (p. 130)
    • 1.8 SYSTEM MODEL: INPUT–OUTPUT DESCRIPTION (p. 131)
      • 1.8-1 Electrical Systems (p. 131)
      • 1.8-2 Mechanical Systems (p. 134)
      • 1.8-3 Electromechanical Systems (p. 138)
    • 1.9 INTERNAL AND EXTERNAL DESCRIPTIONS OF A SYSTEM (p. 139)
    • 1.10 INTERNAL DESCRIPTION: THE STATE-SPACE DESCRIPTION (p. 141)
    • 1.11 MATLAB: WORKING WITH FUNCTIONS (p. 146)
      • 1.11-1 Anonymous Functions (p. 146)
      • 1.11-2 Relational Operators and the Unit Step Function (p. 148)
      • 1.11-3 Visualizing Operations on the Independent Variable (p. 150)
      • 1.11-4 Numerical Integration and Estimating Signal Energy (p. 151)
    • 1.12 SUMMARY (p. 153)
    • REFERENCES (p. 155)
    • PROBLEMS (p. 156)
  • 2 TIME-DOMAIN ANALYSIS OF CONTINUOUS-TIME SYSTEMS (p. 170)
    • 2.1 INTRODUCTION (p. 170)
    • 2.2 SYSTEM RESPONSE TO INTERNAL CONDITIONS: THE ZERO-INPUT RESPONSE (p. 171)
      • 2.2-1 Some Insights into the Zero-Input Behavior of a System (p. 181)
    • 2.3 THE UNIT IMPULSE RESPONSE h(t) (p. 183)
    • 2.4 SYSTEM RESPONSE TO EXTERNAL INPUT: THE ZERO-STATE RESPONSE (p. 188)
      • 2.4-1 The Convolution Integral (p. 190)
      • 2.4-2 Graphical Understanding of Convolution Operation (p. 198)
      • 2.4-3 Interconnected Systems (p. 210)
      • 2.4-4 A Very Special Function for LTIC Systems: The Everlasting Exponential e^{st} (p. 213)
      • 2.4-5 Total Response (p. 215)
    • 2.5 SYSTEM STABILITY (p. 216)
      • 2.5-1 External (BIBO) Stability (p. 216)
      • 2.5-2 Internal (Asymptotic) Stability (p. 218)
      • 2.5-3 Relationship Between BIBO and Asymptotic Stability (p. 219)
    • 2.6 INTUITIVE INSIGHTS INTO SYSTEM BEHAVIOR (p. 223)
      • 2.6-1 Dependence of System Behavior on Characteristic Modes (p. 223)
      • 2.6-2 Response Time of a System: The System Time Constant (p. 225)
      • 2.6-3 Time Constant and Rise Time of a System (p. 226)
      • 2.6-4 Time Constant and Filtering (p. 227)
      • 2.6-5 Time Constant and Pulse Dispersion (Spreading) (p. 229)
      • 2.6-6 Time Constant and Rate of Information Transmission (p. 229)
      • 2.6-7 The Resonance Phenomenon (p. 230)
    • 2.7 MATLAB: M-FILES (p. 232)
      • 2.7-1 Script M-Files (p. 233)
      • 2.7-2 Function M-Files (p. 234)
      • 2.7-3 For-Loops (p. 235)
      • 2.7-4 Graphical Understanding of Convolution (p. 237)
    • 2.8 APPENDIX: DETERMINING THE IMPULSE RESPONSE (p. 240)
    • 2.9 SUMMARY (p. 241)
    • REFERENCES (p. 243)
    • PROBLEMS (p. 243)
  • 3 TIME-DOMAIN ANALYSIS OF DISCRETE-TIME SYSTEMS (p. 257)
    • 3.1 INTRODUCTION (p. 257)
      • 3.1-1 Size of a Discrete-Time Signal (p. 258)
    • 3.2 USEFUL SIGNAL OPERATIONS (p. 260)
    • 3.3 SOME USEFUL DISCRETE-TIME SIGNAL MODELS (p. 265)
      • 3.3-1 Discrete-Time Impulse Function δ[n] (p. 265)
      • 3.3-2 Discrete-Time Unit Step Function u[n] (p. 266)
      • 3.3-3 Discrete-Time Exponential γ^n (p. 267)
      • 3.3-4 Discrete-Time Sinusoid cos(Omega n+θ) (p. 271)
      • 3.3-5 Discrete-Time Complex Exponential e^{jOmega n} (p. 272)
    • 3.4 EXAMPLES OF DISCRETE-TIME SYSTEMS (p. 273)
      • 3.4-1 Classification of Discrete-Time Systems (p. 282)
    • 3.5 DISCRETE-TIME SYSTEM EQUATIONS (p. 285)
      • 3.5-1 Recursive (Iterative) Solution of Difference Equation (p. 286)
    • 3.6 SYSTEM RESPONSE TO INTERNAL CONDITIONS: THE ZERO-INPUT RESPONSE (p. 290)
    • 3.7 THE UNIT IMPULSE RESPONSE h[n] (p. 297)
      • 3.7-1 The Closed-Form Solution of h[n] (p. 298)
    • 3.8 SYSTEM RESPONSE TO EXTERNAL INPUT: THE ZERO-STATE RESPONSE (p. 300)
      • 3.8-1 Graphical Procedure for the Convolution Sum (p. 308)
      • 3.8-2 Interconnected Systems (p. 314)
      • 3.8-3 Total Response (p. 317)
    • 3.9 SYSTEM STABILITY (p. 318)
      • 3.9-1 External (BIBO) Stability (p. 318)
      • 3.9-2 Internal (Asymptotic) Stability (p. 319)
      • 3.9-3 Relationship Between BIBO and Asymptotic Stability (p. 321)
    • 3.10 INTUITIVE INSIGHTS INTO SYSTEM BEHAVIOR (p. 325)
    • 3.11 MATLAB: DISCRETE-TIME SIGNALS AND SYSTEMS (p. 326)
      • 3.11-1 Discrete-Time Functions and Stem Plots (p. 326)
      • 3.11-2 System Responses Through Filtering (p. 328)
      • 3.11-3 A Custom Filter Function (p. 330)
      • 3.11-4 Discrete-Time Convolution (p. 331)
    • 3.12 APPENDIX: IMPULSE RESPONSE FOR A SPECIAL CASE (p. 333)
    • 3.13 SUMMARY (p. 333)
    • PROBLEMS (p. 334)
  • 4 CONTINUOUS-TIME SYSTEM ANALYSIS USING THE LAPLACE TRANSFORM (p. 350)
    • 4.1 THE LAPLACE TRANSFORM (p. 350)
      • 4.1-1 Finding the Inverse Transform (p. 358)
    • 4.2 SOME PROPERTIES OF THE LAPLACE TRANSFORM (p. 369)
      • 4.2-1 Time Shifting (p. 369)
      • 4.2-2 Frequency Shifting (p. 373)
      • 4.2-3 The Time-Differentiation Property (p. 374)
      • 4.2-4 The Time-Integration Property (p. 376)
      • 4.2-5 The Scaling Property (p. 377)
      • 4.2-6 Time Convolution and Frequency Convolution (p. 377)
    • 4.3 SOLUTION OF DIFFERENTIAL AND INTEGRO-DIFFERENTIAL EQUATIONS (p. 380)
      • 4.3-1 Comments on Initial Conditions at 0^− and at 0^+ (p. 383)
      • 4.3-2 Zero-State Response (p. 386)
      • 4.3-3 Stability (p. 391)
      • 4.3-4 Inverse Systems (p. 393)
    • 4.4 ANALYSIS OF ELECTRICAL NETWORKS: THE TRANSFORMED NETWORK (p. 393)
      • 4.4-1 Analysis of Active Circuits (p. 402)
    • 4.5 BLOCK DIAGRAMS (p. 406)
    • 4.6 SYSTEM REALIZATION (p. 408)
      • 4.6-1 Direct Form I Realization (p. 409)
      • 4.6-2 Direct Form II Realization (p. 410)
      • 4.6-3 Cascade and Parallel Realizations (p. 413)
      • 4.6-4 Transposed Realization (p. 416)
      • 4.6-5 Using Operational Amplifiers for System Realization (p. 419)
    • 4.7 APPLICATION TO FEEDBACK AND CONTROLS (p. 424)
      • 4.7-1 Analysis of a Simple Control System (p. 426)
    • 4.8 FREQUENCY RESPONSE OF AN LTIC SYSTEM (p. 432)
      • 4.8-1 Steady-State Response to Causal Sinusoidal Inputs (p. 438)
    • 4.9 BODE PLOTS (p. 439)
      • 4.9-1 Constant Ka_1a_2/b_1b_3 (p. 442)
      • 4.9-2 Pole (or Zero) at the Origin (p. 442)
      • 4.9-3 First-Order Pole (or Zero) (p. 444)
      • 4.9-4 Second-Order Pole (or Zero) (p. 446)
      • 4.9-5 The Transfer Function from the Frequency Response (p. 455)
    • 4.10 FILTER DESIGN BY PLACEMENT OF POLES AND ZEROS OF H(s) (p. 456)
      • 4.10-1 Dependence of Frequency Response on Poles and Zeros of H(s) (p. 456)
      • 4.10-2 Lowpass Filters (p. 459)
      • 4.10-3 Bandpass Filters (p. 461)
      • 4.10-4 Notch (Bandstop) Filters (p. 461)
      • 4.10-5 Practical Filters and Their Specifications (p. 464)
    • 4.11 THE BILATERAL LAPLACE TRANSFORM (p. 465)
      • 4.11-1 Properties of the Bilateral Laplace Transform (p. 471)
      • 4.11-2 Using the Bilateral Transform for Linear System Analysis (p. 472)
    • 4.12 MATLAB: CONTINUOUS-TIME FILTERS (p. 475)
      • 4.12-1 Frequency Response and Polynomial Evaluation (p. 476)
      • 4.12-2 Butterworth Filters and the Find Command (p. 479)
      • 4.12-3 Using Cascaded Second-Order Sections for Butterworth Filter Realization (p. 481)
      • 4.12-4 Chebyshev Filters (p. 483)
    • 4.13 SUMMARY (p. 486)
    • REFERENCES (p. 488)
    • PROBLEMS (p. 488)
  • 5 DISCRETE-TIME SYSTEM ANALYSIS USING THE z-TRANSFORM (p. 508)
    • 5.1 THE z-TRANSFORM (p. 508)
      • 5.1-1 Inverse Transform by Partial Fraction Expansion and Tables (p. 515)
      • 5.1-2 Inverse z-Transform by Power Series Expansion (p. 519)
    • 5.2 SOME PROPERTIES OF THE z-TRANSFORM (p. 521)
      • 5.2-1 Time-Shifting Properties (p. 521)
      • 5.2-2 z-Domain Scaling Property (Multiplication by γ^n) (p. 525)
      • 5.2-3 z-Domain Differentiation Property (Multiplication by n) (p. 526)
      • 5.2-4 Time-Reversal Property (p. 526)
      • 5.2-5 Convolution Property (p. 527)
    • 5.3 z-TRANSFORM SOLUTION OF LINEAR DIFFERENCE EQUATIONS (p. 530)
      • 5.3-1 Zero-State Response of LTID Systems: The Transfer Function (p. 534)
      • 5.3-2 Stability (p. 538)
      • 5.3-3 Inverse Systems (p. 539)
    • 5.4 SYSTEM REALIZATION (p. 539)
    • 5.5 FREQUENCY RESPONSE OF DISCRETE-TIME SYSTEMS (p. 546)
      • 5.5-1 The Periodic Nature of Frequency Response (p. 552)
      • 5.5-2 Aliasing and Sampling Rate (p. 556)
    • 5.6 FREQUENCY RESPONSE FROM POLE-ZERO LOCATIONS (p. 558)
    • 5.7 DIGITAL PROCESSING OF ANALOG SIGNALS (p. 567)
    • 5.8 THE BILATERAL z-TRANSFORM (p. 574)
      • 5.8-1 Properties of the Bilateral z-Transform (p. 579)
      • 5.8-2 Using the Bilateral z-Transform for Analysis of LTID Systems (p. 580)
    • 5.9 CONNECTING THE LAPLACE AND z-TRANSFORMS (p. 583)
    • 5.10 MATLAB: DISCRETE-TIME IIR FILTERS (p. 585)
      • 5.10-1 Frequency Response and Pole-Zero Plots (p. 586)
      • 5.10-2 Transformation Basics (p. 587)
      • 5.10-3 Transformation by First-Order Backward Difference (p. 588)
      • 5.10-4 Bilinear Transformation (p. 589)
      • 5.10-5 Bilinear Transformation with Prewarping (p. 590)
      • 5.10-6 Example: Butterworth Filter Transformation (p. 591)
      • 5.10-7 Problems Finding Polynomial Roots (p. 592)
      • 5.10-8 Using Cascaded Second-Order Sections to Improve Design (p. 592)
    • 5.11 SUMMARY (p. 594)
    • REFERENCES (p. 595)
    • PROBLEMS (p. 595)
  • 6 CONTINUOUS-TIME SIGNAL ANALYSIS: THE FOURIER SERIES (p. 613)
    • 6.1 PERIODIC SIGNAL REPRESENTATION BY TRIGONOMETRIC FOURIER SERIES (p. 613)
      • 6.1-1 The Fourier Spectrum (p. 618)
      • 6.1-2 The Effect of Symmetry (p. 627)
      • 6.1-3 Determining the Fundamental Frequency and Period (p. 629)
    • 6.2 EXISTENCE AND CONVERGENCE OF THE FOURIER SERIES (p. 632)
      • 6.2-1 Convergence of a Series (p. 633)
      • 6.2-2 The Role of Amplitude and Phase Spectra in Waveshaping (p. 635)
    • 6.3 EXPONENTIAL FOURIER SERIES (p. 641)
      • 6.3-1 Exponential Fourier Spectra (p. 644)
      • 6.3-2 Parseval’s Theorem (p. 652)
      • 6.3-3 Properties of the Fourier Series (p. 655)
    • 6.4 LTIC SYSTEM RESPONSE TO PERIODIC INPUTS (p. 657)
    • 6.5 GENERALIZED FOURIER SERIES:SIGNALS AS VECTORS (p. 661)
      • 6.5-1 Component of a Vector (p. 662)
      • 6.5-2 Signal Comparison and Component of a Signal (p. 663)
      • 6.5-3 Extension to Complex Signals (p. 665)
      • 6.5-4 Signal Representation by an Orthogonal Signal Set (p. 667)
    • 6.6 NUMERICAL COMPUTATION OF D_n (p. 679)
    • 6.7 MATLAB: FOURIER SERIES APPLICATIONS (p. 681)
      • 6.7-1 Periodic Functions and the Gibbs Phenomenon (p. 681)
      • 6.7-2 Optimization and Phase Spectra (p. 684)
    • 6.8 SUMMARY (p. 687)
    • REFERENCES (p. 688)
    • PROBLEMS (p. 689)
  • 7 CONTINUOUS-TIME SIGNAL ANALYSIS: THE FOURIER TRANSFORM (p. 700)
    • 7.1 APERIODIC SIGNAL REPRESENTATION BY THE FOURIER INTEGRAL (p. 700)
      • 7.1-1 Physical Appreciation of the Fourier Transform (p. 707)
    • 7.2 TRANSFORMS OF SOME USEFUL FUNCTIONS (p. 709)
      • 7.2-1 Connection Between the Fourier and Laplace Transforms (p. 720)
    • 7.3 SOME PROPERTIES OF THE FOURIER TRANSFORM (p. 721)
    • 7.4 SIGNAL TRANSMISSION THROUGH LTIC SYSTEMS (p. 741)
      • 7.4-1 Signal Distortion During Transmission (p. 743)
      • 7.4-2 Bandpass Systems and Group Delay (p. 746)
    • 7.5 IDEAL AND PRACTICAL FILTERS (p. 750)
    • 7.6 SIGNAL ENERGY (p. 753)
    • 7.7 APPLICATION TO COMMUNICATIONS: AMPLITUDE MODULATION (p. 756)
      • 7.7-1 Double-Sideband, Suppressed-Carrier (DSB-SC) Modulation (p. 757)
      • 7.7-2 Amplitude Modulation (AM) (p. 762)
      • 7.7-3 Single-Sideband Modulation (SSB) (p. 766)
      • 7.7-4 Frequency-Division Multiplexing (p. 769)
    • 7.8 DATA TRUNCATION: WINDOW FUNCTIONS (p. 769)
      • 7.8-1 Using Windows in Filter Design (p. 775)
    • 7.9 MATLAB: FOURIER TRANSFORM TOPICS (p. 775)
      • 7.9-1 The Sinc Function and the Scaling Property (p. 777)
      • 7.9-2 Parseval’s Theorem and Essential Bandwidth (p. 778)
      • 7.9-3 Spectral Sampling (p. 779)
      • 7.9-4 Kaiser Window Functions (p. 780)
    • 7.10 SUMMARY (p. 782)
    • REFERENCES (p. 783)
    • PROBLEMS (p. 784)
  • 8 SAMPLING: THE BRIDGE FROM CONTINUOUS TO DISCRETE (p. 796)
    • 8.1 THE SAMPLING THEOREM (p. 796)
      • 8.1-1 Practical Sampling (p. 801)
    • 8.2 SIGNAL RECONSTRUCTION (p. 805)
      • 8.2-1 Practical Difficulties in Signal Reconstruction (p. 808)
      • 8.2-2 Some Applications of the Sampling Theorem (p. 816)
    • 8.3 ANALOG-TO-DIGITAL (A/D) CONVERSION (p. 819)
    • 8.4 DUAL OF TIME SAMPLING: SPECTRAL SAMPLING (p. 822)
    • 8.5 NUMERICAL COMPUTATION OF THE FOURIER TRANSFORM: THE DISCRETE FOURIER TRANSFORM (p. 825)
      • 8.5-1 Some Properties of the DFT (p. 838)
      • 8.5-2 Some Applications of the DFT (p. 840)
    • 8.6 THE FAST FOURIER TRANSFORM (FFT) (p. 844)
    • 8.7 MATLAB: THE DISCRETE FOURIER TRANSFORM (p. 847)
      • 8.7-1 Computing the Discrete Fourier Transform (p. 847)
      • 8.7-2 Improving the Picture with Zero Padding (p. 849)
      • 8.7-3 Quantization (p. 851)
    • 8.8 SUMMARY (p. 854)
    • REFERENCES (p. 855)
    • PROBLEMS (p. 855)
  • 9 FOURIER ANALYSIS OF DISCRETE-TIME SIGNALS (p. 865)
    • 9.1 DISCRETE-TIME FOURIER SERIES (DTFS) (p. 865)
      • 9.1-1 Periodic Signal Representation by Discrete-Time Fourier Series (p. 866)
      • 9.1-2 Fourier Spectra of a Periodic Signal x[n] (p. 868)
    • 9.2 APERIODIC SIGNAL REPRESENTATION BY FOURIER INTEGRAL (p. 875)
      • 9.2-1 Nature of Fourier Spectra (p. 878)
      • 9.2-2 Connection Between the DTFT and the z-Transform (p. 886)
    • 9.3 PROPERTIES OF THE DTFT (p. 887)
    • 9.4 LTI DISCRETE-TIME SYSTEM ANALYSIS BY DTFT (p. 898)
      • 9.4-1 Distortionless Transmission (p. 900)
      • 9.4-2 Ideal and Practical Filters (p. 902)
    • 9.5 DTFT CONNECTION WITH THE CTFT (p. 903)
      • 9.5-1 Use of DFT and FFT for Numerical Computation of the DTFT (p. 905)
    • 9.6 GENERALIZATION OF THE DTFT TO THE z-TRANSFORM (p. 906)
    • 9.7 MATLAB: WORKING WITH THE DTFS AND THE DTFT (p. 909)
      • 9.7-1 Computing the Discrete-Time Fourier Series (p. 909)
      • 9.7-2 Measuring Code Performance (p. 911)
      • 9.7-3 FIR Filter Design by Frequency Sampling (p. 912)
    • 9.8 SUMMARY (p. 918)
    • REFERENCE (p. 918)
    • PROBLEMS (p. 919)
  • 10 STATE-SPACE ANALYSIS (p. 928)
    • 10.1 MATHEMATICAL PRELIMINARIES (p. 929)
      • 10.1-1 Derivatives and Integrals of aMatrix (p. 929)
      • 10.1-2 The Characteristic Equation of a Matrix: The Cayley–Hamilton Theorem (p. 930)
      • 10.1-3 Computation of an Exponential and a Power of aMatrix (p. 932)
    • 10.2 INTRODUCTION TO STATE SPACE (p. 933)
    • 10.3 A SYSTEMATIC PROCEDURE TO DETERMINE STATE EQUATIONS (p. 936)
      • 10.3-1 Electrical Circuits (p. 936)
      • 10.3-2 State Equations from a Transfer Function (p. 939)
    • 10.4 SOLUTION OF STATE EQUATIONS (p. 946)
      • 10.4-1 Laplace Transform Solution of State Equations (p. 947)
      • 10.4-2 Time-Domain Solution of State Equations (p. 953)
    • 10.5 LINEAR TRANSFORMATION OF A STATE VECTOR (p. 959)
      • 10.5-1 Diagonalization of Matrix A (p. 963)
    • 10.6 CONTROLLABILITY AND OBSERVABILITY (p. 967)
      • 10.6-1 Inadequacy of the Transfer Function Description of a System (p. 973)
    • 10.7 STATE-SPACE ANALYSIS OF DISCRETE-TIME SYSTEMS (p. 973)
      • 10.7-1 Solution in State Space (p. 975)
      • 10.7-2 The z-Transform Solution (p. 979)
    • 10.8 MATLAB: TOOLBOXES AND STATE-SPACE ANALYSIS (p. 981)
      • 10.8-1 z-Transform Solutions to Discrete-Time, State-Space Systems (p. 981)
      • 10.8-2 Transfer Functions from State-Space Representations (p. 984)
      • 10.8-3 Controllability and Observability of Discrete-Time Systems (p. 985)
      • 10.8-4 Matrix Exponentiation and the Matrix Exponential (p. 988)
    • 10.9 SUMMARY (p. 989)
    • REFERENCES (p. 990)
    • PROBLEMS (p. 990)
  • INDEX (p. 995)

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