Signals and Systems Using MATLAB, Fourth Edition features a pedagogically rich and accessible approach to what can commonly be a mathematically dry subject. Historical notes and common mistakes combined with applications in controls, communications, and signal processing help students understand and appreciate the usefulness of the techniques described in the text. This new edition features more worked examples and a variety of new end-of-chapter problems, suggestions for labs, and more explanation of MATLAB code.
1. 0.1: Introduction - p. 4 2. 0.2: Examples of signal processing applications - p. 4 3. 0.3: Implementation of digital signal processing algorithms - p. 7 4. 0.4: Continuous or discrete? - p. 10 5. 0.5: Complex or real? - p. 20 6. 0.6: Soft introduction to MATLAB - p. 33 7. 0.7: Problems - p. 53 8. Chapter 1 Continuous-time signals - p. 65 9. 1.1: Introduction - p. 65 10. 1.2: Classification of time-dependent signals - p. 66 11. 1.3: Continuous-time signals - p. 67 12. 1.4: Representation of continuous-time signals using basic signals - p. 84 13. 1.5: Time scaling, modulation, windowing, and integration - p. 99 14. 1.6: Special signals—the sampling and the sinc signals - p. 109 15. 1.7: What have we accomplished? Where do we go from here? - p. 110 16. 1.8: Problems - p. 110 17. Chapter 2 Continuous-time systems - p. 123 18. 2.1: Introduction - p. 123 19. 2.2: System concept and classification - p. 124 20. 2.3: Linear time-invariant (LTI) continuous-time systems - p. 126 21. 2.4: The convolution integral - p. 144 22. 2.5: Causality - p. 158 23. 2.6: Bounded-input bounded-output (BIBO) stability - p. 162 24. 2.7: What have we accomplished? Where do we go from here? - p. 167 25. 2.8: Problems - p. 167 26. Chapter 3 The Laplace transform - p. 180 27. 3.1: Introduction - p. 180 28. 3.2: The two-sided Laplace transform - p. 181 29. 3.3: The one-sided Laplace transform - p. 190 30. 3.4: Properties of the one-sided Laplace transform - p. 198 31. 3.5: Inverse Laplace transform - p. 211 32. 3.6: The transfer function of LTI systems - p. 225 33. 3.7: Analysis of LTI systems represented by differential equations - p. 232 34. 3.8: Inverse of two-sided Laplace transforms - p. 240 35. 3.9: Application of Laplace transform to control theory - p. 243 36. 3.9.1: Application to classical control - p. 245 37. 3.9.2: Stability and stabilization - p. 250 38. 3.9.3: Transient analysis of first- and second-order control systems - p. 253 39. 3.9.4: State-variable representation of LTI systems - p. 259 40. 3.10: What have we accomplished? Where do we go from here? - p. 267 41. 3.11: Problems - p. 267 42. 3.11.1: Basic problems - p. 267 43. 3.11.2: Problem using MATLAB - p. 276 44. Chapter 4 Frequency analysis: the Fourier series - p. 283 45. 4.1: Introduction - p. 283 46. 4.2: Eigenfunctions revisited - p. 284 47. 4.3: Complex exponential Fourier series - p. 291 48. 4.3.1: Line spectrum—power distribution over frequency - p. 294 49. 4.3.2: Trigonometric Fourier series - p. 296 50. 4.3.3: Fourier series and Laplace transform - p. 300 51. 4.3.4: Reflection and even and odd periodic signals - p. 303 52. 4.3.5: Convergence of the Fourier series - p. 318 53. 4.3.6: Time and frequency shifting - p. 321 54. 4.4: Response of LTI systems to periodic signals - p. 325 55. 4.5: Operations using Fourier series - p. 332 56. 4.6: What have we accomplished? Where do we go from here? - p. 343 57. 4.7: Problems - p. 344 58. Chapter 5 Frequency analysis: the Fourier transform - p. 356 59. 5.1: Introduction - p. 356 60. 5.2: From the Fourier series to the Fourier transform - p. 356 61. 5.3: Existence of the Fourier transform - p. 358 62. 5.4: Fourier transforms from the Laplace transform - p. 359 63. 5.5: Linearity, inverse proportionality, and duality - p. 360 64. 5.6: Spectral representation - p. 370 65. 5.7: Convolution and filtering - p. 382 66. 5.8: Additional properties - p. 398 67. 5.9: Application of Fourier analysis to communications and filtering - p. 405 68. 5.9.1: Application to communications - p. 405 69. 5.9.2: Analog filter design - p. 416 70. 5.10: What have we accomplished? What is next? - p. 434 71. 5.11: Problems - p. 436 72. Chapter 6 Sampling theory - p. 451 73. 6.1: Introduction - p. 451 74. 6.2: Uniform sampling - p. 452 75. 6.3: Practical aspects of sampling - p. 473 76. 6.4: Application to digital communications - p. 480 77. 6.5: What have we accomplished? Where do we go from here? - p. 484 78. 6.6: Problems - p. 484 79. Chapter 7 Discrete-time signals and systems - p. 491 80. 7.1: Introduction - p. 492 81. 7.2: Discrete-time signals - p. 492 82. 7.2.1: Periodic and aperiodic discrete-time signals - p. 494 83. 7.2.2: Finite energy and finite power discrete-time signals - p. 498 84. 7.2.3: Even and odd discrete-time signals - p. 501 85. 7.2.4: Basic discrete-time signals - p. 504 86. 7.3: Discrete-time systems - p. 515 87. 7.3.1: Recursive and nonrecursive discrete-time systems - p. 517 88. 7.3.2: Dynamic discrete-time systems represented by difference equations - p. 521 89. 7.3.3: The convolution sum - p. 523 90. 7.3.4: Linear and nonlinear filtering with MATLAB - p. 530 91. 7.3.5: Causality and stability of discrete-time systems - p. 533 92. 7.4: Two-dimensional discrete signals and systems - p. 536 93. 7.5: What have we accomplished? Where do we go from here? - p. 546 94. 7.6: Problems - p. 547 95. 7.6.1: Basic problems - p. 547 96. 7.6.2: Problems using MATLAB - p. 555 97. Chapter 8 The Z-transform - p. 563 98. 8.1: Introduction - p. 564 99. 8.2: Laplace transform of sampled signals - p. 564 100. 8.3: Two-sided Z-transform - p. 567 101. 8.4: One-sided Z-transform - p. 573 102. 8.5: One-sided Z-transform inverse - p. 589 103. 8.5.1: Long-division method - p. 590 104. 8.5.2: Partial fraction expansion - p. 591 105. 8.5.3: Inverse Z-transform with MATLAB - p. 594 106. 8.5.4: Solution of difference equations - p. 598 107. 8.5.5: Inverse of two-sided Z-transforms - p. 606 108. 8.6: State variable representation - p. 609 109. 8.7: Two-dimensional Z-transform - p. 619 110. 8.8: What have we accomplished? Where do we go from here? - p. 629 111. 8.9: Problems - p. 629 112. Chapter 9 Fourier analysis of discrete-time signals and systems - p. 644 113. 9.1: Introduction - p. 644 114. 9.2: The discrete-time Fourier transform (DTFT) - p. 644 115. 9.2.1: Sampling, Z-transform, eigenfunctions, and the DTFT - p. 645 116. 9.2.2: Duality in time and in frequency - p. 647 117. 9.2.3: Computation of the DTFT using MATLAB® - p. 650 118. 9.2.4: Time and frequency supports - p. 652 119. 9.2.5: Decimation and interpolation - p. 654 120. 9.2.6: Energy/power of aperiodic discrete-time signals - p. 659 121. 9.2.7: Time and frequency shifts - p. 660 122. 9.2.8: Symmetry - p. 662 123. 9.2.9: Convolution sum - p. 668 124. 9.3: Fourier series of discrete-time periodic signals - p. 670 125. 9.4: The discrete Fourier transform (DFT) - p. 686 126. 9.5: Two-dimensional discrete transforms - p. 707 127. 9.6: What have we accomplished? Where do we go from here? - p. 712 128. 9.7: Problems - p. 713 129. 9.7.1: Basic problems - p. 713 130. 9.7.2: Problems using MATLAB - p. 719 131. Chapter 10 Introduction to the design of discrete filters - p. 730 132. 10.1: Introduction - p. 730 133. 10.2: Frequency selective discrete filters - p. 731 134. 10.3: Filter specifications - p. 739 135. 10.4: IIR filter design - p. 743 136. 10.5: FIR filter design - p. 768 137. 10.6: Realization of discrete filters - p. 779 138. 10.7: Two-dimensional filtering of images - p. 788 139. 10.8: What have we accomplished? Where do we go from here? - p. 800 140. 10.9: Problems - p. 800 141. Appendix A Useful formulas - p. 813 142. References - p. 817 143. Index - p. 821
Signals and Systems Using MATLAB, Fourth Edition features a pedagogically rich and accessible approach to what can commonly be a mathematically dry subject. Historical notes and common mistakes combined with applications in controls, communications, and signal processing help students understand and appreciate the usefulness of the techniques described in the text. This new edition features more worked examples and a variety of new end-of-chapter problems, suggestions for labs, and more explanation of MATLAB code.
1. 0.1: Introduction - p. 4 2. 0.2: Examples of signal processing applications - p. 4 3. 0.3: Implementation of digital signal processing algorithms - p. 7 4. 0.4: Continuous or discrete? - p. 10 5. 0.5: Complex or real? - p. 20 6. 0.6: Soft introduction to MATLAB - p. 33 7. 0.7: Problems - p. 53 8. Chapter 1 Continuous-time signals - p. 65 9. 1.1: Introduction - p. 65 10. 1.2: Classification of time-dependent signals - p. 66 11. 1.3: Continuous-time signals - p. 67 12. 1.4: Representation of continuous-time signals using basic signals - p. 84 13. 1.5: Time scaling, modulation, windowing, and integration - p. 99 14. 1.6: Special signals—the sampling and the sinc signals - p. 109 15. 1.7: What have we accomplished? Where do we go from here? - p. 110 16. 1.8: Problems - p. 110 17. Chapter 2 Continuous-time systems - p. 123 18. 2.1: Introduction - p. 123 19. 2.2: System concept and classification - p. 124 20. 2.3: Linear time-invariant (LTI) continuous-time systems - p. 126 21. 2.4: The convolution integral - p. 144 22. 2.5: Causality - p. 158 23. 2.6: Bounded-input bounded-output (BIBO) stability - p. 162 24. 2.7: What have we accomplished? Where do we go from here? - p. 167 25. 2.8: Problems - p. 167 26. Chapter 3 The Laplace transform - p. 180 27. 3.1: Introduction - p. 180 28. 3.2: The two-sided Laplace transform - p. 181 29. 3.3: The one-sided Laplace transform - p. 190 30. 3.4: Properties of the one-sided Laplace transform - p. 198 31. 3.5: Inverse Laplace transform - p. 211 32. 3.6: The transfer function of LTI systems - p. 225 33. 3.7: Analysis of LTI systems represented by differential equations - p. 232 34. 3.8: Inverse of two-sided Laplace transforms - p. 240 35. 3.9: Application of Laplace transform to control theory - p. 243 36. 3.9.1: Application to classical control - p. 245 37. 3.9.2: Stability and stabilization - p. 250 38. 3.9.3: Transient analysis of first- and second-order control systems - p. 253 39. 3.9.4: State-variable representation of LTI systems - p. 259 40. 3.10: What have we accomplished? Where do we go from here? - p. 267 41. 3.11: Problems - p. 267 42. 3.11.1: Basic problems - p. 267 43. 3.11.2: Problem using MATLAB - p. 276 44. Chapter 4 Frequency analysis: the Fourier series - p. 283 45. 4.1: Introduction - p. 283 46. 4.2: Eigenfunctions revisited - p. 284 47. 4.3: Complex exponential Fourier series - p. 291 48. 4.3.1: Line spectrum—power distribution over frequency - p. 294 49. 4.3.2: Trigonometric Fourier series - p. 296 50. 4.3.3: Fourier series and Laplace transform - p. 300 51. 4.3.4: Reflection and even and odd periodic signals - p. 303 52. 4.3.5: Convergence of the Fourier series - p. 318 53. 4.3.6: Time and frequency shifting - p. 321 54. 4.4: Response of LTI systems to periodic signals - p. 325 55. 4.5: Operations using Fourier series - p. 332 56. 4.6: What have we accomplished? Where do we go from here? - p. 343 57. 4.7: Problems - p. 344 58. Chapter 5 Frequency analysis: the Fourier transform - p. 356 59. 5.1: Introduction - p. 356 60. 5.2: From the Fourier series to the Fourier transform - p. 356 61. 5.3: Existence of the Fourier transform - p. 358 62. 5.4: Fourier transforms from the Laplace transform - p. 359 63. 5.5: Linearity, inverse proportionality, and duality - p. 360 64. 5.6: Spectral representation - p. 370 65. 5.7: Convolution and filtering - p. 382 66. 5.8: Additional properties - p. 398 67. 5.9: Application of Fourier analysis to communications and filtering - p. 405 68. 5.9.1: Application to communications - p. 405 69. 5.9.2: Analog filter design - p. 416 70. 5.10: What have we accomplished? What is next? - p. 434 71. 5.11: Problems - p. 436 72. Chapter 6 Sampling theory - p. 451 73. 6.1: Introduction - p. 451 74. 6.2: Uniform sampling - p. 452 75. 6.3: Practical aspects of sampling - p. 473 76. 6.4: Application to digital communications - p. 480 77. 6.5: What have we accomplished? Where do we go from here? - p. 484 78. 6.6: Problems - p. 484 79. Chapter 7 Discrete-time signals and systems - p. 491 80. 7.1: Introduction - p. 492 81. 7.2: Discrete-time signals - p. 492 82. 7.2.1: Periodic and aperiodic discrete-time signals - p. 494 83. 7.2.2: Finite energy and finite power discrete-time signals - p. 498 84. 7.2.3: Even and odd discrete-time signals - p. 501 85. 7.2.4: Basic discrete-time signals - p. 504 86. 7.3: Discrete-time systems - p. 515 87. 7.3.1: Recursive and nonrecursive discrete-time systems - p. 517 88. 7.3.2: Dynamic discrete-time systems represented by difference equations - p. 521 89. 7.3.3: The convolution sum - p. 523 90. 7.3.4: Linear and nonlinear filtering with MATLAB - p. 530 91. 7.3.5: Causality and stability of discrete-time systems - p. 533 92. 7.4: Two-dimensional discrete signals and systems - p. 536 93. 7.5: What have we accomplished? Where do we go from here? - p. 546 94. 7.6: Problems - p. 547 95. 7.6.1: Basic problems - p. 547 96. 7.6.2: Problems using MATLAB - p. 555 97. Chapter 8 The Z-transform - p. 563 98. 8.1: Introduction - p. 564 99. 8.2: Laplace transform of sampled signals - p. 564 100. 8.3: Two-sided Z-transform - p. 567 101. 8.4: One-sided Z-transform - p. 573 102. 8.5: One-sided Z-transform inverse - p. 589 103. 8.5.1: Long-division method - p. 590 104. 8.5.2: Partial fraction expansion - p. 591 105. 8.5.3: Inverse Z-transform with MATLAB - p. 594 106. 8.5.4: Solution of difference equations - p. 598 107. 8.5.5: Inverse of two-sided Z-transforms - p. 606 108. 8.6: State variable representation - p. 609 109. 8.7: Two-dimensional Z-transform - p. 619 110. 8.8: What have we accomplished? Where do we go from here? - p. 629 111. 8.9: Problems - p. 629 112. Chapter 9 Fourier analysis of discrete-time signals and systems - p. 644 113. 9.1: Introduction - p. 644 114. 9.2: The discrete-time Fourier transform (DTFT) - p. 644 115. 9.2.1: Sampling, Z-transform, eigenfunctions, and the DTFT - p. 645 116. 9.2.2: Duality in time and in frequency - p. 647 117. 9.2.3: Computation of the DTFT using MATLAB® - p. 650 118. 9.2.4: Time and frequency supports - p. 652 119. 9.2.5: Decimation and interpolation - p. 654 120. 9.2.6: Energy/power of aperiodic discrete-time signals - p. 659 121. 9.2.7: Time and frequency shifts - p. 660 122. 9.2.8: Symmetry - p. 662 123. 9.2.9: Convolution sum - p. 668 124. 9.3: Fourier series of discrete-time periodic signals - p. 670 125. 9.4: The discrete Fourier transform (DFT) - p. 686 126. 9.5: Two-dimensional discrete transforms - p. 707 127. 9.6: What have we accomplished? Where do we go from here? - p. 712 128. 9.7: Problems - p. 713 129. 9.7.1: Basic problems - p. 713 130. 9.7.2: Problems using MATLAB - p. 719 131. Chapter 10 Introduction to the design of discrete filters - p. 730 132. 10.1: Introduction - p. 730 133. 10.2: Frequency selective discrete filters - p. 731 134. 10.3: Filter specifications - p. 739 135. 10.4: IIR filter design - p. 743 136. 10.5: FIR filter design - p. 768 137. 10.6: Realization of discrete filters - p. 779 138. 10.7: Two-dimensional filtering of images - p. 788 139. 10.8: What have we accomplished? Where do we go from here? - p. 800 140. 10.9: Problems - p. 800 141. Appendix A Useful formulas - p. 813 142. References - p. 817 143. Index - p. 821
