Linear Systems And Signals 3rd Edition Solutions Pdf Free download

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About Linear Systems And Signals 3rd Edition Solutions Pdf Free download

Linear Systems and Signals, Third Edition, has been refined and streamlined to deliver unparalleled coverage and clarity. It emphasizes a physical appreciation of concepts through heuristic reasoning and the use of metaphors, analogies, and creative explanations. The text uses mathematics not only to prove axiomatic theory but also to enhance physical and intuitive understanding. Hundreds of fully worked examples provide a hands-on, practical grounding of concepts and theory. Its thorough content, practical approach, and structural adaptability make Linear Systems and Signals, Third Edition, the ideal text for undergraduates.

TABLE OF CONTENTS: Linear Systems And Signals 3rd Edition Solutions Pdf Free download

  1. CONTENTS
  2. PREFACE
  3. B BACKGROUND
  4. B.1 COMPLEX NUMBERS
  5. B.1-1 A Historical Note
  6. B.1-2 Algebra of Complex Numbers
  7. B.2 SINUSOIDS
  8. B.2-1 Addition of Sinusoids
  9. B.2-2 Sinusoids in Terms of Exponentials
  10. B.3 SKETCHING SIGNALS
  11. B.3-1 Monotonic Exponentials
  12. B.3-2 The Exponentially Varying Sinusoid
  13. B.4 CRAMER’S RULE
  14. B.5 PARTIAL FRACTION EXPANSION
  15. B.5-1 Method of Clearing Fractions
  16. B.5-2 The Heaviside “Cover-Up” Method
  17. B.5-3 Repeated Factors of Q(x)
  18. B.5-4 A Combination of Heaviside “Cover-Up” and Clearing Fractions
  19. B.5-5 Improper F(x) with m = n
  20. B.5-6 Modified Partial Fractions
  21. B.6 VECTORS AND MATRICES
  22. B.6-1 Some Definitions and Properties
  23. B.6-2 Matrix Algebra
  24. B.7 MATLAB: ELEMENTARY OPERATIONS
  25. B.7-1 MATLAB Overview
  26. B.7-2 Calculator Operations
  27. B.7-3 Vector Operations
  28. B.7-4 Simple Plotting
  29. B.7-5 Element-by-Element Operations
  30. B.7-6 Matrix Operations
  31. B.7-7 Partial Fraction Expansions
  32. B.8 APPENDIX: USEFUL MATHEMATICAL FORMULAS
  33. B.8-1 Some Useful Constants
  34. B.8-2 Complex Numbers
  35. B.8-3 Sums
  36. B.8-4 Taylor and Maclaurin Series
  37. B.8-5 Power Series
  38. B.8-6 Trigonometric Identities
  39. B.8-7 Common Derivative Formulas
  40. B.8-8 Indefinite Integrals
  41. B.8-9 L’Hôpital’s Rule
  42. B.8-10 Solution of Quadratic and Cubic Equations
  43. REFERENCES
  44. PROBLEMS
  45. 1 SIGNALS AND SYSTEMS
  46. 1.1 SIZE OF A SIGNAL
  47. 1.1-1 Signal Energy
  48. 1.1-2 Signal Power
  49. 1.2 SOME USEFUL SIGNAL OPERATIONS
  50. 1.2-1 Time Shifting
  51. 1.2-2 Time Scaling
  52. 1.2-3 Time Reversal
  53. 1.2-4 Combined Operations
  54. 1.3 CLASSIFICATION OF SIGNALS
  55. 1.3-1 Continuous-Time and Discrete-Time Signals
  56. 1.3-2 Analog and Digital Signals
  57. 1.3-3 Periodic and Aperiodic Signals
  58. 1.3-4 Energy and Power Signals
  59. 1.3-5 Deterministic and Random Signals
  60. 1.4 SOME USEFUL SIGNAL MODELS
  61. 1.4-1 The Unit Step Function u(t)
  62. 1.4-2 The Unit Impulse Function δ(t)
  63. 1.4-3 The Exponential Function e^{st}
  64. 1.5 EVEN AND ODD FUNCTIONS
  65. 1.5-1 Some Properties of Even and Odd Functions
  66. 1.5-2 Even and Odd Components of a Signal
  67. 1.6 SYSTEMS
  68. 1.7 CLASSIFICATION OF SYSTEMS
  69. 1.7-1 Linear and Nonlinear Systems
  70. 1.7-2 Time-Invariant and Time-Varying Systems
  71. 1.7-3 Instantaneous and Dynamic Systems
  72. 1.7-4 Causal and Noncausal Systems
  73. 1.7-5 Continuous-Time and Discrete-Time Systems
  74. 1.7-6 Analog and Digital Systems
  75. 1.7-7 Invertible and Noninvertible Systems
  76. 1.7-8 Stable and Unstable Systems
  77. 1.8 SYSTEM MODEL: INPUT–OUTPUT DESCRIPTION
  78. 1.8-1 Electrical Systems
  79. 1.8-2 Mechanical Systems
  80. 1.8-3 Electromechanical Systems
  81. 1.9 INTERNAL AND EXTERNAL DESCRIPTIONS OF A SYSTEM
  82. 1.10 INTERNAL DESCRIPTION: THE STATE-SPACE DESCRIPTION
  83. 1.11 MATLAB: WORKING WITH FUNCTIONS
  84. 1.11-1 Anonymous Functions
  85. 1.11-2 Relational Operators and the Unit Step Function
  86. 1.11-3 Visualizing Operations on the Independent Variable
  87. 1.11-4 Numerical Integration and Estimating Signal Energy
  88. 1.12 SUMMARY
  89. REFERENCES
  90. PROBLEMS
  91. 2 TIME-DOMAIN ANALYSIS OF CONTINUOUS-TIME SYSTEMS
  92. 2.1 INTRODUCTION
  93. 2.2 SYSTEM RESPONSE TO INTERNAL CONDITIONS: THE ZERO-INPUT RESPONSE
  94. 2.2-1 Some Insights into the Zero-Input Behavior of a System
  95. 2.3 THE UNIT IMPULSE RESPONSE h(t)
  96. 2.4 SYSTEM RESPONSE TO EXTERNAL INPUT: THE ZERO-STATE RESPONSE
  97. 2.4-1 The Convolution Integral
  98. 2.4-2 Graphical Understanding of Convolution Operation
  99. 2.4-3 Interconnected Systems
  100. 2.4-4 A Very Special Function for LTIC Systems: The Everlasting Exponential e^{st}
  101. 2.4-5 Total Response
  102. 2.5 SYSTEM STABILITY
  103. 2.5-1 External (BIBO) Stability
  104. 2.5-2 Internal (Asymptotic) Stability
  105. 2.5-3 Relationship Between BIBO and Asymptotic Stability
  106. 2.6 INTUITIVE INSIGHTS INTO SYSTEM BEHAVIOR
  107. 2.6-1 Dependence of System Behavior on Characteristic Modes
  108. 2.6-2 Response Time of a System: The System Time Constant
  109. 2.6-3 Time Constant and Rise Time of a System
  110. 2.6-4 Time Constant and Filtering
  111. 2.6-5 Time Constant and Pulse Dispersion (Spreading)
  112. 2.6-6 Time Constant and Rate of Information Transmission
  113. 2.6-7 The Resonance Phenomenon
  114. 2.7 MATLAB: M-FILES
  115. 2.7-1 Script M-Files
  116. 2.7-2 Function M-Files
  117. 2.7-3 For-Loops
  118. 2.7-4 Graphical Understanding of Convolution
  119. 2.8 APPENDIX: DETERMINING THE IMPULSE RESPONSE
  120. 2.9 SUMMARY
  121. REFERENCES
  122. PROBLEMS
  123. 3 TIME-DOMAIN ANALYSIS OF DISCRETE-TIME SYSTEMS
  124. 3.1 INTRODUCTION
  125. 3.1-1 Size of a Discrete-Time Signal
  126. 3.2 USEFUL SIGNAL OPERATIONS
  127. 3.3 SOME USEFUL DISCRETE-TIME SIGNAL MODELS
  128. 3.3-1 Discrete-Time Impulse Function δ[n]
  129. 3.3-2 Discrete-Time Unit Step Function u[n]
  130. 3.3-3 Discrete-Time Exponential γ^n
  131. 3.3-4 Discrete-Time Sinusoid cos(Omega n+θ)
  132. 3.3-5 Discrete-Time Complex Exponential e^{jOmega n}
  133. 3.4 EXAMPLES OF DISCRETE-TIME SYSTEMS
  134. 3.4-1 Classification of Discrete-Time Systems
  135. 3.5 DISCRETE-TIME SYSTEM EQUATIONS
  136. 3.5-1 Recursive (Iterative) Solution of Difference Equation
  137. 3.6 SYSTEM RESPONSE TO INTERNAL CONDITIONS: THE ZERO-INPUT RESPONSE
  138. 3.7 THE UNIT IMPULSE RESPONSE h[n]
  139. 3.7-1 The Closed-Form Solution of h[n]
  140. 3.8 SYSTEM RESPONSE TO EXTERNAL INPUT: THE ZERO-STATE RESPONSE
  141. 3.8-1 Graphical Procedure for the Convolution Sum
  142. 3.8-2 Interconnected Systems
  143. 3.8-3 Total Response
  144. 3.9 SYSTEM STABILITY
  145. 3.9-1 External (BIBO) Stability
  146. 3.9-2 Internal (Asymptotic) Stability
  147. 3.9-3 Relationship Between BIBO and Asymptotic Stability
  148. 3.10 INTUITIVE INSIGHTS INTO SYSTEM BEHAVIOR
  149. 3.11 MATLAB: DISCRETE-TIME SIGNALS AND SYSTEMS
  150. 3.11-1 Discrete-Time Functions and Stem Plots
  151. 3.11-2 System Responses Through Filtering
  152. 3.11-3 A Custom Filter Function
  153. 3.11-4 Discrete-Time Convolution
  154. 3.12 APPENDIX: IMPULSE RESPONSE FOR A SPECIAL CASE
  155. 3.13 SUMMARY
  156. PROBLEMS
  157. 4 CONTINUOUS-TIME SYSTEM ANALYSIS USING THE LAPLACE TRANSFORM
  158. 4.1 THE LAPLACE TRANSFORM
  159. 4.1-1 Finding the Inverse Transform
  160. 4.2 SOME PROPERTIES OF THE LAPLACE TRANSFORM
  161. 4.2-1 Time Shifting
  162. 4.2-2 Frequency Shifting
  163. 4.2-3 The Time-Differentiation Property
  164. 4.2-4 The Time-Integration Property
  165. 4.2-5 The Scaling Property
  166. 4.2-6 Time Convolution and Frequency Convolution
  167. 4.3 SOLUTION OF DIFFERENTIAL AND INTEGRO-DIFFERENTIAL EQUATIONS
  168. 4.3-1 Comments on Initial Conditions at 0^− and at 0^+
  169. 4.3-2 Zero-State Response
  170. 4.3-3 Stability
  171. 4.3-4 Inverse Systems
  172. 4.4 ANALYSIS OF ELECTRICAL NETWORKS: THE TRANSFORMED NETWORK
  173. 4.4-1 Analysis of Active Circuits
  174. 4.5 BLOCK DIAGRAMS
  175. 4.6 SYSTEM REALIZATION
  176. 4.6-1 Direct Form I Realization
  177. 4.6-2 Direct Form II Realization
  178. 4.6-3 Cascade and Parallel Realizations
  179. 4.6-4 Transposed Realization
  180. 4.6-5 Using Operational Amplifiers for System Realization
  181. 4.7 APPLICATION TO FEEDBACK AND CONTROLS
  182. 4.7-1 Analysis of a Simple Control System
  183. 4.8 FREQUENCY RESPONSE OF AN LTIC SYSTEM
  184. 4.8-1 Steady-State Response to Causal Sinusoidal Inputs
  185. 4.9 BODE PLOTS
  186. 4.9-1 Constant Ka_1a_2/b_1b_3
  187. 4.9-2 Pole (or Zero) at the Origin
  188. 4.9-3 First-Order Pole (or Zero)
  189. 4.9-4 Second-Order Pole (or Zero)
  190. 4.9-5 The Transfer Function from the Frequency Response
  191. 4.10 FILTER DESIGN BY PLACEMENT OF POLES AND ZEROS OF H(s)
  192. 4.10-1 Dependence of Frequency Response on Poles and Zeros of H(s)
  193. 4.10-2 Lowpass Filters
  194. 4.10-3 Bandpass Filters
  195. 4.10-4 Notch (Bandstop) Filters
  196. 4.10-5 Practical Filters and Their Specifications
  197. 4.11 THE BILATERAL LAPLACE TRANSFORM
  198. 4.11-1 Properties of the Bilateral Laplace Transform
  199. 4.11-2 Using the Bilateral Transform for Linear System Analysis
  200. 4.12 MATLAB: CONTINUOUS-TIME FILTERS
  201. 4.12-1 Frequency Response and Polynomial Evaluation
  202. 4.12-2 Butterworth Filters and the Find Command
  203. 4.12-3 Using Cascaded Second-Order Sections for Butterworth Filter Realization
  204. 4.12-4 Chebyshev Filters
  205. 4.13 SUMMARY
  206. REFERENCES
  207. PROBLEMS
  208. 5 DISCRETE-TIME SYSTEM ANALYSIS USING THE z-TRANSFORM
  209. 5.1 THE z-TRANSFORM
  210. 5.1-1 Inverse Transform by Partial Fraction Expansion and Tables
  211. 5.1-2 Inverse z-Transform by Power Series Expansion
  212. 5.2 SOME PROPERTIES OF THE z-TRANSFORM
  213. 5.2-1 Time-Shifting Properties
  214. 5.2-2 z-Domain Scaling Property (Multiplication by γ^n)
  215. 5.2-3 z-Domain Differentiation Property (Multiplication by n)
  216. 5.2-4 Time-Reversal Property
  217. 5.2-5 Convolution Property
  218. 5.3 z-TRANSFORM SOLUTION OF LINEAR DIFFERENCE EQUATIONS
  219. 5.3-1 Zero-State Response of LTID Systems: The Transfer Function
  220. 5.3-2 Stability
  221. 5.3-3 Inverse Systems
  222. 5.4 SYSTEM REALIZATION
  223. 5.5 FREQUENCY RESPONSE OF DISCRETE-TIME SYSTEMS
  224. 5.5-1 The Periodic Nature of Frequency Response
  225. 5.5-2 Aliasing and Sampling Rate
  226. 5.6 FREQUENCY RESPONSE FROM POLE-ZERO LOCATIONS
  227. 5.7 DIGITAL PROCESSING OF ANALOG SIGNALS
  228. 5.8 THE BILATERAL z-TRANSFORM
  229. 5.8-1 Properties of the Bilateral z-Transform
  230. 5.8-2 Using the Bilateral z-Transform for Analysis of LTID Systems
  231. 5.9 CONNECTING THE LAPLACE AND z-TRANSFORMS
  232. 5.10 MATLAB: DISCRETE-TIME IIR FILTERS
  233. 5.10-1 Frequency Response and Pole-Zero Plots
  234. 5.10-2 Transformation Basics
  235. 5.10-3 Transformation by First-Order Backward Difference
  236. 5.10-4 Bilinear Transformation
  237. 5.10-5 Bilinear Transformation with Prewarping
  238. 5.10-6 Example: Butterworth Filter Transformation
  239. 5.10-7 Problems Finding Polynomial Roots
  240. 5.10-8 Using Cascaded Second-Order Sections to Improve Design
  241. 5.11 SUMMARY
  242. REFERENCES
  243. PROBLEMS
  244. 6 CONTINUOUS-TIME SIGNAL ANALYSIS: THE FOURIER SERIES
  245. 6.1 PERIODIC SIGNAL REPRESENTATION BY TRIGONOMETRIC FOURIER SERIES
  246. 6.1-1 The Fourier Spectrum
  247. 6.1-2 The Effect of Symmetry
  248. 6.1-3 Determining the Fundamental Frequency and Period
  249. 6.2 EXISTENCE AND CONVERGENCE OF THE FOURIER SERIES
  250. 6.2-1 Convergence of a Series
  251. 6.2-2 The Role of Amplitude and Phase Spectra in Waveshaping
  252. 6.3 EXPONENTIAL FOURIER SERIES
  253. 6.3-1 Exponential Fourier Spectra
  254. 6.3-2 Parseval’s Theorem
  255. 6.3-3 Properties of the Fourier Series
  256. 6.4 LTIC SYSTEM RESPONSE TO PERIODIC INPUTS
  257. 6.5 GENERALIZED FOURIER SERIES:SIGNALS AS VECTORS
  258. 6.5-1 Component of a Vector
  259. 6.5-2 Signal Comparison and Component of a Signal
  260. 6.5-3 Extension to Complex Signals
  261. 6.5-4 Signal Representation by an Orthogonal Signal Set
  262. 6.6 NUMERICAL COMPUTATION OF D_n
  263. 6.7 MATLAB: FOURIER SERIES APPLICATIONS
  264. 6.7-1 Periodic Functions and the Gibbs Phenomenon
  265. 6.7-2 Optimization and Phase Spectra
  266. 6.8 SUMMARY
  267. REFERENCES
  268. PROBLEMS
  269. 7 CONTINUOUS-TIME SIGNAL ANALYSIS: THE FOURIER TRANSFORM
  270. 7.1 APERIODIC SIGNAL REPRESENTATION BY THE FOURIER INTEGRAL
  271. 7.1-1 Physical Appreciation of the Fourier Transform
  272. 7.2 TRANSFORMS OF SOME USEFUL FUNCTIONS
  273. 7.2-1 Connection Between the Fourier and Laplace Transforms
  274. 7.3 SOME PROPERTIES OF THE FOURIER TRANSFORM
  275. 7.4 SIGNAL TRANSMISSION THROUGH LTIC SYSTEMS
  276. 7.4-1 Signal Distortion During Transmission
  277. 7.4-2 Bandpass Systems and Group Delay
  278. 7.5 IDEAL AND PRACTICAL FILTERS
  279. 7.6 SIGNAL ENERGY
  280. 7.7 APPLICATION TO COMMUNICATIONS: AMPLITUDE MODULATION
  281. 7.7-1 Double-Sideband, Suppressed-Carrier (DSB-SC) Modulation
  282. 7.7-2 Amplitude Modulation (AM)
  283. 7.7-3 Single-Sideband Modulation (SSB)
  284. 7.7-4 Frequency-Division Multiplexing
  285. 7.8 DATA TRUNCATION: WINDOW FUNCTIONS
  286. 7.8-1 Using Windows in Filter Design
  287. 7.9 MATLAB: FOURIER TRANSFORM TOPICS
  288. 7.9-1 The Sinc Function and the Scaling Property
  289. 7.9-2 Parseval’s Theorem and Essential Bandwidth
  290. 7.9-3 Spectral Sampling
  291. 7.9-4 Kaiser Window Functions
  292. 7.10 SUMMARY
  293. REFERENCES
  294. PROBLEMS
  295. 8 SAMPLING: THE BRIDGE FROM CONTINUOUS TO DISCRETE
  296. 8.1 THE SAMPLING THEOREM
  297. 8.1-1 Practical Sampling
  298. 8.2 SIGNAL RECONSTRUCTION
  299. 8.2-1 Practical Difficulties in Signal Reconstruction
  300. 8.2-2 Some Applications of the Sampling Theorem
  301. 8.3 ANALOG-TO-DIGITAL (A/D) CONVERSION
  302. 8.4 DUAL OF TIME SAMPLING: SPECTRAL SAMPLING
  303. 8.5 NUMERICAL COMPUTATION OF THE FOURIER TRANSFORM: THE DISCRETE FOURIER TRANSFORM
  304. 8.5-1 Some Properties of the DFT
  305. 8.5-2 Some Applications of the DFT
  306. 8.6 THE FAST FOURIER TRANSFORM (FFT)
  307. 8.7 MATLAB: THE DISCRETE FOURIER TRANSFORM
  308. 8.7-1 Computing the Discrete Fourier Transform
  309. 8.7-2 Improving the Picture with Zero Padding
  310. 8.7-3 Quantization
  311. 8.8 SUMMARY
  312. REFERENCES
  313. PROBLEMS
  314. 9 FOURIER ANALYSIS OF DISCRETE-TIME SIGNALS
  315. 9.1 DISCRETE-TIME FOURIER SERIES (DTFS)
  316. 9.1-1 Periodic Signal Representation by Discrete-Time Fourier Series
  317. 9.1-2 Fourier Spectra of a Periodic Signal x[n]
  318. 9.2 APERIODIC SIGNAL REPRESENTATION BY FOURIER INTEGRAL
  319. 9.2-1 Nature of Fourier Spectra
  320. 9.2-2 Connection Between the DTFT and the z-Transform
  321. 9.3 PROPERTIES OF THE DTFT
  322. 9.4 LTI DISCRETE-TIME SYSTEM ANALYSIS BY DTFT
  323. 9.4-1 Distortionless Transmission
  324. 9.4-2 Ideal and Practical Filters
  325. 9.5 DTFT CONNECTION WITH THE CTFT
  326. 9.5-1 Use of DFT and FFT for Numerical Computation of the DTFT
  327. 9.6 GENERALIZATION OF THE DTFT TO THE z-TRANSFORM
  328. 9.7 MATLAB: WORKING WITH THE DTFS AND THE DTFT
  329. 9.7-1 Computing the Discrete-Time Fourier Series
  330. 9.7-2 Measuring Code Performance
  331. 9.7-3 FIR Filter Design by Frequency Sampling
  332. 9.8 SUMMARY
  333. REFERENCE
  334. PROBLEMS
  335. 10 STATE-SPACE ANALYSIS
  336. 10.1 MATHEMATICAL PRELIMINARIES
  337. 10.1-1 Derivatives and Integrals of aMatrix
  338. 10.1-2 The Characteristic Equation of a Matrix: The Cayley–Hamilton Theorem
  339. 10.1-3 Computation of an Exponential and a Power of aMatrix
  340. 10.2 INTRODUCTION TO STATE SPACE
  341. 10.3 A SYSTEMATIC PROCEDURE TO DETERMINE STATE EQUATIONS
  342. 10.3-1 Electrical Circuits
  343. 10.3-2 State Equations from a Transfer Function
  344. 10.4 SOLUTION OF STATE EQUATIONS
  345. 10.4-1 Laplace Transform Solution of State Equations
  346. 10.4-2 Time-Domain Solution of State Equations
  347. 10.5 LINEAR TRANSFORMATION OF A STATE VECTOR
  348. 10.5-1 Diagonalization of Matrix A
  349. 10.6 CONTROLLABILITY AND OBSERVABILITY
  350. 10.6-1 Inadequacy of the Transfer Function Description of a System
  351. 10.7 STATE-SPACE ANALYSIS OF DISCRETE-TIME SYSTEMS
  352. 10.7-1 Solution in State Space
  353. 10.7-2 The z-Transform Solution
  354. 10.8 MATLAB: TOOLBOXES AND STATE-SPACE ANALYSIS
  355. 10.8-1 z-Transform Solutions to Discrete-Time, State-Space Systems
  356. 10.8-2 Transfer Functions from State-Space Representations
  357. 10.8-3 Controllability and Observability of Discrete-Time Systems
  358. 10.8-4 Matrix Exponentiation and the Matrix Exponential
  359. 10.9 SUMMARY
  360. REFERENCES
  361. PROBLEMS
  362. INDEX

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