Preface |
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xi | |
Acknowledgments |
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xvi | |
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1 | (62) |
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Chapter 0 From the Ground Up! |
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3 | (60) |
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0.1 Signals and Systems and Digital Technologies |
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3 | (2) |
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0.2 Examples of Signal Processing Applications |
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5 | (4) |
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0.2.1 Compact-Disc Player |
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5 | (1) |
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0.2.2 Software-Defined Radio and Cognitive Radio |
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6 | (2) |
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0.2.3 Computer-Controlled Systems |
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8 | (1) |
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9 | (11) |
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0.3.1 Continuous-Time and Discrete-Time Representations |
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10 | (2) |
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0.3.2 Derivatives and Finite Differences |
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12 | (1) |
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0.3.3 Integrals and Summations |
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13 | (3) |
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0.3.4 Differential and Difference Equations |
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16 | (4) |
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20 | (9) |
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0.4.1 Complex Numbers and Vectors |
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20 | (3) |
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0.4.2 Functions of a Complex Variable |
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23 | (1) |
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0.4.3 Phasors and Sinusoidal Steady State |
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24 | (2) |
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26 | (3) |
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0.5 Soft Introduction to MATLAB |
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29 | (34) |
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0.5.1 Numerical Computations |
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30 | (13) |
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0.5.2 Symbolic Computations |
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43 | (10) |
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53 | (10) |
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Part 2 Theory and Application of Continuous-Time Signals and Systems |
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63 | (354) |
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Chapter 1 Continous-Time Signals |
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65 | (52) |
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65 | (1) |
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1.2 Classification of Time-Dependent Signals |
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66 | (1) |
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1.3 Continuous-Time Signals |
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67 | (18) |
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1.3.1 Basic Signal Operations---Time Shifting and Reversal |
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71 | (4) |
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1.3.2 Even and Odd Signals |
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75 | (2) |
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1.3.3 Periodic and Aperiodic Signals |
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77 | (2) |
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1.3.4 Finite-Energy and Finite Power Signals |
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79 | (6) |
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1.4 Representation Using Basic Signals |
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85 | (21) |
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1.4.1 Complex Exponentials |
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85 | (3) |
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1.4.2 Unit-Step, Unit-Impulse, and Ramp Signals |
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88 | (12) |
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1.4.3 Special Signals---the Sampling Signal and the Sinc |
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100 | (2) |
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1.4.4 Basic Signals Operations---Time Scaling, Frequency Shifting, and Windowing |
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102 | (3) |
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1.4.5 Generic Representation of Signals |
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105 | (1) |
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1.5 What Have We Accomplished? Where do we Go from Here? |
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106 | (11) |
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108 | (9) |
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Chapter 2 Continuous-Time Systems |
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117 | (48) |
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117 | (1) |
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118 | (1) |
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2.2.1 System Classification |
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118 | (1) |
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2.3 LTI Continuous-Time Systems |
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119 | (37) |
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120 | (5) |
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125 | (5) |
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2.3.3 Representation of Systems by Differential Equations |
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130 | (5) |
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2.3.4 Application of Superposition and Time Invariance |
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135 | (1) |
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2.3.5 Convolution Integral |
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136 | (7) |
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143 | (2) |
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2.3.7 Graphical Computation of Convolution Integral |
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145 | (2) |
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2.3.8 Interconnection of Systems---Block Diagrams |
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147 | (6) |
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2.3.9 Bounded-Input Bounded-Output Stability |
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153 | (3) |
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2.4 What have We Accomplished? Where Do We Go from Here? |
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156 | (9) |
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157 | (8) |
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Chapter 3 The laplace Transform |
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165 | (72) |
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165 | (1) |
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3.2 The Two-Sided Laplace Transform |
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166 | (10) |
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3.2.1 Eigenfunctions of LTI Systems |
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167 | (5) |
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3.2.2 Poles and Zeros and Region of Convergence |
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172 | (4) |
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3.3 The One-Sided Laplace Transform |
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176 | (21) |
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185 | (3) |
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188 | (5) |
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193 | (1) |
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194 | (2) |
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3.3.5 Convolution Integral |
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196 | (1) |
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3.4 Inverse Laplace Transform |
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197 | (17) |
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3.4.1 Inverse of One-Sided Laplace Transforms |
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197 | (12) |
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3.4.2 Inverse of Functions Containing e-ps Terms |
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209 | (3) |
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3.4.3 Inverse of Two-Sided Laplace Transforms |
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212 | (2) |
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3.5 Analysis of LTI-Systems |
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214 | (12) |
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3.5.1 LTI Systems Represented by Ordinary Differential Equations |
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214 | (7) |
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3.5.2 Computation of the Convolution Integral |
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221 | (5) |
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3.6 What Have We Accomplished? Where Do We Go from Here? |
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226 | (11) |
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226 | (11) |
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Chapter 4 Frequency Analysis: The Fourier Series |
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237 | (62) |
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237 | (1) |
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4.2 Eigenfunctions Revisited |
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238 | (7) |
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4.3 Complex Exponential Fourier Series |
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245 | (3) |
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248 | (3) |
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4.4.1 Parseval's Theorem---Power Distribution over Frequency |
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248 | (2) |
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4.4.2 Symmetry of Line Spectra |
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250 | (1) |
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4.5 Trigonometric Fourier Series |
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251 | (4) |
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4.6 Fourier Coefficients from Laplace |
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255 | (10) |
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4.7 Convergence of the Fourier Series |
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265 | (5) |
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4.8 Time and Frequency Shifting |
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270 | (3) |
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4.9 Response of LTI Systems to Periodic Signals |
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273 | (6) |
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4.9.1 Sinusoidal Steady State |
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274 | (2) |
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4.9.2 Filtering of Periodic Signals |
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276 | (3) |
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4.10 Other Properties of the Fourier Series |
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279 | (10) |
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4.10.1 Reflection and Even and Odd Periodic Signals |
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279 | (3) |
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4.10.2 Linearity of Fourier Series---Addition of Periodic Signals |
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282 | (2) |
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4.10.3 Multiplicationof Periodic Signals |
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284 | (1) |
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4.10.4 Derivatives and Integrals of Periodic Signals |
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285 | (4) |
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4.11 What Have We Accomplished? Where Do We Go from Here? |
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289 | (10) |
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290 | (9) |
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Chapter 5 Frequency Analysis: The Fourier Transform |
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299 | (60) |
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299 | (1) |
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5.2 From the Fourier Series to the Fourier Transform |
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300 | (2) |
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5.3 Existence of the Fourier Transform |
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302 | (1) |
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5.4 Fourier Transforms from the Laplace Transform |
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302 | (2) |
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5.5 Linearity, Inverse Proportionality, and Duality |
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304 | (9) |
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304 | (1) |
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5.5.2 Inverse Proportionality of Time and Frequency |
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305 | (5) |
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310 | (3) |
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5.6 Spectral Representation |
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313 | (14) |
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313 | (4) |
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5.6.2 Fourier Transform of Periodic Signals |
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317 | (3) |
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5.6.3 Parseval's Energy Conservation |
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320 | (2) |
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5.6.4 Symmetry of Spectral Representations |
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322 | (5) |
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5.7 Convolution and Filtering |
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327 | (17) |
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5.7.1 Basics of Filtering |
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329 | (3) |
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332 | (5) |
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5.7.3 Frequency Response from Poles and Zeros |
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337 | (4) |
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341 | (3) |
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344 | (6) |
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344 | (2) |
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5.8.2 Differentiation and Integration |
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346 | (4) |
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5.9 What Have We Accomplished? What Is Next? |
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350 | (9) |
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350 | (9) |
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Chapter 6 Application to Control and Communications |
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359 | (58) |
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359 | (1) |
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6.2 System Connections and Block Diagrams |
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360 | (3) |
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6.3 Application to Classic Control |
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363 | (14) |
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6.3.1 Stability and Stabilization |
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369 | (2) |
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6.3.2 Transient Analysis of First- and Second-Order Control Systems |
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371 | (6) |
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6.4 Application to Communications |
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377 | (13) |
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6.4.1 AM with Suppressed Carrier |
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379 | (1) |
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380 | (2) |
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382 | (1) |
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6.4.4 Quadrature AM and Frequency-Division Multiplexing |
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383 | (2) |
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385 | (5) |
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390 | (19) |
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390 | (3) |
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6.5.2 Butterworth Low-Pass Filter Design |
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393 | (3) |
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6.5.3 Chebyshev Low-Pass Filter Design |
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396 | (6) |
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6.5.4 Frequency Transformations |
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402 | (3) |
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6.5.5 Filter Design with MATLAB |
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405 | (4) |
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6.6 What Have We Accomplished? What Is Next? |
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409 | (8) |
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409 | (8) |
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Part 3 Theory and Application of Discrete- Time Signals and Systems |
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417 | (326) |
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Chapter 7 Sampling Theory |
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419 | (32) |
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419 | (1) |
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420 | (17) |
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7.2.1 Pulse Amplitude Modulation |
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420 | (1) |
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7.2.2 Ideal Impulse Sampling |
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421 | (7) |
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7.2.3 Reconstruction of the Original Continuous-Time Signal |
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428 | (4) |
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7.2.4 Signal Reconstruction from Sinc Interpolation |
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432 | (1) |
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7.2.5 Sampling Simulation with MATLAB |
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433 | (4) |
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7.3 The Nyquist-Shannon Sampling Theorem |
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437 | (2) |
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7.3.1 Sampling of Modulated Signals |
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438 | (1) |
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7.4 Practical Aspects of Sampling |
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439 | (7) |
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7.4.1 Sample-and-Hold Sampling |
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439 | (2) |
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7.4.2 Quantization and Conding |
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441 | (3) |
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7.4.3 Sampling, Quantizing, and Coding with MATLAB |
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444 | (2) |
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7.5 What Have We Accomplished? Where Do We Go from Here? |
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446 | (5) |
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447 | (4) |
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Chapter 8 Discrete-Time Signals and Systems |
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451 | (60) |
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451 | (1) |
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8.2 Discrete-Time Signals |
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452 | (26) |
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8.2.1 Periodic and Aperiodic Signals |
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454 | (4) |
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8.2.2 Finite-Energy and Finite-Power Discrete-Time Signals |
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458 | (3) |
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8.2.3 Even and Odd Signals |
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461 | (4) |
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8.2.4 Basic Discrete-Time Signals |
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465 | (13) |
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8.3 Discrete-Time Systems |
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478 | (24) |
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8.3.1 Recursive and Nonrecursive Discrete-Time Systems |
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481 | (5) |
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8.3.2 Discrete-Time Systems Represented by Difference Equations |
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486 | (1) |
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8.3.3 The Convolution Sum |
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487 | (7) |
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8.3.4 Linear and Nonlinear Filtering with MATLAB |
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494 | (3) |
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8.3.5 Causality and Stability of Discrete-Time Systems |
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497 | (5) |
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8.4 What Have We Accomplished? Where Do We Go from Here? |
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502 | (9) |
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502 | (9) |
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Chapter 9 The Z-Transform |
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511 | (60) |
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511 | (1) |
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9.2 Laplace Transform of Sampled Signals |
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512 | (3) |
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9.3 Two-Sided Z-Transform |
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515 | (6) |
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9.3.1 Region of Convergence |
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516 | (5) |
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9.4 One-Sided Z-Transform |
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521 | (21) |
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9.4.1 Computing the Z-Transform with Symbolic MATLAB |
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522 | (1) |
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9.4.2 Signal Behavior and Poles |
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522 | (4) |
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9.4.3 Convolution Sum and Transfer Function |
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526 | (11) |
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9.4.4 Interconnection of Discrete-Time Systems |
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537 | (2) |
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9.4.5 Initial and Final Value Properties |
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539 | (3) |
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9.5 One-Sided Z-Transform Inverse |
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542 | (22) |
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9.5.1 Long-Division Method |
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542 | (2) |
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9.5.2 Partial Fraction Expansion |
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544 | (3) |
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9.5.3 Inverse Z-Transform with MATLAB |
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547 | (3) |
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9.5.4 Solution of Difference Equations |
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550 | (11) |
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9.5.5 Inverse of Two-Sided Z-Transforms |
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561 | (3) |
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9.6 What Have We Accomplished? Where Do We Go from Here? |
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564 | (7) |
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564 | (7) |
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Chapter 10 Fourier Analysis of Discrete-Time Signals and Systems |
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571 | (68) |
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571 | (1) |
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10.2 Discrete-Time Fourier Transform |
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572 | (24) |
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10.2.1 Sampling, Z-Transform, Eigenfunctions, and the DTFT |
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573 | (2) |
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10.2.2 Duality in Time and Frequency |
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575 | (2) |
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10.2.3 Computation of the DTFT Using MATLAB |
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577 | (3) |
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10.2.4 Time and Frequency Supports |
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580 | (5) |
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10.2.5 Parseval's Energy Result |
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585 | (2) |
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10.2.6 Time and Frequency Shifts |
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587 | (2) |
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589 | (6) |
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595 | (1) |
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10.3 Fourier Series of Discrete-Time Periodic Signals |
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596 | (18) |
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10.3.1 Complex Exponential Discrete Fourier Series |
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599 | (2) |
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10.3.2 Connection with the Z-Transform |
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601 | (1) |
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10.3.3 DTFT of Perodic Signals |
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602 | (2) |
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10.3.4 Response of LTI Systems to Periodic Signals |
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604 | (3) |
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10.3.5 Circular Shifting and Periodic Convolution |
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607 | (7) |
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10.4 Discrete Fourier Transform |
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614 | (14) |
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10.4.1 DFT of Periodic Discrete-Time Signals |
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614 | (2) |
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10.4.2 DFT of Aperiodic Discrete-Time Signals |
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616 | (1) |
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10.4.3 Computation of the DFT via the FFT |
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617 | (5) |
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10.4.4 Linear and Circular Convolution Sums |
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622 | (6) |
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10.5 What Have We Accomplished? Where Do We Go from Here? |
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628 | (11) |
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629 | (10) |
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Chapter 11 Introduction to the Design of Discrete Filters |
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639 | (70) |
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639 | (2) |
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11.2 Frequency-Selective Discrete Filters |
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641 | (7) |
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641 | (2) |
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11.2.2 IIR and FIR Discrete Filters |
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643 | (5) |
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11.3 Filter Specifications |
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648 | (5) |
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11.3.1 Frequency-Domain Specifications |
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648 | (4) |
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11.3.2 Time-Domain Specifications |
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652 | (1) |
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653 | (26) |
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11.4.1 Transformation Design of IIR Discrete Filters |
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654 | (4) |
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11.4.2 Design of Butterworth Low-Pass Discrete Filters |
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658 | (8) |
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11.4.3 Design of Chebyshev Low-Pass Discrete Filters |
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666 | (6) |
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11.4.4 Rational Frequency Transformations |
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672 | (5) |
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11.4.5 General IIR Filter Design with MATLAB |
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677 | (2) |
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679 | (10) |
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11.5.1 Window Design Method |
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681 | (2) |
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683 | (6) |
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11.6 Realization of Discrete Filters |
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689 | (12) |
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11.6.1 Realization of IIR Filters |
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690 | (9) |
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11.6.2 Realization of FIR Filters |
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699 | (2) |
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11.7 What Have We Accomplished? Where Do We Go from Here? |
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701 | (8) |
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701 | (8) |
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Chapter 12 Applications of Discrete-Time Signals and Systems |
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709 | (34) |
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709 | (1) |
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12.2 Application to Digital Signal Processing |
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710 | (12) |
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12.2.1 Fast Fourier Transform |
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711 | (4) |
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12.2.2 Computation of the Inverse DFT |
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715 | (1) |
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12.2.3 General Approach of FFT Algorithms |
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716 | (6) |
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12.3 Application to Sampled-Data and Digital Control Systems |
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722 | (7) |
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12.3.1 Open-Loop Sampled-Data System |
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724 | (2) |
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12.3.2 Closed-Loop Sampled-Data System |
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726 | (3) |
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12.4 Application to Digital Communications |
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729 | (13) |
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12.4.1 Pulse Code Modulation |
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730 | (3) |
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12.4.2 Time-Division Multiplexing |
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733 | (2) |
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12.4.3 Spread Spectrum and Orthogonal Frequency-Division Multiplexing |
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735 | (7) |
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12.5 What Have We Accomplished? Where Do We Go from Here? |
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742 | (1) |
Appendix Useful Formulas |
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743 | (3) |
Bibliography |
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746 | (3) |
Index |
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749 | |