Preface |
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xiii | |
Authors |
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xvii | |
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1 Introduction to Matlab? |
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1 | (76) |
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1 | (1) |
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1 | (1) |
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2 | (6) |
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1.3.1 Simple Arithmetic Operations |
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3 | (1) |
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3 | (1) |
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3 | (1) |
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1.3.4 Priority of Operations |
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3 | (1) |
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4 | (1) |
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5 | (1) |
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6 | (1) |
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7 | (1) |
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7 | (1) |
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8 | (3) |
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1.4.1 Commands save-load-exit-quit |
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9 | (1) |
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10 | (1) |
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1.5 Commands diary and clc |
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10 | (1) |
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11 | (5) |
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11 | (1) |
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1.6.2 Commands length/size |
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11 | (1) |
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1.6.3 Addition/Subtraction |
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12 | (1) |
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1.6.4 Multiplication, Division, and Power |
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13 | (1) |
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14 | (1) |
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1.6.6 Dot Product of Two Vectors |
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14 | (1) |
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15 | (1) |
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16 | (11) |
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1.7.1 Matrix Concatenation |
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17 | (1) |
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1.7.2 Working with Matrices |
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17 | (2) |
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1.7.3 Addition/Subtraction |
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19 | (1) |
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1.7.4 Multiplication of Matrices |
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19 | (2) |
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1.7.4.1 The Dot Product as a Special Case of Matrix Multiplication |
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21 | (1) |
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21 | (1) |
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1.7.6 Inverse of a Matrix |
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22 | (1) |
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1.7.7 Determinant of a Matrix |
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22 | (1) |
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1.7.8 Division of Matrices |
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23 | (1) |
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1.7.9 Transpose of a Matrix |
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24 | (1) |
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1.7.10 Special Forms of Matrices |
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25 | (1) |
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26 | (1) |
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27 | (16) |
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1.8.1 Plotting in Two Dimensions |
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27 | (2) |
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29 | (1) |
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1.8.3 The Command linspace |
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29 | (1) |
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1.8.4 Plotting Several Functions in One Figure |
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30 | (2) |
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1.8.5 Formatting a Figure |
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32 | (2) |
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1.8.6 Plotting in Different Figures |
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34 | (2) |
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1.8.7 Commands for Plotting |
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36 | (2) |
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1.8.8 Plotting Discrete-Time Functions |
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38 | (1) |
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1.8.9 Graph in Polar Coordinates |
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39 | (1) |
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1.8.10 Piecewise Functions |
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39 | (1) |
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1.8.11 Plotting in Three Dimensions |
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40 | (1) |
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1.8.11.1 Plotting Curves in Three Dimensions |
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41 | (1) |
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1.8.11.2 Plotting Surfaces in Three Dimensions |
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41 | (2) |
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43 | (5) |
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43 | (1) |
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1.9.2 Forms of Complex Numbers |
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44 | (1) |
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1.9.3 Operations with Complex Numbers |
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45 | (1) |
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1.9.4 Graph of Complex Numbers |
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46 | (2) |
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48 | (6) |
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48 | (3) |
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51 | (3) |
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1.11 Input/Output Commands |
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54 | (1) |
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55 | (2) |
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1.13 Logical/Relational Operators |
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57 | (1) |
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58 | (4) |
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62 | (4) |
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1.15.1 Differentiation of a Function |
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62 | (1) |
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1.15.2 Integration of a Function |
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63 | (1) |
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1.15.3 Summation of a Function |
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63 | (1) |
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64 | (1) |
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1.15.5 Solving Algebraic Equations |
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64 | (1) |
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1.15.6 Solving Differential Equations |
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65 | (1) |
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66 | (1) |
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66 | (2) |
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1.17 (Pseudo)Random Numbers |
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68 | (1) |
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69 | (6) |
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75 | (2) |
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77 | (70) |
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2.1 Categorization by the Variable Type |
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77 | (4) |
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2.1.1 Continuous-Time Signals |
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77 | (1) |
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2.1.2 Discrete-Time Signals |
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78 | (1) |
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79 | (2) |
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2.2 Basic Continuous-Time Signals |
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81 | (18) |
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81 | (1) |
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2.2.2 Exponential Signals |
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82 | (1) |
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2.2.3 Complex Exponential Signals |
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83 | (1) |
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84 | (5) |
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2.2.5 Unit Impulse or Dirac Delta Function |
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89 | (4) |
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93 | (3) |
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2.2.7 Rectangular Pulse Function |
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96 | (3) |
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2.3 Discrete-Time Signals |
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99 | (12) |
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2.3.1 Unit Impulse Sequence |
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100 | (2) |
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102 | (2) |
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2.3.3 Real Exponential Sequence |
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104 | (1) |
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2.3.4 Complex Exponential Sequence |
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105 | (4) |
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2.3.5 Sinusoidal Sequence |
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109 | (2) |
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2.4 Properties of Signals |
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111 | (15) |
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111 | (1) |
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2.4.1.1 Sum of Periodic Continuous-Time Signals |
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112 | (2) |
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2.4.1.2 Construction of Periodic Signals |
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114 | (4) |
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118 | (1) |
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2.4.3 Even and Odd Signals |
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119 | (2) |
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2.4.4 Energy and Power Signals |
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121 | (3) |
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2.4.5 Deterministic and Stochastic Signals |
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124 | (2) |
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2.5 Transformations of the Time Variable for Continuous-Time Signals |
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126 | (6) |
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2.5.1 Time Reversal or Reflection |
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126 | (1) |
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127 | (2) |
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129 | (3) |
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2.6 Transformations of the Time Variable for Discrete-Time Signals |
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132 | (3) |
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135 | (10) |
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145 | (2) |
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147 | (32) |
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3.1 Systems Classification |
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147 | (4) |
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3.1.1 Classification according to the Number of Inputs and Outputs |
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147 | (4) |
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3.1.2 Continuous-Time and Discrete-Time Signals |
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151 | (1) |
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3.1.3 Deterministic and Stochastic Systems |
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151 | (1) |
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3.2 Properties of Systems |
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151 | (17) |
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3.2.1 Causal and Noncausal Systems |
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151 | (1) |
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3.2.2 Static (Memoryless) and Dynamic (with Memory) Systems |
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152 | (3) |
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3.2.3 Linear and Nonlinear Systems |
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155 | (3) |
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3.2.4 Time-Invariant and Time-Variant Systems |
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158 | (7) |
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3.2.5 Invertible and Non-Invertible Systems |
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165 | (1) |
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3.2.5.1 Construction of the Inverse System |
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166 | (1) |
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3.2.6 Stable and Unstable Systems |
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167 | (1) |
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168 | (8) |
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176 | (3) |
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4 Time Domain System Analysis |
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179 | (70) |
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4.1 Continous-Time Convolution |
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179 | (1) |
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4.2 Continuous-Time Convolution |
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179 | (20) |
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4.2.1 Computation of Convolution |
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180 | (6) |
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186 | (2) |
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188 | (1) |
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4.2.4 Continuous-Time Convolution Examples |
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189 | (10) |
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4.3 Convolution Properties |
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199 | (3) |
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4.4 Interconnections of Systems |
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202 | (4) |
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206 | (2) |
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4.6 Discrete-Time Convolution |
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208 | (15) |
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4.6.1 The Unit Impulse Sequence as Input to a System |
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208 | (3) |
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4.6.2 Computation of Discrete-Time Convolution |
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211 | (8) |
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4.6.3 Discrete-Time Convolution Examples |
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219 | (4) |
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4.7 Systems Described by Difference Equations |
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223 | (1) |
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224 | (10) |
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224 | (4) |
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4.8.2 Infinite Impulse Response Filters |
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228 | (4) |
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4.8.3 Finite Impulse Response Filters |
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232 | (2) |
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4.9 Stability Criterion for Discrete-Time Systems |
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234 | (1) |
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4.10 Systems Described by Differential Equations |
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235 | (1) |
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4.11 Step Response of a System |
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236 | (1) |
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237 | (8) |
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245 | (4) |
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249 | (52) |
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5.1 Orthogonality of Complex Exponential Signals |
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249 | (1) |
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5.2 Complex Exponential Fourier Series |
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250 | (3) |
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5.3 Trigonometric Fourier Series |
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253 | (3) |
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5.4 Fourier Series in the Cosine with Phase Form |
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256 | (2) |
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5.5 Plotting the Fourier Series Coefficients |
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258 | (5) |
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5.6 Fourier Series of Complex Signals |
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263 | (2) |
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5.7 Fourier Series of Periodic Signals |
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265 | (5) |
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270 | (2) |
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5.9 Properties of Fourier Series |
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272 | (5) |
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272 | (1) |
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273 | (2) |
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275 | (1) |
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275 | (1) |
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5.9.5 Signal Multiplication |
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276 | (1) |
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277 | (3) |
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277 | (1) |
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278 | (2) |
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280 | (1) |
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5.12 Criterion for the Approximation of a Signal by a Fourier Series Expansion |
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281 | (2) |
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5.13 Relationship between Complex Exponential and Trigonometric Fourier Series Coefficients |
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283 | (2) |
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285 | (12) |
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297 | (4) |
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301 | (26) |
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6.1 Mathematical Definition |
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301 | (1) |
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6.2 The Commands fourier and ifourier |
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302 | (2) |
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6.3 Fourier Transform Pairs |
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304 | (1) |
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6.4 Properties of Fourier Transform |
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305 | (6) |
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6.5 Convolution in Time and Frequency |
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311 | (1) |
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6.6 Symmetry of the Real and Imaginary Parts of Fourier Transform |
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312 | (1) |
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313 | (1) |
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6.8 Autocorrelation and Cross-Correlation |
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314 | (4) |
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318 | (6) |
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324 | (3) |
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7 Fourier Analysis of Discrete-Time Signals |
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327 | (46) |
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7.1 Discrete-Time Fourier Transform |
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327 | (2) |
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7.2 Properties of Discrete-Time Fourier Transform |
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329 | (7) |
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7.3 Parseval's Theorem for Discrete-Time Fourier Transform |
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336 | (1) |
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7.4 Discrete Fourier Transform |
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336 | (3) |
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7.5 Properties of Discrete Fourier Transform |
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339 | (2) |
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7.6 Inverse Discrete Fourier Transform |
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341 | (1) |
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7.7 Circular Shift of a Sequence |
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342 | (5) |
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7.7.1 Discrete Fourier Transform of a Circularly Shifted Sequence |
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346 | (1) |
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347 | (6) |
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7.8.1 Discrete Fourier Transform of Circular Convolution |
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351 | (1) |
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7.8.2 Relationship between Linear and Circular Convolution |
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352 | (1) |
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7.9 Fast Fourier Transform |
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353 | (4) |
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7.10 Relationship between DFT and DTFT |
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357 | (3) |
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7.11 Relationship between Fourier Transform and Discrete Fourier Transform |
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360 | (1) |
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7.12 Linear Convolution Computation via Fast Fourier Transform |
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361 | (1) |
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362 | (8) |
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370 | (3) |
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373 | (42) |
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8.1 Continuous-Time Frequency Response |
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373 | (3) |
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376 | (7) |
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8.2.1 The Command invfreqs |
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381 | (2) |
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383 | (1) |
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8.4 System Response to Sinusoidal Input |
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384 | (5) |
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389 | (5) |
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8.6 Frequency Response of Discrete-Time Systems |
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394 | (2) |
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396 | (3) |
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8.7.1 The Command invfreqz |
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397 | (2) |
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8.8 System Response to Discrete-Time Sinusoidal Input |
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399 | (1) |
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8.9 Moving Average Filter |
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399 | (2) |
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401 | (10) |
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411 | (4) |
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415 | (28) |
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9.1 Mathematical Definition |
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415 | (1) |
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9.2 Commands laplace and ilaplace |
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416 | (3) |
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9.3 Region of Convergence |
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419 | (1) |
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9.4 Laplace Transform Pairs |
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420 | (1) |
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9.5 Laplace Transform Properties and Theorems |
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421 | (4) |
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9.6 Partial Fraction Expansion of a Rational Function |
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425 | (7) |
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9.6.1 The Command residue |
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429 | (3) |
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9.7 Convolution in Time and in Complex Frequency |
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432 | (1) |
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9.7.1 Convolution in the Time Domain |
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432 | (1) |
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9.7.2 Convolution in the Complex Frequency Domain |
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433 | (1) |
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9.8 Using the Laplace Transform to Solve Differential Equations |
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433 | (3) |
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436 | (5) |
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441 | (2) |
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443 | (28) |
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10.1 Mathematical Definition |
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443 | (1) |
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10.2 Commands ztrans and iztrans |
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444 | (2) |
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10.3 Region of Convergence |
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446 | (1) |
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446 | (1) |
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10.5 Properties of z-Transform |
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447 | (6) |
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10.6 Partial Fraction Expansion of a Rational Function |
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453 | (4) |
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10.6.1 Commands residue and residuez |
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455 | (2) |
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10.7 Using the z-Transform to Solve Difference Equations |
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457 | (3) |
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460 | (7) |
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467 | (4) |
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471 | (52) |
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11.1 Continuous-Time Systems |
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471 | (2) |
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473 | (2) |
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11.3 Stability of Continuous-Time Systems |
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475 | (2) |
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11.4 Transfer Function in Zero/Pole/Gain Form |
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477 | (1) |
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11.5 Interconnections of Systems |
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478 | (3) |
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11.6 Continuous-Time System Response |
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481 | (4) |
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11.7 Discrete-Time Systems |
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485 | (1) |
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11.8 The Command tf for Discrete-Time Systems |
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486 | (1) |
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11.9 Stability of Discrete-Time Systems |
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486 | (3) |
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11.10 Discrete-Time System Response |
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489 | (5) |
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489 | (2) |
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491 | (2) |
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11.10.3 The Command dlsim |
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493 | (1) |
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11.11 Conversion between Continuous-Time and Discrete-Time Systems |
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494 | (1) |
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11.12 Transfer Function and Frequency Response |
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495 | (3) |
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498 | (1) |
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11.14 State-Space Representation |
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499 | (9) |
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11.14.1 Construction of a State-Space Model |
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503 | (3) |
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11.14.2 Discrete-Time State-Space Models |
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506 | (2) |
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508 | (10) |
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518 | (5) |
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12 Suggested Laboratory Exercises |
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523 | (10) |
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12.1 Laboratory 1: Introduction to MATLAB |
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523 | (1) |
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12.2 Laboratory 2: Signals |
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524 | (1) |
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12.3 Laboratory 3: Systems |
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525 | (1) |
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12.4 Laboratory 4: Time Domain System Analysis |
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525 | (1) |
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12.5 Laboratory 5: Fourier Series |
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526 | (1) |
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12.6 Laboratory 6: Fourier Transform |
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527 | (1) |
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12.7 Laboratory 7: Fourier Analysis of Discrete-Time Systems |
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528 | (1) |
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12.8 Laboratory 8: Frequency Response |
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528 | (1) |
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12.9 Laboratory 9: Laplace Transform |
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529 | (1) |
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12.10 Laboratory 10: z-Transform |
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530 | (1) |
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12.11 Laboratory 11: Transfer Function |
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531 | (2) |
Appendix A Signal Crossword |
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533 | (2) |
Appendix B Notation |
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535 | (2) |
Bibliography |
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537 | (2) |
Index |
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539 | |