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Linear Operators and Matrices |
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1 | (19) |
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1 | (1) |
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Vector Spaces Over Fields |
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2 | (2) |
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Linear Operators and Matrix Representations |
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4 | (2) |
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6 | (2) |
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Determinant, Inverse, and Rank |
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8 | (3) |
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11 | (4) |
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Characteristics: Eigenvalues, Eigenvectors, and Singular Values |
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15 | (2) |
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17 | (2) |
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Bilinear Operators and Matrices |
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19 | (18) |
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19 | (1) |
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20 | (1) |
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21 | (1) |
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22 | (1) |
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23 | (3) |
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26 | (1) |
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27 | (1) |
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28 | (3) |
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31 | (2) |
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33 | (2) |
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35 | (2) |
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37 | (46) |
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37 | (1) |
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38 | (6) |
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44 | (24) |
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Laplace Transform Analysis of Linear Systems |
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68 | (10) |
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Conclusions and Further Reading |
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78 | (1) |
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Appendix A: The Dirac Delta (Impulse) Function |
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79 | (1) |
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Appendix B: Relationships among the Laplace, Fourier, and z-Transforms |
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80 | (3) |
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Fourier Series, Fourier Transforms and the DFT |
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83 | (30) |
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83 | (2) |
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Fourier Series Representation of Continuous Time Periodic Signals |
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85 | (4) |
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The Classical Fourier Transform for Continuous Time Signals |
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89 | (4) |
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The Discrete Time Fourier Transform |
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93 | (4) |
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The Discrete Fourier Transform |
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97 | (5) |
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Family Tree of Fourier Transforms |
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102 | (2) |
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Selected Applications of Fourier Methods |
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104 | (6) |
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110 | (3) |
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113 | (18) |
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113 | (1) |
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Definition of the z-Transform |
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114 | (3) |
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117 | (3) |
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Properties of the z-Transform |
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120 | (4) |
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Role of the z-Transform in Linear Time-Invariant Systems |
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124 | (2) |
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Variations of the z-Transform |
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126 | (2) |
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128 | (3) |
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131 | (86) |
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131 | (2) |
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Signal Representation Using Basis Functions |
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133 | (13) |
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The Short-Time Fourier Transform |
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146 | (7) |
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Digital Filter Banks and Subband Coders |
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153 | (8) |
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Deeper study of Wavelets, Filter banks, and Short-Time Fourier Transforms |
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161 | (1) |
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The Space of L1 and L2 Signals |
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162 | (7) |
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Riesz Basis, Biorthogonality, and Other Fine Points |
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169 | (7) |
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176 | (4) |
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Short-Time Fourier Transform: Invertibility, Orthonormality, and Localization |
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180 | (3) |
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Wavelets and Multiresolution |
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183 | (13) |
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Orthonormal Wavelet Basis from Paraunitary Filter Banks |
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196 | (9) |
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Compactly Supported Orthonormal Wavelets |
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205 | (2) |
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207 | (7) |
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214 | (3) |
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217 | (28) |
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217 | (1) |
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217 | (6) |
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Cuts, Circuits, and Orthogonality |
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223 | (2) |
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Incidence, Circuit, and Cut Matrices of a Graph |
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225 | (3) |
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Orthogonality Relation and Ranks of Circuit and Cut Matrices |
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228 | (2) |
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Spanning Tree Enumeration |
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230 | (3) |
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Graphs and Electrical Networks |
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233 | (3) |
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Tellegen's Theorem and Network Sensitivity Computation |
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236 | (4) |
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Arc Coloring Theorem and the No-Gain Property |
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240 | (5) |
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245 | (12) |
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245 | (1) |
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Adjacency Matrix of a Directed Graph |
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245 | (3) |
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248 | (4) |
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252 | (5) |
| Index |
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257 | |
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