Principles of random signal analysis and low noise design MNw

Cover......Page 1
Title......Page 3
Copyright......Page 4
Contents......Page 5
Preface......Page 9
About the Author......Page 11
1. Introduction......Page 12
2.2 Background Theory......Page 14
2.3 Functions, Signals and Systems......Page 18
2.4 Signal Properties......Page 23
2.5 Measure and Lebesgue Integration......Page 34
2.6 Signal Classification......Page 46
2.7 Convergence......Page 47
2.8 Fourier Theory......Page 49
2.9 Random Processes......Page 55
2.10 Miscellaneous Results......Page 56
Appendix 1 Proof of Theorem 2.11......Page 57
Appendix 3 Proof of Theorem 2.17......Page 58
Appendix 4 Proof of Theorem 2.27......Page 60
Appendix 5 Proof of Theorem 2.28......Page 61
Appendix 6 Proof of Theorem 2.30......Page 63
Appendix 7 Proof of Theorem 2.31......Page 64
Appendix 8 Proof of Theorem 2.32......Page 67
3.1 Introduction......Page 70
3.2 Definition......Page 71
3.3 Properties......Page 76
3.4 Random Processes......Page 78
3.5 Existence Criteria......Page 84
3.6 Impulsive Case......Page 85
3.7 Power Spectral Density via Autocorrelation......Page 89
Appendix 1: Proof of Theorem 3.4......Page 95
Appendix 2: Proof of Theorem 3.5......Page 96
Appendix 3: Proof of Theorem 3.8......Page 99
Appendix 4: Proof of Theorem 3.10......Page 100
4.2 Boundedness of Power Spectral Density......Page 103
4.3 Power Spectral Density via Signal Decomposition......Page 106
4.4 Simplifying Evaluation of Power Spectral Density......Page 109
4.5 The Cross Power Spectral Density......Page 113
4.6 Power Spectral Density of a Sum of Random Processes......Page 118
4.7 Power Spectral Density of a Periodic Signal......Page 123
4.8 Power Spectral Density - Periodic Component Case......Page 130
4.9 Graphing Impulsive Power Spectral Densities......Page 133
Appendix 1: Proof of Theorem 4.2......Page 134
Appendix 2: Proof of Theorem 4.4......Page 137
Appendix 4: Proof of Theorem 4.6......Page 139
Appendix 5: Proof of Theorem 4.8......Page 141
Appendix 6: Proof of Theorem 4.10......Page 143
Appendix 7: Proof of Theorem 4.11......Page 145
Appendix 8: Proof of Theorem 4.12......Page 147
5.2 Signaling Random Processes......Page 149
5.3 Digital to Analogue Converter Quantization......Page 163
5.4 Jitter......Page 166
5.5 Shot Noise......Page 171
5.6 Generalized Signaling Processes......Page 177
Appendix 1: Proof of Theorem 5.1......Page 179
Appendix 2: Proof of Theorem 5.2......Page 182
Appendix 3: Proof of Equation 5.73......Page 184
Appendix 4: Proof of Theorem 5.3......Page 185
Appendix 5: Proof of Theorem 5.4......Page 187
Appendix 6: Proof of Theorem 5.5......Page 188
6.2 Sampled Signals......Page 190
6.3 Quadrature Amplitude Modulation......Page 196
6.4 Random Walks......Page 203
6.5 1f Noise......Page 209
Appendix 1: Proof of Theorem 6.1......Page 211
Appendix 2: Proof of Theorem 6.2......Page 212
Appendix 3: Proof of Theorem 6.3......Page 213
Appendix 4: Proof of Equation 6.39......Page 215
7.2 Power Spectral Density after a Memoryless Transformation......Page 217
7.3 Examples......Page 222
Appendix 1: Proof of Theorem 7.1......Page 234
Appendix 2: Fourier Results for Raised Cosine Frequency Modulation......Page 235
8.1 Introduction......Page 240
8.2 Impulse Response......Page 241
8.4 Fourier and Laplace Transform of Output......Page 243
8.5 Input-Output Power Spectral Density Relationship......Page 249
8.6 Multiple Input-Multiple Output Systems......Page 254
Appendix 1: Proof of Theorem 8.1......Page 257
Appendix 2: Proof of Theorem 8.2......Page 259
Appendix 3: Proof of Theorem 8.3......Page 260
Appendix 4: Proof of Theorem 8.4......Page 262
Appendix 5: Proof of Theorem 8.6......Page 263
Appendix 6: Proof of Theorem 8.7......Page 264
Appendix 7: Proof of Theorem 8.8......Page 266
9.1 Introduction......Page 267
9.2 Gaussian White Noise......Page 270
9.3 Standard Noise Sources......Page 275
9.4 Noise Models for Standard Electronic Devices......Page 277
9.5 Noise Analysis for Linear Time Invariant Systems......Page 280
9.6 Input Equivalent Current and Voltage Sources......Page 289
9.7 Transferring Noise Sources......Page 293
9.9 Noise Equivalent Bandwidth......Page 296
9.10 Power Spectral Density of a Passive Network......Page 298
Appendix 1: Proof of Theorem 9.2......Page 302
Appendix 2: Proof of Theorem 9.4......Page 305
Appendix 3: Proof of Conjecture for Ladder Structure......Page 307
Notation......Page 311
References......Page 313
Index......Page 318