Nonlinear Transformations of Random Processes
The objective of this book is to provide a comprehensive background on nonlinear noise problems for practical applicatio
328 12 3MB
English Pages 169 Year 1962
Table of contents :
Deutsch R.Nonlinear transformations of random processes (International series in applied mathematics)(P-H,1962)(ASIN B0000CLLIJ)(600dpi)(169p) ......Page 4
Copyright ......Page 5
Preface vii ......Page 7
CONTENTS ix ......Page 9
1.1 Notion of an Envelope, 1 ......Page 12
1.2 Envelopes and Pre-Envelopes, 3 ......Page 14
1.3 Correlation and Spectrum Relations for Envelope Functions, 5 ......Page 16
1.4 Example of Envelope Calculations, 10 ......Page 21
2.2 Characteristic Function Method, 13 ......Page 24
2.3 Nonlinear Devices having Gaussian Inputs, 15 ......Page 26
2.4 Examples, 21 ......Page 32
2.5 Comments, 26 ......Page 37
3.1 Computation of Moments, 27 ......Page 38
3.2 Envelope Detector, 28 ......Page 39
3.3 Envelope Square Law Detector, 30 ......Page 41
3.4 Logarithmic Transformation, 31 ......Page 42
3.5 Random Telegraph Signals, 33 ......Page 44
3.6 Quadratic Transformations of Non-Gaussian Processes, 35 ......Page 46
4.2 A Common Fallacy, 42 ......Page 53
4.3 Output Moments of a Power Law Device, 44 ......Page 55
4.4 Series Representation of a Random Process, 45 ......Page 56
4.5 Squaring and Filtering, 47 ......Page 58
4.6 Reduction to Differential Equation, 50 ......Page 61
4.7 Solution using Cumulants, 51 ......Page 62
4.8 Filtered Thermal Noise, 54 ......Page 65
4.9 Product of Two Processes, 57 ......Page 68
5.1 Simple Detection Model, 62 ......Page 73
5.2 Simple Detectors, 64 ......Page 75
5.3 Detection of the Sum of Random Processes, 71 ......Page 82
6.1 General Analytical Techniques, 75 ......Page 86
6.2 First Probability Frequency Functions, 76 ......Page 87
6.3 Correlation Function Expansions, 82 ......Page 93
6.4 Second-Order Frequency Function, 88 ......Page 99
6.5 Wiener’s Method, 94 ......Page 105
6.6 Representation of Nonlinear Operators, 105 ......Page 116
6.7 Representation of a Frequency Function by its Moments, 109 ......Page 120
7.1 General Remarks, 112 ......Page 123
7.2 Integral Equation, 115 ......Page 126
7.3 Partial Differential Equation, 118 ......Page 129
7.4 Solution of the Reduced Equation, 119 ......Page 130
7.5 Moments, 120 ......Page 131
7.6 Examples, 121 ......Page 132
8.1 Introduction, 125 ......Page 136
8.2 Periodic Samples Random Process, 126 ......Page 137
8.3 Sampling Theorem, 127 ......Page 138
8.4 Signal Quantizing, 134 ......Page 145
APPENDIX: NOTES ON HYPERGEOMETRIC FUNCTIONS, 139 ......Page 150
REFERENCES, 147 ......Page 158
INDEX, 155 ......Page 166
cover......Page 1
back cover 158 ......Page 169
Deutsch R.Nonlinear transformations of random processes (International series in applied mathematics)(P-H,1962)(ASIN B0000CLLIJ)(600dpi)(169p) ......Page 4
Copyright ......Page 5
Preface vii ......Page 7
CONTENTS ix ......Page 9
1.1 Notion of an Envelope, 1 ......Page 12
1.2 Envelopes and Pre-Envelopes, 3 ......Page 14
1.3 Correlation and Spectrum Relations for Envelope Functions, 5 ......Page 16
1.4 Example of Envelope Calculations, 10 ......Page 21
2.2 Characteristic Function Method, 13 ......Page 24
2.3 Nonlinear Devices having Gaussian Inputs, 15 ......Page 26
2.4 Examples, 21 ......Page 32
2.5 Comments, 26 ......Page 37
3.1 Computation of Moments, 27 ......Page 38
3.2 Envelope Detector, 28 ......Page 39
3.3 Envelope Square Law Detector, 30 ......Page 41
3.4 Logarithmic Transformation, 31 ......Page 42
3.5 Random Telegraph Signals, 33 ......Page 44
3.6 Quadratic Transformations of Non-Gaussian Processes, 35 ......Page 46
4.2 A Common Fallacy, 42 ......Page 53
4.3 Output Moments of a Power Law Device, 44 ......Page 55
4.4 Series Representation of a Random Process, 45 ......Page 56
4.5 Squaring and Filtering, 47 ......Page 58
4.6 Reduction to Differential Equation, 50 ......Page 61
4.7 Solution using Cumulants, 51 ......Page 62
4.8 Filtered Thermal Noise, 54 ......Page 65
4.9 Product of Two Processes, 57 ......Page 68
5.1 Simple Detection Model, 62 ......Page 73
5.2 Simple Detectors, 64 ......Page 75
5.3 Detection of the Sum of Random Processes, 71 ......Page 82
6.1 General Analytical Techniques, 75 ......Page 86
6.2 First Probability Frequency Functions, 76 ......Page 87
6.3 Correlation Function Expansions, 82 ......Page 93
6.4 Second-Order Frequency Function, 88 ......Page 99
6.5 Wiener’s Method, 94 ......Page 105
6.6 Representation of Nonlinear Operators, 105 ......Page 116
6.7 Representation of a Frequency Function by its Moments, 109 ......Page 120
7.1 General Remarks, 112 ......Page 123
7.2 Integral Equation, 115 ......Page 126
7.3 Partial Differential Equation, 118 ......Page 129
7.4 Solution of the Reduced Equation, 119 ......Page 130
7.5 Moments, 120 ......Page 131
7.6 Examples, 121 ......Page 132
8.1 Introduction, 125 ......Page 136
8.2 Periodic Samples Random Process, 126 ......Page 137
8.3 Sampling Theorem, 127 ......Page 138
8.4 Signal Quantizing, 134 ......Page 145
APPENDIX: NOTES ON HYPERGEOMETRIC FUNCTIONS, 139 ......Page 150
REFERENCES, 147 ......Page 158
INDEX, 155 ......Page 166
cover......Page 1
back cover 158 ......Page 169
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