## Random Processes In Electrical And Mechanical Systems – Lebedev

In this post, we will see the book Random Processes In Electrical And Mechanical Systems by V. L. Lebedev.

# About the book

This book deals with stationary and non-stationary random processes in linear systems and in inertialess nonlinear systems which have either one or several in­puts and outputs. The application of the mathematical methods expounded is illus­trated by many practical examples related to various physical and engineering pro­blems.

The book was translated from Russian by J. Flancreich and M. Segal  and was published in 1961 by The Israel Program for Scientific Translations.

You can get the book here.

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# Contents

Preface 1

## Chapter One. GENERAL CONCEPTS OF RANDOM PROCESSES 3

§ 1. Dynamical and statistical laws 3
§ 2. Random processes 5
§ 3. The role of the theory of random processes in engineering 6

## Chapter Two. RANDOM FUNCTIONS AND THEIR LINEAR TRANSFORMATIONS 8

§ 4. The concept of random function 8
§ 5. Stationary and nonstationary random functions 9
§ 6. Moments 9
§ 7. The derivative of a random function 14
§ 8. Integral transformations of random functions 18
§ 9. A set of several integral transformations of the random function 20
§ 10. Linear transformations of random functions 21

## Chapter Three. RANDOM FORCES UPON A LINEAR SYSTEM WITH LUMPED CONSTANTS 24

§ 11. Statement of the problem and terminology 24
§ 12. The method of stochastic differential equations 25
§ 13. The method of impulse characteristics 28
§ 14. The spectral method 32
§ 15. An RC circuit excited by a stationary fluctuating voltage 42
§ 16. Uncorrelated input 47
§ 17. The problem of two RC-circuits with a common input 50
§ 18. The problem of two RC-circuits with a common output 53

## Chapter Four. SOME LINEAR PROBLEMS IN THE THEORY OF RANDOM PROCESSES 57

§ 19. One-dimensional Brownian motion 57
§ 20. Thermal noise in electric circuits 59
§ 21. Thermal noise in an electrical oscillation circuit 61
§ 22. Thermal motion of a galvanometer 64
§ 23. The passage of irregular telegraph signals through a linear filter 69
§ 24. The optimal filter problem 73
§ 25. Elements of the theory of potential-noise stability 79

## Chapter Five. RANDOM FORCE ON A NONLINEAR SYSTEM

§ 26. Simplest problem of random force on an inertialess
nonlinear system
§ 27. The general problem of random force on an inertialess
nonlinear system
§ 28. Random process in inertial nonlinear systems

## Chapter Six. SOME NONLINEAR PROBLEMS IN THE THEORY OF RANDOM PROCESSES 93

§ 29. Action of fluctuation noise on a detector with exponential
characteristic 93
§ 30. Statistical properties of the noise voltage envelope at the output of a selective system 96
§ 31. Statistical properties of the phase of a noise voltage at the output of a selective system 104
§ 32. Statistical dependence between envelopes of noise
voltages at the outputs of two selective four-poles with their inputs connected in parallel 108
§ 33. Statistical properties of the voltage envelope at the
output of a selective system under action of non-modulated signal and fluctuation noise 112
§ 34. Statistical properties of the voltage phase at the output
of a selective system under action of a nor modulated
signal and fluctuation noise 115
§ 35. Computation of the detector output for given statistical
properties of the applied voltage envelope 116

Bibliography 119 