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.

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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

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