Nonlinear problems in random theory

Norbert Wiener9780262230049, 9780262730129, 0262230046, 026273012X

A series of lectures on the role of nonlinear processes in physics, mathematics, electrical engineering, physiology, and communication theory. From the preface: “For some time I have been interested in a group of phenomena depending upon random processes. One the one hand, I have recorded the random shot effect as a suitable input for testing nonlinear circuits. On the other hand, for some of the work that Professor W. A. Rosenblith and I have been doing concerning the nature of the electroencephalogram, and in particular of the alpha rhythm, it has occurred to me to use the model of a system of random nonlinear oscillators excited by a random input. . . . At the beginning we had contemplated a series of only four or five lectures. My ideas developed pari passu with the course, and by the end of the term we found ourselves with a set of fifteen lectures. The last few of these were devoted to the application of my ideas to problems in the statistical mechanics of gases. This work is both new and tentative, and I found that I had to supplement my course by the writing over of these with the help of Professer Y. W. Lee. “

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Table of contents :
Contents……Page 7
Foreword……Page 3
Preface……Page 5
Lecture 1 The Random Function of Time and Phase……Page 8
Lecture 2 Homogeneous Polynomial Functionals and Their Averages……Page 23
Lecture 3 Orthogonal Functions……Page 35
Lecture 4 Orthogonal Functions and Autocorrelation Functions……Page 46
Lecture 5 Application to Frequency-Modulation Problems – I……Page 56
Lecture 6 Application to Frequency-Modulation Problems – II……Page 63
Lecture 7 Application to Frequency-Modulation Problems – III……Page 70
Lecture 8 Application to the Study of Brain Waves, Random Time, and Coupled Oscillators……Page 74
Lecture 9 Some Thoughts on Quantum Theory……Page 85
Lecture 10 Nonlinear Systems – I……Page 95
Lecture 11 Nonlinear Systems – II……Page 104
Lecture 12 Coding……Page 108
Lecture 13 Decoding……Page 117
Lecture 14 A New Approach to Statistical Mechanics – I……Page 125
Lecture 15 A New Approach to Statistical Mechanics – II……Page 130
Index……Page 136