Fourier Transforms: And Convolutions for the Experimentalist

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Elsevier, Oct 22, 2013 - Technology & Engineering - 128 pages
Fourier Transforms and Convolutions for the Experimentalist provides the experimentalist with a guide to the principles and practical uses of the Fourier transformation. It aims to bridge the gap between the more abstract account of a purely mathematical approach and the rule of thumb calculation and intuition of the practical worker. The monograph springs from a lecture course which the author has given in recent years and for which he has drawn upon a number of sources, including a set of notes compiled by the late Dr. I. C. Browne from a series of lectures given by Mr. J . A. Ratcliffe of the Cavendish Laboratory. The book begins with an introduction to Fourier Transform. It provides a definition o Fourier Transform, describes its applications, and presents the formal mathematical statement of the transform. Separate chapters discuss the elementary transform, extended functions, and direct applications of Fourier transforms. The final two chapters deal with limitations, products, and convolutions; and the differentiation of Fourier transforms.
 

Contents

CHAPTER I INTRODUCTION
1
CHAPTER II THE ELEMENTARY TRANSFORM
10
THE SUPERPOSITION OR SUMMATION PROPERTY
19
CHAPTER IV THE DIRECT APPLICATION OF FOURIER TRANSFORMS
31
CHAPTER V LIMITATIONS PRODUCTS AND CONVOLUTIONS
45
CHAPTER VI THE DIFFERENTIATION OF FOURIER TRANSFORMS
68
CHAPTER VII THE AUTOCORRELATION FUNCTION AND THE TRANSFER FUNCTION OF A SYSTEM LINEAR IN INTENSITY
82
ANALOGUE COMPUTERS OF FOURIER TRANSFORMS
106
J1x xχ in radians
111
INDEX
116
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