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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.
What is a Fourier Transform?
Typical Applications of the Transform
Formal Statement of the Fourier Transform
The Meaning of Negative Frequencies
II The Elementary Transform
The Spatial Relationships
Time and Frequency
The Delta Function
III Extended Functions: The Superposition or Summation Property
The Superposition of Elementary Functions
The Rectangular Function
A List of Common Fourier Pairs
IV The Direct Application of Fourier Transforms
Frequency and Time Relationships in Simple Circuits
One Dimensional Aerial Systems
Optical Shots and Gratings
An Optical Example — The Rayleigh Refractometer
Examples in Acoustics
Two Dimensional Fourier Transforms
The Numerical Evaluation of Fourier Transforms
V Limitations, Products and Convolutions
The Effect of Interposing Limits
Physical Interpretation of Convolutions
Some Examples of Convolutions
The Solution of Fourier Transforms by the Application of the Convolution Theorem
The Isosceles Triangle
The Doublet Pulse
Convolutions involving the Sine Integral Si(x)
Two Dimensional Convolutions
VI The Differentiation of Fourier Transforms
Differentiation and Repeated Differentiation
The Fourier Transform of a Step Function or Straight Edge
The Convolution — Differentiation Relationship
The Differential Operator h(x)
The Integral Operator
VII The Auto-Correlation Function and The Transfer Function of a System Linear in Intensity
The Auto-correlation Function
The Transfer Function of a System Linear in Intensity
Examples on Chapter VII:
1. The Telescope
2. Stellar Interferometers
Note on Fourier Synthesis of Apertures
Appendix I Analogue Computers of Fourier Transforms
(i) The Diffraction Computer
(ii) A Mechanical Computer
(iii) A Coherent Electronic Computer
(iv) A Coherent Electronic Computer with an Incoherent Source
Tables of J1X/X, Si(x), sin X/X
- No. of pages:
- © Pergamon 1961
- 1st January 1961
- eBook ISBN:
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