Fourier Transforms: And Convolutions for the ExperimentalistFourier 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
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 |
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aerial systems amplitude and phase amplitude pattern analysis angle angular aperture distribution aperture function applied auto-correlation function axis behaviour cathode ray tube centre Chapter circuit cisoid coherent complex compute consider constant convolution theorem convolved corresponding curve delay line delta function derived detector differentiation diffraction pattern dimensional doublet pulse elementary equivalent example field of view filter finite form sin X/X Fourier series Fourier transform Fraunhofer Fraunhofer diffraction fringe pattern func Gaussian Gaussian function give impulse incoherent infinity intensity distribution interferometer apertures left hand light limit linear mate Michelson Michelson stellar interferometer multiplying obtain operation optical system output pair phase function plot point source power spectrum radiation pattern rectangle Rectangular Function rectangular pulse result reverse rotating seen shown in Fig Si(x simple sine spacing spectral line star step function symmetrical telescope tion transfer function transform relationship variable vector wavelength whilst width x/y function zero frequency