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A Student's Guide to Fourier Transforms: With Applications by J. F. James PDF

By J. F. James

ISBN-10: 0521004284

ISBN-13: 9780521004282

This new version of a winning textbook for undergraduate scholars in physics, machine technological know-how and electric engineering describes vital modern principles in functional technology and knowledge expertise at an comprehensible point, illustrated with labored examples and copious diagrams. the sphere is roofed largely instead of intensive, and comprises references to extra prolonged works on a number of issues. This re-creation is a bit of extended, and comprises extra new fabric within the functions sections.

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Extra resources for A Student's Guide to Fourier Transforms: With Applications in Physics and Engineering

Sample text

It looks like a straight line but it is not transformable, since it can be shown that between any two rational numbers, however close, there is at least one irrational number, and between any two irrational numbers there is at least one rational number, so that the function is everywhere discontinuous. I have deliberately avoided the word 'photon', for fear of causing apoplexy among strict quantum theory purists. 2 Theorems 21 x __ Fig. 1. A triple-valued function like this can not be Fourier-transformed.

7. Intensity pattern from interference between three slits of width a, separated by b. 5 The transmission diffraction grating There are two obvious ways of representing the aperture function. In either case we assume that there are N slits, each of width w, each separated from its neighbours by a, the grating constant, and that N is a large (10 4 ---+ 10 5 ) number. B. ) A diagram here is helpful: the second factor (in the square brackets) is the product of a Dirac comb and a very broad (because w is very small) sine-function; and the convolution of this with the first factor, a very narrow sine-function, represents the diffraction produced by the whole aperture of the grating.

The double-sawtooth waveform: This can not be regarded as the convolution of two rectangular waveforms of equal mark-space4 ratio, since the etlect of integration is to give an embarrassing infinity. Instead it is the convolution of a top-hat of width a with another identical top-hat and with a Dirac comb of period 2a. Thus: I1 a (t) * I1 a (t) * 1lI2a (t) ~ (a/2) sinc2 rrva . 1lIl- (v) 2a So that the amplitudes, which occur at v = 1/2a, l/a, 3/2a, ... are: 2a/rr 2 , 0, 2a/9rr 2 , 0, 2a/25rr 2 , ...

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A Student's Guide to Fourier Transforms: With Applications in Physics and Engineering by J. F. James


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