The Evolution of Applied Harmonic Analysis: Models of the Real World

Front Cover
Springer Science & Business Media, 2004 - Mathematics - 349 pages
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"...can be thoroughly recommended to any reader who is curious about the physical world and the intellectual underpinnings that have lead to our expanding understanding of our physical environment and to our halting steps to control it. Everyone who uses instruments that are based on harmonic analysis will benefit from the clear verbal descriptions that are supplied."

— R.N. Bracewell, Stanford University

A sweeping exploration of essential concepts and applications in modern mathematics and science through the unifying framework of Fourier analysis! This unique, extensively illustrated book describes the evolution of harmonic analysis, integrating theory and applications in a way that requires only some general mathematical sophistication and knowledge of calculus in certain sections.

Key features:

* Historical sections interwoven with key scientific developments showing how, when, where, and why harmonic analysis evolved

* Exposition driven by more than 150 illustrations and numerous examples

* Concrete applications of harmonic analysis to signal processing, computerized music, Fourier optics, radio astronomy, crystallography, CT scanning, nuclear magnetic resonance imaging and spectroscopy

* Includes a great deal of material not found elsewhere in harmonic analysis books

* Accessible to specialists and non-specialists

The Evolution of Applied Harmonic Analysis will engage graduate and advanced undergraduate students, researchers, and practitioners in the physical and life sciences, engineering, and mathematics.

  

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Contents

Joseph Fourier The Man and the Mathematician
1
12 The beginnings
2
13 The revolutionary
4
14 At the Ecole Normale
7
15 From imprisonment to the Ecole Polytechnique
9
16 Fourier Napoleon and the Egyptian campaign
12
17 The prefect of Isere and the Analytical Theory of Heat
16
18 Fourier and the Hundred Days
22
58 Storage rings among the biggest machines in the world
164
59 Spectrum of the synchrotron light
168
510 Brightness and undulators
173
511 Applications and the futuristic free electron laser
174
Xray Crystallography Protein Structure and DNA
179
62 Braggs law and the basic role of symmetries
185
63 How to see the invisible
192
64 The phase problem and the direct methods
196

19 Return to Paris
25
Introduction to Harmonic Analysis
31
22 Heat diffusion
39
23 Fourier coefficients and series
43
24 Dirichlet function and theorem
46
25 Lord Kelvin Michelson and Gibbs phenomenon
49
26 The construction of a cellar
53
27 The Fourier transform
56
28 Dilations and the uncertainty principle
59
210 Waves a unifying concept in science
62
Telecommunications and Space Exploration
65
32 More and more hertz
71
33 Tables of Fourier transforms
76
34 The Dirac delta function and related topics
79
35 Convolution
81
36 Filters noise and false alarms
84
37 Sampling and quantization
87
38 The discrete Fourier transform
91
39 The fast Fourier transform
93
history of the FFT
97
311 Unsteady combustion and space propulsion
101
312 The Mars project from von Braun to Korolev and Rubbia
108
Sound Music and Computers
113
ultrasonic reflections in air and water
116
43 Bels decibels and harmonic analysis of a single tone
117
pitch loudness and timbre
119
45 The tempered scale
122
cello clarinet trumpet and bass drum
124
dynamic spectra
125
48 The beginnings of the electronic music synthesizers
127
49 Additive synthesis
132
410 Subtractive synthesis and frequency modulation
136
the vibrating membrane
138
412 Convolution and some special effects
141
413 Computer music and art music
142
Fourier Optics and the Synchrotron Light
143
a close look at new worlds
147
the Fourier transform in two dimensions
149
54 Optical transforms
152
55 Xrays and the unfolding of the electromagnetic spectrum
157
56 Synchrotron radiation first seen in the stars
160
57 Unique features of the synchrotron light
163
65 Brief history of genetics
197
66 DNA through xrays
202
work for a century
206
68 Seeing the hydrogen atom
210
a timeresolved structure
211
The Radon Transform and Computerized Tomography
215
72 Beyond classical radiology
217
73 CT versus MRI
222
74 Projections
223
75 The Radon transform
224
76 Inverting the Radon transform by convolution and back projections
227
77 CT images
231
Nuclear Magnetic Resonance Imaging and Spectroscopy
237
82 Nuclear spin and magnetic moment
245
83 The swing and the phenomenon of resonance
247
the Larmor frequency
248
85 Relaxation process
250
86 Relaxation times
251
chemical shift and coupling constant
255
88 Prion protein
259
continuous wave versus pulses
261
810 The road to NMR imaging in the work of Damadian
263
811 The principle of image formation
266
812 MRIguided interventions
270
813 Functional MRI
272
Radioastronomy and Modern Cosmology
275
92 How radioastronomy was born
280
93 The most mortifying episode of English naval history and radar
283
94 Radio waves and radiotelescopes
285
95 Resolving power
287
96 Interferometry
290
97 The principle of image formation in a radiotelescope
292
98 Aperture synthesis
294
99 Synthesis by Earths rotation
298
910 Quasars pulsars and the Big Bang
300
911 A flat foreverexpanding Universe
306
912 Search for extraterrestrial intelligence
308
Appendix
311
Bibliography
315
Index
337
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