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

Cover......Page 1
Applied and Numerical Harmonic Analysi Publications......Page 2
The Evolution of Applied Harmonic Analysis: Models of the Real World......Page 4
QA403.P74 2003 515.2433„dc2 I......Page 5
Contents......Page 6
Foreword......Page 10
Preface......Page 14
Overview......Page 15
Aims and Scope......Page 17
Acknowledgments......Page 18
1.1 An adventurous life......Page 24
1.2 The beginnings......Page 25
1.3 The revolutionary......Page 27
1.4 At the École Normale......Page 30
1.5 From imprisonment to the École Polytechnique......Page 32
1.6 Fourier, Napoleon, and the Egyptian campaign......Page 35
1.7 The prefect of Isère and the Analytical Theory of Heat......Page 39
1.8 Fourier and the \"Hundred Days\"......Page 45
1.9 Return to Paris......Page 48
2.1 How trigonometric series came about: the vibrating string......Page 54
2.2 Heat diffusion......Page 62
2.3 Fourier coefficients and series......Page 66
2.4 Dirichiet function and theorem......Page 69
2.5 Lord Kelvin, Michelson, and Gibbs phenomenon......Page 72
2.6 The construction of a cellar......Page 76
2.7 The Fourier transform......Page 79
2.9 Translations and interference fringes......Page 82
2.10 Waves, a unifying concept in science......Page 85
3.1 The great electrical revolution......Page 88
3.2 More and more hertz......Page 94
3.3 Tables of Fourier transforms......Page 99
3.4 The Dirac delta function and related topics......Page 102
3.5 Convolution......Page 104
3.6 Filters, noise, and false alarms......Page 107
3.7 Sampling and quantization......Page 110
3.8 The discrete Fourier transform......Page 114
3.9 The fast Fourier transform......Page 116
3.10 Gauss and the asteroids: history of the FFT......Page 120
3.11 Unsteady combustion and space propulsion......Page 124
3.12 The Mars project from von Braun to Korolev and Rubbia......Page 131
4.1 Understanding sound: some history......Page 136
4.2 Bats, whales, and sea lions: ultrasonic reflections in air and water......Page 139
4.3 Bels, decibels, and harmonic analysis of a single tone......Page 140
4.4 Sound processing by the ear: pitch, Joudness, and timbre......Page 142
4.5 The tempered scale......Page 145
4.6 Analysis of complex tones: cello, clarinet, trumpet, and bass drum......Page 147
4.7 Three tenors in Verdi\'s Rigoletto: dynamic spectra......Page 148
4.8 The beginnings of the electronic music synthesizers......Page 150
4.9 Additive synthesis......Page 155
4.10 Subtractive synthesis and frequency modulation......Page 159
4.11 Bessel functions and drums: the vibrating membrane......Page 161
4.12 Convolution and some special effects......Page 164
4.13 Computer music and art music......Page 165
5.1 The long search on the nature of light......Page 166
5.2 Spectroscopy: a close look at new worlds......Page 170
5.3 The mathematical model for diffraction: the Fourier transform in two dimensions......Page 172
5.4 Optical transforms......Page 175
5.5 X-rays and the unfolding of the electromagnetic spectrum......Page 180
5.6 Synchrotron radiation, first seen in the stars......Page 183
5.7 Unique features of the synchrotron light......Page 186
5.8 Storage rings, among the biggest machines in the world......Page 187
5.9 Spectrum of the synchrotron light......Page 191
5.10 Brightness and undulators......Page 196
5.11 Applications and the futuristicfree electron laser......Page 197
6.1 Crystallography from Steno to von Laue......Page 202
6.2 Bragg\'s law and the basic role of symmetries......Page 208
6.3 How to see the invisible......Page 215
6.4 The phase problem and the direct methods......Page 219
6.5 Brief history of genetics......Page 220
6.6 DNA through x-rays......Page 225
6.7 Protein structure: work for a century......Page 229
6.8 Seeing the hydrogen atom......Page 233
6.9 Vision at the nanosecond: a time-resolved structure......Page 234
7.1 Computerized axial tomography, a technique from the 1970s......Page 238
7.2 Beyond classical radiology......Page 240
7.3 CT versus Mill......Page 245
7.4 Projections......Page 246
7.5 The Radon transform......Page 247
7.6 Inverting the Radon transform by convolution and back projections......Page 250
7.8 Local tomography and microtomography......Page 254
8.1 \"We are all radio stations\"......Page 260
8.2 Nuclear spin and magnetic moment......Page 268
8.3 The swing and the phenomenon of resonance......Page 270
8.4 Driving a resonance: the Larmor frequency......Page 271
8.5 Relaxation process......Page 273
8.6 Relaxation times......Page 274
8.7 NMR spectroscopy: chemical shift and coupling constant......Page 278
8.8 Prion protein......Page 282
8.9 Collecting NMR spectra: continuous wave versus pulses......Page 284
8.10 The road to NMR imaging in the work of Damadian......Page 286
8.11 The principle of image formation......Page 289
8.12 MRI-guided interventions......Page 293
8.13 Functional MRI......Page 295
9.1 Astronomical observations: \"six thousand years for a witness\"......Page 298
9.2 How radioastronomy was born......Page 303
9.3 The most \"mortifying\" episode of English naval history and radar......Page 306
9.4 Radio waves and radiotelescopes......Page 308
9.5 Resolving power......Page 310
9.6 Interferometry......Page 313
9.7 The principle of image formation in a radiotelescope......Page 315
9.8 Aperture synthesis......Page 317
9.9 Synthesis by Earth\'s rotation......Page 321
9.10 Quasars, pulsars, and the Big Bang......Page 323
9.11 A \"flat\" forever-expanding Universe......Page 329
9.12 Search for extraterrestrial intelligence......Page 331
Wavelets: a new frontier......Page 334
Bibliography......Page 338
Index......Page 360
Applied and Numerical Harmonic Analysis Publications (Continued from Page i)......Page 374