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Bracewell R.N. — The Fourier Transform and its applications
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Название: The Fourier Transform and its applicationsАвтор: Bracewell R.N. Аннотация: I ransform methods provide a unifying mathematical approach to the study of electrical networks, devices for energy conversion and control, antennas, and other components of electrical systems, as well as to complete linear systems and to many other physical systems and devices, whether electrical or not. These same methods apply equally to the subjects of electrical communication by wire or optical fiber, to wireless radio propagation, and to ionized media—which are all concerned with the interconnection of electrical systems—and to information theory which, among other things, relates to the acquisition, processing, and presentation of data. Other theoretical techniques are used in handling these basic fields of electrical engineering, but transform methods are virtually indispensable in all of them. Fourier analysis as applied to electrical engineering is sufficiently important to have earned a permanent place in the curriculum—indeed much of the mathematical development took place in connection with alternating current theory, signal analysis, and information theory as formulated in connection with electrical communication.
Язык: Рубрика: Математика /Статус предметного указателя: Готов указатель с номерами страниц ed2k: ed2k stats Издание: 3rd editionГод издания: 2000Количество страниц: 618Добавлена в каталог: 10.04.2011Операции: Положить на полку |
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Filters, fixed-frequency 147 Filters, general 251 Filters, low-pass 66 75 Filters, measuring 167 Filters, reception 468 Filters, rectangular 224—226 227 Filters, smoothing 468 Filters, time-invariant 39 Finite difference 84 180—184 189 206 Finite difference as convolution 33 84—85 Finite Fourier transform 217 242—243 Finite impulse response (FIR) 204 Finite resolution 93 Finite transforms 242—243 First difference theorem 301 First moment 153—156 189 First moment and Mellin transform 344 First moment in two dimensions 333 First moment of waveform 206 Fixed-frequency filters 147 Flanagan, J. L. 493 506 Flannery, B. P. 21 141 149 289 302 304 321 325 Flow diagram 278 311 Flow/pressure 203 Focus 369 Formula interpretation 18—20 FORTRAN 142 149 323 Forward difference 33 Foster, R. M 22 573 Four-terminal network 200 Fourier integral transform pairs 305 Fourier kernels 329 339—340 346—347 Fourier series and convolution theorem 115—119 Fourier series and Gibbs phonomenon 240 250 Fourier series and Hartley transform 293—295 306—307 Fourier series and Laplace transform 22 381 Fourier series and sampling 82 230 Fourier series and Schroedinger's equation 197 Fourier series and shah 82 83 247—248 Discrete Fourier series as extreme case of transform 237 Fourier series in three dimensions 340—343 375 378 Fourier series in two dimensions 284 329—331 332—335 Fourier series of Abel transform 373 Fourier series of autocorrelation function 122 Fourier series of derivative 124 Fourier series of Gaussian function 58 105 Fourier series of generalized function 127 Fourier series of Hilbert transform 360 Fourier series of null functions 87—88 Fourier series of point response function 416 Fourier series of product 117 Fourier series of sine 2 67—68 Fourier series, applications 370 405 Fourier series, conditions for existence 8—10 Fourier series, convergence 57 Fourier series, definition 5—6 Fourier series, double 91 Fourier series, eigenfunctions 194 196 514 Fourier series, examples 134 369 Fourier series, exercises 374 375 377 Fourier series, finite 217 242—243 Fourier series, half-order 367 Fourier series, notation 7 Fourier series, numerical 140—142 Fourier series, reciprocal properties 18—20 194 266 Fourier series, recovery of original function 326 Fourier series, slow 136 142 Fourier series, software packages 141—142 Fourier series, spectroscopy 148 Fourier series, symmetry properties 15 Fourier series, tables 107 130 Fourier series, theorems 130 332—333 Fourier transform 124 125 126 333 Fourier transform and frequency 435 Fourier transform and heat 480—481 Fourier transform and Laplace transform 385 Fourier transform and noise 463 464—465 Fourier transform and pulse shape 75 77—78 Fourier transform as ordinary function 98 Fourier transform for Fourier transform 124 125 130 145 Fourier transform for Mellin transform 346 Fourier transform of 140 420 Fourier transform of convolution integral 126 127 130 Fourier transform of fractional Fourier transform 369 Fourier transform of Gaussian function 60 Fourier transform of impulse 85 87 126 Fourier transform of segmented function 145 Fourier transform of unit step function 72 Fourier transform of, for Laplace transform 385 Fourier transform of, in two dimensions 333 Fourier transform, half-order 127 351 487 Fourier transform, Laplace transform of 386 Fourier transform, product 128 Fourier transform, table of 508 Fourier transform, transform 98 Fourier transform, transform of 105 Fourier transformin two dimensions 59 Fourier's integral theorem 6 21—22 Fourier, J. B. J. 55 236 Fourpole (see Filters) Fractional convolution 369 Fractional Fourier transform 367—370 505 Fractional order derivatives 127 351 353 Fraunhofer diffraction 66 420 Frequency analysis 135 305 489 Frequency division 494—495 Frequency response 3 200 Fresnel diffraction 171 420—421 Friedman, B. 93 99 Friis, H. 423 Fringe visibility 416 Functional 3 25 G-stiing 489 G-string 489 Gabor, Dennis 490 499 501 502 505 galvanometers 28 Gardner, W. A. 428 442 447 469 Gaskill, J. D. 422 Gate function 2 57 Gate function, Fourier transform of 105 137 Gate function, Hilbert transform of 365 Gate function, Laplace transform of 388 Gauss, C. F. 141 Gaussian amplitude distribution 463 Gaussian diffusion 480 Gaussian envelope 247 Gaussian function 58 575 Gaussian function and central-limit theorem 186—188 Gaussian function, derivatives 60 Gaussian function, double humped 218 531 Gaussian functions 412 Gaussian tendency 187 Gaussian tendency and sampling 249 Gaussian tendency of sine function 52 Generalized function 4 75 Generalized function, concept 92—94 Generalized function, derivative 97 Generalized function, exercise 103 Geophysics xvii George, N. 372 Gertner, I. 289 Gibbs phenomenon 81 240—242 250 Gold, B 289 Good, I, J. 275 289 Goodman, J. W. 21 422 422 447 469 Graded refractive index 368 379 Graphical representation of functions 55 Graphical representation of imaginary quantities 68 Graphical representation of impulse symbol 80 Graphics 129 251—252 Gratings 82 147 148 Gravity and convolution theorem 118 Gravity for two-dimensional Fourier transform 333 Gravity for waveforms and spectra 206 Gravity, center of and centroid 155 Gray, R. M 22 428 442 469 Grebenkemper, C. J. 403 Green's function 4 481 Griffiths, J. 422 Grossman, A. 500 506 Group theory 367 Guo, H. 308 325 Gyration, radius of 159 344 Half-order derivative 127 351 487 Half-power, width to 167 Hankel transform 335—339 343 357 Hankel transform in n dimensions 343 Hankel transform, exercise 376 Hao, H. 300 325 Harmonic response 3 39 209 Harmonics 255 Hartley oscillator 296—297 Hartley transform 142 147 293 573 Hartley transform and Fourier transform 144 306—307 Hartley transform in two dimensions 299—300 Hartley transform, and spectral analysis 493 Hartley transform, complex 306—307 327 Hartley transform, convolution theorem 298—300 320 Hartley transform, decomposition formula 310 Hartley transform, discrete (DHT) 293 Hartley transform, factorization 317 Hartley transform, fast (FHT) 308 322 Hartley transform, instrumentation 147 Hartley transform, intensity 337 Hartley transform, matrix formulation 317 Hartley transform, microwave 307 Hartley transform, numerical example 314 Hartley transform, optical 307 Hartley transform, physical aspect 307 Hartley transform, power spectrum 314 Hartley transform, theorems 298 300—301 310 375—376 Hartley, R. V. L. xix 200 211 293 296—297 325 Haus, H. A. 423 Haykin, S. 503 506 Heat conduction, diffusion along a poker 477 Heat conduction, Fourier's theory 475 595 Heat conduction, Green's function 481 Heat conduction, irreversibility 476 Heat conduction, one-dimensional diffusion 475—480 Heat conduction, point concentration 480 Heat conduction, problems 485 Heat conduction, spatial sinusoid diffusion 481—485 Heat conduction, thermal-electric analogy 487 Heaviside step function 61—65 70 265 Heaviside, O. 74 381 Helicoid 113 Helix 362 Helliwell, R. A. 370 372 493 506 Helmholtz, H. von 74 Herivel, J. 596 Hermite polynomial pairs 194 197 Hermite — Gauss functions 194 575 Hermitian 14 191 298 Hermitian spectrum 199 Hermitian, autocorrelation 50 51 Hermitian, characteristic 435—436 Hermitian, exercises 373 Hermitian, transfer 373 Heydt, G. T 222 297 308 Hilbert transform 329 Hilbert transform of noise 465—466 Hilbert transform, analytic signal 361 Hilbert transform, causality 363 Hilbert transform, computing 364—367 Hilbert transform, definition 359 Hilbert transform, envelope 363 Hilbert transform, Fourier transform of 359 Hilbert transform, instantaneous frequency 363 493 Hilbert transform, instantaneous phase 498 Hilbert transform, phasor generalization 361 Hilbert transform, tables 365 Hilbert transform, theorems 372 Hilgevoord, J. 290 Histograms, distribution of sum 429 Histograms, noise amplitude 448 Histograms, Poisson distribution 441 Hobson, E. W. 55 Hou, H. S. 314 325 Humbert, P. 22 Huygens, C. 408 Hydrology 253 Impedance 485 Improper function 74—75 (see also Impulse symbol) Impulse response and finite resolution 93 Impulse response and null functions 87—88 Impulse response and pulse shape 75 79 Impulse response and unit step function 75—78 Impulse response as generalized function 92 95 Impulse response for fictitious impulse 4 Impulse response in digital filtering 204 Impulse response in electrical networks 74—75 Impulse response in proofs of theorems 128 Impulse response of filter 200—204 Impulse response, causal 519 Impulse response, continuous-time 205 Impulse response, convenience 74 Impulse response, derivatives 85—87 97 126 Impulse response, duplication 84 Impulse response, exercises 216—217 Impulse response, Fourier transform 200—201 Impulse response, Fourier transform of 106 Impulse response, graphical representation 80 Impulse response, Impulse symbol 4 74 Impulse response, Laplace transform 381 390—392 Impulse response, Laplace transform of 388 Impulse response, notation 4 85 Impulse response, pairs 84 154 414 Impulse response, problems 99 517 Impulse response, product 103 431 Impulse response, properties 80—81 Impulse response, rectangular 216 Impulse response, replicating property 83—84 Impulse response, ring impulse 104 338 Impulse response, sampling property 81—83 Impulse response, sifting property 78—81 86 Impulse response, transfer function 390—392 Impulse response, two-dimensional 334 375 377 Impulse response, utility 80 92 Impulse train 365 401 Impulse train, periodic 245—246 IMSL 142 149 Independence 451—454 Index replacement rule 274 Index reversal 291 Inequalities 174—176 206 Inequalities for waveforms and spectra 206 Inequalities to ordinate and slope 174—176 Inequalities, Bessel's 176 Inequalities, limits to autocorrelation 49 Inequalities, Schwarz's 49 176 178 189 Inertia 156—157 Infinite impulse train 2 Infinitesimal dipole 85 Information loss 45 47 Infrared 486 Initial-value problems 392—396 Instantaneous frequency 363 374 Integral as convolution 63 Integral cosine transform examples 301 Integral, Laplace transform of 385
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