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| Bracewell R. — The Fourier Transform and Its Applications |
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| Предметный указатель |
Faltung$ 24 26 27
Fast Fourier transform (FFT) see also Cooley — Tukey algorithm; FFT
Fast Fourier transform (FFT), and 365 data values 283—284
Fast Fourier transform (FFT), and critical spacing 149
Fast Fourier transform (FFT), and permutation 321
Fast Fourier transform (FFT), and shift theorem 276
Fast Fourier transform (FFT), and stretching theorem 276
Fast Fourier transform (FFT), applications 281—282
Fast Fourier transform (FFT), factorization of transform matrix 275—276
Fast Fourier transform (FFT), power spectra 285—288
Fast Fourier transform (FFT), practical considerations 278—280
Fast Fourier transform (FFT), timing 283 292
Fast Fourier transform (FFT), versus FHT 305 315
Fast Hartley transform (FHT), algorithm 309—314
Fast Hartley transform (FHT), matrix formulation 317—320
Fast Hartley transform (FHT), subroutine 322—324
Fast Hartley transform (FHT), timing 308 314—317
Fast Hartley transform (FHT), versus FFT 308—309 315
FFT 141 275 281
FHT see Fast Hartley transform
Filtering, numerical 224 225
Filters 198
Filters, analogue 250 495
Filters, analogy with antennas 416
Filters, and Hilbert transform 359
Filters, and random input 450—455 462 466 473
Filters, bandpass 250—251 494
Filters, characteristic waveform 201—202
Filters, constant — Q 501—502
Filters, definition 200
Filters, digital 299
Filters, fixed-frequency 147
Filters, general 251
Filters, low-pass 66 75
Filters, measuring 167
Filters, of noise 45—46 171
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 difference, for Laplace transform 385
Finite difference, Fourier transform of 182
Finite difference, in two dimensions 333
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
Fortran 90 141 142
Forward difference 33
Foster, R. M. 21 573
Four-terminal network 200
Fourier kernels 329 339—340 346—347
Fourier series and  82 83 247—248
Fourier series and Gibbs phonomenon 240 250
Fourier series and sampling 235 237 256
Fourier series as extreme case of transform 237
Fourier series convergence 57
Fourier series, double 91
Fourier transform see also Abel — Fourier — Hankel ring; Discrete Fourier transform; Fast Fourier transform; Fractional Fourier transform; Slow Fourier transform
Fourier transform, and convolution theorem 115—119
Fourier transform, and Hartley transform 293—295 306—307
Fourier transform, and Laplace transform 22 381
Fourier transform, and sampling 82 230
Fourier transform, and Schr dinger’s equation 197
Fourier transform, applications 370 405
Fourier transform, conditions for existence 8—10
Fourier transform, definition 5—6
Fourier transform, eigenfunctions 194 196 514
Fourier transform, examples 134 369
Fourier transform, finite 217 242—243
Fourier transform, half-order 367
Fourier transform, in three dimensions 340—343 375 378
Fourier transform, in two dimensions 284 329—331 332—335
Fourier transform, in two dimensions, exercises 374 375 377
Fourier transform, notation 7
Fourier transform, numerical 140—142
Fourier transform, of  67—68
Fourier transform, of Abel transform 373
Fourier transform, of autocorrelation function 122
Fourier transform, of derivative 124
Fourier transform, of Gaussian function 58 105
Fourier transform, of generalized function 127
Fourier transform, of Hilbert transform 360
Fourier transform, of null functions 87—88
Fourier transform, of point response function 416
Fourier transform, of product 117
Fourier transform, reciprocal properties 18—20 194 266
Fourier transform, recovery of original function 326
Fourier transform, slow 136 142
Fourier transform, software packages 141—142
Fourier transform, spectroscopy 148
Fourier transform, symmetry properties 15
Fourier transform, tables 107 130
Fourier transform, theorems 130 332—333
Fourier, biography 594—596
Fourier, J. B. J. 55 236
Fourier’s integral theorem 6 21—22
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-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, and frequency 435
Gaussian function, and heat 480—481
Gaussian function, and noise 463 464—465
Gaussian function, and pulse shape 75 77—78
Gaussian function, derivatives 60
Gaussian function, double humped 218 531
Gaussian function, Fourier transform of 139
Gaussian function, in two dimensions 59
Gaussian function, table of 508
Gaussian function, transform of 105
| Gaussian functions 412
Generalized function 4 75
Generalized function, as ordinary function 98
Generalized function, concept 92—94
Generalized function, derivative 97
Generalized function, exercise 103
Generalized function, Fourier transform 127—128
Generalized function, product 128
Generalized function, transform 98
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, center of, and centroid 155
Gravity, center of, and convolution theorem 118
Gravity, center of, for two-dimensional Fourier transform 333
Gravity, center of, for waveforms and spectra 206
Gray, R. M. 21 428 442 469
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, exercise 376
Hankel transform, in  dimensions 343
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, 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, in two dimensions 299—300
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 step function, Fourier transform see Pictorial Dictionary
Heaviside step function, Fourier transform of 583
Heaviside step function, Laplace transform of 388
Heaviside, O. 74 381
Helicoid 113
Helix 362
Helliwell, R. A. 370 371 493 506
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. 211 297 308
Hilbert transform 329
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, of noise 465—466
Hilbert transform, phasor generalization 361
Hilbert transform, tables 365
Hilbert transform, theorems 372
Hilgevoord, J. 190
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
Huyghens’ principle 408 416 417
Hydrology 253
Impedance 485
Improper function 74—75 (see also Impulse symbol)
Impulse response, continuous-time 205
Impulse response, convenience 74
Impulse response, exercises 216—217
Impulse response, for fictitious impulse 4
Impulse response, Fourier transform 200—201
Impulse response, in digital filtering 204
Impulse response, Laplace transform 381 390—392
Impulse response, of filter 200—204
Impulse response, rectangular 216
Impulse response, transfer function 390—392
Impulse symbol,  4 74
Impulse symbol, , and finite resolution 93
Impulse symbol, , and null functions 87—88
Impulse symbol, , and pulse shape 75 79
Impulse symbol, , and unit step function 75—78
Impulse symbol, , as generalized function 92 95
Impulse symbol, , causal 519
Impulse symbol, , derivatives 85—87 97 126
Impulse symbol, , duplication 84
Impulse symbol, , Fourier transform of 106
Impulse symbol, , graphical representation 80
Impulse symbol, , in electrical networks 74—75
Impulse symbol, , in proofs of theorems 128
Impulse symbol, , Laplace transform of 388
Impulse symbol, , notation 4 85
Impulse symbol, , pairs 84 154 414
Impulse symbol, , problems 99 517
Impulse symbol, , product 103 431
Impulse symbol, , properties 80—81
Impulse symbol, , replicating property 83—84
Impulse symbol, , ring impulse 104 338
Impulse symbol, , sampling property 81—83
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