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| Bracewell R. — The Fourier Transform and Its Applications |
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| Предметный указатель |
 27
 symbol xx 3 74—78 414
symbol, Fourier transform 246—248
symbol, in Fourier series 237
symbol, in sampling 81—82 221—222 251
symbol, notation 82n 256
symbol, replicating property 82—84
symbol, sifting property 82
 transform 347 350 374
 7 8 367
 291—292
 272—273 284
Abel transform 351—356
Abel transform, cycle of transforms 329 357
Abel transform, exercise 376
Abel transform, modified 352
Abel transform, programs 356
Abel transform, tables 354 377
Abel — Fourier — Hankel ring 329 357
Abel — Fourier — Hankel ring, exercises 376 377
Abramovitz, M. 190 195
Abscissa, and integration in closed form 137—140
Abscissa, and ordinate equal unity 68
Abscissa, mean-square 158—159 173
Abscissa, of center of gravity 118
Abscissa, of centroid 155—156 173 430
Abscissa, of symmetry 23
Abscissa, value at origin 152
Abscissa-scaling theorem see Similarity theorem
Absolute strength 287
Absorption coefficient 148
Acoustic perception 194
Addition theorem, and discrete Fourier transform 268
Addition theorem, for Fourier transform 110—111 112 130 207 268
Addition theorem, for Hankel transform 339
Addition theorem, for Hilbert transform 372
Addition theorem, for Laplace transform 385 387
Addition theorem, for two-dimensional Fourier transform 332
Addition theorem, in two dimensions 329
Addition theorem, problems 130
Addition theorem, proof 129
Addition theorem, waveform, spectrum and filter applicability 205—207 207
Additivity 367
Admittance operator 381
Affine theorem 129 327 333
Ahmed, N. 304 324 371
Aliasing and DFT 281
Aliasing and Hilbert transform 366
Aliasing and periodic impulse trains 246
Aliasing and undersampling 229—230
Aliasing sunspot exercise 254
Alternating Current 92 198 359
AM radio signal 363
Amplitude distribution 450—455 463
Analogue, thermal 479 541
Analogy, antennas and waveforms 410—411
Analytic signal 361—363
Angular spectrum 409—417 417—419
Animal sounds 493
Annual running means 228—229
Annular slot 104 338
Antenna theory 165 167 419
Antennas, analogy with waveforms 410—411
Antennas, and convolution theorem 413—414
Antennas, and modulation theorem 414—415
Antennas, and sine function 66
Antennas, angular spectrum 409—417
Antennas, aperture distribution 407—412 415 417—419
Antennas, array factor 413
Antennas, beam swinging 412—413
Antennas, beam width 411—412
Antennas, evanescent field 410 418 548
Antennas, Huyghens’ principle 408 416
Antennas, in microwave spectroheliograph 402
Antennas, in radio telescope 403
Antennas, interferometers 414—415
Antennas, monopulse 423
Antennas, parabolic 427
Antennas, paraboloidal 420 472
Antennas, radiation pattern 418
Antennas, random array 473
Antennas, related applications 422
Antennas, sidelobes 424
Antennas, slot 424 425
Antennas, spatial frequency 415 417
Antennas, spectral sensitivity 415—416
Antennas, surface tolerance 472—473
Antennas, triangular 426
Antennas, two-dimensional theory 417—419
Antennas, Very Large Array (VLA) 404
Antihermitian 23
Apertures distribution 407—412
Apertures distribution, fine detail 418
Apertures distribution, in two dimensions 417
Apodization 426
Area under a function 152—153
Array factor 413
Array-of-arrays rule 413—414
Arrays 90—91 225
Associate law 27 214 252
Asterisk notation xx 3
Asterisk notation, algebra 26—27
Asterisk notation, defined 70
Asterisk notation, for serial product 31
Asterisk notation, in statistics 432—434
Asymptotic behavior 163—164 174
Autocorrelation function, and amplitude distribution 455—458
Autocorrelation function, and DFT 263—264 270 282
Autocorrelation function, and noise 471
Autocorrelation function, and power spectra 286 288
Autocorrelation function, common form  40—42
Autocorrelation function, complex form  41
Autocorrelation function, Hermitian 50 51
Autocorrelation function, irreversibility 45
Autocorrelation function, maximum at origin 48—49
Autocorrelation function, nonnormalized form of  43
Autocorrelation function, normalized form  41 122
Autocorrelation function, normalized form of 43 122
Autocorrelation function, of digital signal 471
Autocorrelation function, of disk 53
Autocorrelation function, of error component 140
Autocorrelation function, of Hilbert transform 372
Autocorrelation function, of ring impulse 104
Autocorrelation function, of sequence 270 455
Autocorrelation function, pentagram notation 40 46 70
Autocorrelation function, problems 133—134 192—193
Autocorrelation theorem 122—124 130 270
Autocorrelation theorem, and energy spectrum 47
Autocorrelation theorem, and random input 460
Autocorrelation theorem, for Fourier transform 130
Autocorrelation theorem, for Laplace transform 385
Autocorrelation theorem, for waveforms and spectra 206
Autocorrelation theorem, in two dimensions 332
Autocorrelation theorem, versions 119
Autocorrelation width 168—171 467 472
Autocovariance 286
Axis of symmetry 23
Back projection 358
Back projection, modified 357
Bailey, D. H. 370 371
Band-limited function 219—221 229 254—255
Band-limited function, Hilbert transform of 373
Bandpass filters 250—251 494
Bandpass noise 464—466
Bandpass signal 250
Bandwidth duration product 177
Bandwith 167
Bar notation, for transforms 7 117
Barcode, periodic 217
Barker code 52
| Baron, John 323
Barrel of money example 431
Barshan, B. 372 505 506
Bartelt, H. 370
BASIC 141 149
Bastiaans, M. J. 499 505
Bat chirps 493
Beam splitting 148
Beam swinging 412—413
Beam width 165 167 411—412
Bed-of-nails symbol 90
Bell, R. J. 230 148 149
Bergland, G. D. 275 288
Bernoulli, D. 236 443—445
Bessel function 336 337
Bessel function, Abel transform of 354
Bessel function, as kernel 336 343
Bessel function, Fourier transform of 377 584
Bessel function, Hankel transform of 338 377
Bessel’s inequality 176
Beurling, A. 21
Binomial coefficients 50 292 327 462
Biomedicine xvii
Biot, J. B. 595
Birdsong 490 493
Bit reversal 278 321
Black Box 251
Black-body radiation 119
Blackman, R. B. 248 288
Blurring 24
Boashash, B. 499 505
Bochner, S. 21
Borel’s theorem 24
Born, M. 422
Bounded variation 9
Boxcar function 57
Bracewell, on affine theorem 129 333
Bracewell, on chirplets 503 506
Bracewell, on complex integrals 370
Bracewell, on fringe visibility 416
Bracewell, on Hartley transform 141 299 300 307 323
Bracewell, on modified back projection 357
Bracewell, on radio telescope 403
Bracewell, on Radon transform 358
Bracewell, on sunspots 366 402
Bracewell, R. N. 22 49 130 149 288 324 371 422 469
Bremmer, H. 22 74 381 398 484 485
Bridge deflections 3 115
Brigham, E. O. 21 288
Broadening 162—163
Brown, B. F 22 381 398
Brown, J. 422
Buneman, O. 141 300 305 315 317 324
Burrus, C. S. 308 325
C programming language 141 323
Cables 351 475—479
Cables, problems 212 215 401 488
Calculator 31 35 39
Campbell, G. A. 21 573
Capacitors, elastic 213
Capacitors, initial charge 395—396
Carleman, T. 21 120
Carrier telephony 250
Carslaw, H. S. xviii 21 484 485
Cas function 295—296 326
Cas function, cas-cas transform 300
Cassiopeia A 404
CAT scan 356
Cauchy distribution 168 581
Cauchy function 581
Cauchy principal value 359 376
Cauchy, A. L., v 72 74 376
Causality 359 363—364 373 519
Center of gravity 155 173 206 333
Central curvature 156 189
Central difference 33
Central ordinate 152—153 189
Central slope 154 189
Central-limit theorem 186—191
Central-limit theorem, and convolution 435 454
Central-limit theorem, and sampling theorem 249
Central-limit theorem, examples 431 441
Central-limit theorem, exercises 150 249 445
Centroid 155—156 173 206 333
Centroid, abscissas of 430
Champeney, D. C. 21
Chandrasekharan, K. 21
Chang, K. — Y. 333
Characteristic equation 389
Characteristic function 435
Characteristic impedance 485
Chemistry 287
Chen, D. 506
Cherry, L. 493 506
Chinese hat function 53
Chirp radar 500
Chirp signals 135 502—504
Chirplet see Elementary chirp signals
Circuit diagram 203
Circuit theory 199
Circuits, switching 396—397
Circular distributions, in one dimension 351
Circumflex notation 63
Clarke, R. H. 422
clocks 148
Closed form, integration in 136—140
Cochran, W. T. 278 288
Cohen, L. 499 505
Coherence 471—472
Collin, R. E. 422
Colvin, R. S. 403
Commutative law 26—27 172
Commutativity 367
Compactness 160—162
Complementary error integral (erfc) 58—59
Complex conjugate 14—16 119 268
Complex reflection coefficient 148
Complex transform 18
Composition product 24
Computer code, for slow Fourier transform 142—143
Computer graphics 251—252
Computer-assisted tomography (CAT) 356
Computing Fourier transforms 136—137 140—144
Conduction, of heat see Heat conduction
Conductivity, and spectral measurement 148
Conductivity, thermal 476
Consistency 367
Continuity, of transformation 215—216
Continuous-time impulse response 205
Continuous-variable theory 273
Contour integral 139
Control systems, and sampled data 347
Convergence, and Laplace integral 382—384
Convergence, of periodic functions 236—238
Convolution 118 (see also Deconvolution)
Convolution theorem, and diffusion 481—482
Convolution theorem, and Fourier series 238
Convolution theorem, and spectroheliograph 402
Convolution theorem, for DFT 269 290
Convolution theorem, for Fourier transform 115—119 129—130 332
Convolution theorem, for Hankel transform 339
Convolution theorem, for Hartley transform 298—299 320
Convolution theorem, for Hilbert transform 359 372
Convolution theorem, for Laplace transform 385
Convolution theorem, for waveforms and spectra 206
Convolution theorem, for z transform 351
Convolution theorem, in heat conduction 481—482
Convolution theorem, in statistics 434—435
Convolution, algorithm 298—299
Convolution, and  replication 82—83
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