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Bracewell R. — The Fourier Transform and Its Applications
Bracewell R. — The Fourier Transform and Its Applications



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Название: The Fourier Transform and Its Applications

Автор: Bracewell R.

Язык: en

Рубрика: Математика/

Статус предметного указателя: Готов указатель с номерами страниц

ed2k: ed2k stats

Издание: 3-d edition

Год издания: 2000

Количество страниц: 630

Добавлена в каталог: 24.02.2013

Операции: Положить на полку | Скопировать ссылку для форума | Скопировать ID
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Предметный указатель
$E(x)$      27
$Shah$ symbol      xx 3 74—78 414
$Shah$ symbol, Fourier transform      246—248
$Shah$ symbol, in Fourier series      237
$Shah$ symbol, in sampling      81—82 221—222 251
$Shah$ symbol, notation      82n 256
$Shah$ symbol, replicating property      82—84
$Shah$ symbol, sifting property      82
$z$ transform      347 350 374
$\mathcal{F}$      7 8 367
$\verb"dht(f,N)"$      291—292
$\verb"fft( )"$      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 $f \star f$      40—42
Autocorrelation function, complex form $f^{*} \star f$      41
Autocorrelation function, Hermitian      50 51
Autocorrelation function, irreversibility      45
Autocorrelation function, maximum at origin      48—49
Autocorrelation function, nonnormalized form of $C(x)$      43
Autocorrelation function, normalized form $\gamma(x)$      41 122
Autocorrelation function, normalized form of $C(x)$      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 $shah$ replication      82—83
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