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| Ïîèñê ïî óêàçàòåëÿì |
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| Bracewell R. — The Fourier Transform and Its Applications |
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| Ïðåäìåòíûé óêàçàòåëü |
Convolution, and Abel transform 351—356
Convolution, and amplitude distribution 454—455
Convolution, and cross correlation 46—47
Convolution, and digital filtering 204—205
Convolution, and energy spectrum 47—48
Convolution, and harmonic response 3
Convolution, and Hilbert transform 359
Convolution, and interpolation 224
Convolution, and linearity and time invariance 209
Convolution, and mean-square abscissa 158
Convolution, and noise 454—455
Convolution, and time invariance and linearity 209—211
Convolution, associative nature 27 117 214
Convolution, autocorrelation 40—45 53—54
Convolution, between truncated exponentials 27—28
Convolution, by discrete cosine transform 327—328
Convolution, commutative nature 26 117
Convolution, computing 39—40
Convolution, cyclic 264—265 289
Convolution, definition 24
Convolution, derivative of 126 130
Convolution, DHT of 320
Convolution, distributive nature 27 117
Convolution, equivalent width under 167
Convolution, examples 27—30
Convolution, graphical construction 29
Convolution, Hilbert transform of 372
Convolution, in antenna theory 413—414
Convolution, in heat conduction 480
Convolution, in image processing 320
Convolution, in matrix notation 36 515
Convolution, in spectral analysis 495—496
Convolution, in statistics 430 433—435 454
Convolution, in two dimensions 53 290 291 331
Convolution, integral of 118
Convolution, inversion 269 413
Convolution, moments of 118
Convolution, numerical evaluation 32
Convolution, of band-limited functions 255—256
Convolution, optimal method 282 283
Convolution, self-convolution 40 52 119
Convolution, significance 25—27
Convolution, smoothing effect 162—163
Convolution, speed of 54
Convolution, sum 30 264—265 269
Convolution, variance of 191
Cooley — Tukey algorithm 141 275
Cooley, J. W. 141 149 275 289
Cornu spiral 20 546
Correlation coefficient 45 46 455 470
Correlation diagrams 452—456
Correspondences, between functions and transforms 151—152 189
Correspondences, summary 189
Correspondences, waveforms and spectra 198—200 206
COSFT algorithm 302
Cosine bell 291 416 579
Cosine on pedestal 589
Cosine transform, and evenness 16—17
Cosine transform, and Hankel’s theorem 340
Cosine transform, discrete 301—304 306 327—328
Cosine transform, exercise 150
Cosine transform, widths 168
Cosinusoid 18—19 45 116
Cotangent 401 533 587
Cotangent, hyperbolic 530
Covariance 453 (see also Autocovariance)
Critical damping 28 468
Critical sampling 223—224
Critical spacing 143 144 149
Cross correlation 46—47 270 282
Cross correlation, exercise 51
Cross correlation, in two dimensions 331
Cumulant 556
Cumulative frequency distribution 428
Cumulative spectrum 47—48
Cusp, at the origin 157 188
Cutoff frequency 66—67 221
Cutoff transform 220—221 329 357
Cycle of transforms 329 357 376 377
Cycles per unit 18 19
Cyclic convolution 264—265 289—290 292
Cygnus  446 447
Dashed line notation 68
Data compression 303—304
data density 143 144
Data digital filtering 299 320
Data sampling 82 347
Daubechies, L 500 505
days of the week 150
DCT 328 502
DCT, DCT1 and DCT2 301—304
Deans, S. R. 329 358 371
Decay product 28
Deconvolution 34 54
Deconvolution, exercises 51 250
Definite integral theorem, derivation 152—153
Definite integral theorem, for Hankel transform 339
Definite integral theorem, for two-dimensional Fourier transform 333
Definite integral theorem, for waveforms and spectra 206
Degree of evenness 51
Degrees of freedom 140
Delta function 70 74
Delta function, notation 103 104 126—127
Delta function, sifting property 102
Depth, of modulation 207
Derivative Fourier transform 124—125 126 333
Derivative of a convolution 126 130
Derivative of fractional Fourier transform 369
Derivative of Gaussian function 60
Derivative theorem and Laplace transform 385
Derivative theorem for Fourier transform 124—125 130 145
Derivative theorem for Mellin transform 346
Derivative theorem of convolution integral 126—127 130
Derivative, for Mellin transform 346
Derivative, half-order 127 351 487
Derivative, Laplace transform of 386
Derivative, of impulse 85—87 126
Derivative, of segmented function 145
Derivative, of unit step function 72
Detection, of noise waveform 466 473
DFT 258
DFT, definition 260 264
DFT, examples 265
DFT, inverse 261 264
DFT, leakage 280
DFT, packing theorem 271 290
DFT, truncation error 253 280
DFT, two-dimensional 284 290
DHT see Discrete Hartley transform
Dielectric loss 479
Differential equations, in intial value problems 392 396
Differential equations, Schrodinger’s 370
Differential equations, with constant coefficients 385 393 396
Differentiation theorem for Fourier transform 332
Differentiation theorem for Hankel transform 339
Differentiation theorem for Laplace transform 385
Differentiation theorem for waveforms and spectra 206
Diffraction gratings 82 147 148
Diffraction, antenna analogy 419—420
Diffraction, Fraunhofer 66 368
Diffraction, Fresnel 171 420—421
Diffraction, in two dimensions 92 374 377 417—419
Diffraction, optical and radio 406
Diffraction, problem solutions 545
Diffraction, three dimensional 375
Diffraction, X-ray 340 375
Diffusion equation 475—480 481
Diffusion, cylindrical 486—487
Diffusion, exercise 487
Diffusion, Gaussian 480—481
| Diffusion, in two dimensions 426
Diffusion, notation 479
Diffusion, of a spatial sinusoid 481—485
Diffusion, spherical 487
Diffusion, versus wave propagation 476
Digital data compression 303—304
Digital filtering 299 320
Digital signals, and linear filter theory 203 218
Digital signals, and sampling theorem 219
Digital signals, and spectrograms 492—493
Digital signals, autocorrelation 471
Dilation equation 506
Dipoles 85 92
Dirac, P. A. M. 74—75
Direct Current 170 198
Direction cosines 417—418
Dirichlet, P. G. L. 236
Dirichlet’s discontinuous factor 57
Discontinuity see also Gibbs phenomenon; Impulse symbol
Discontinuity, and central-limit theorem 190
Discontinuity, and large slope in short interval 174
Discontinuity, and smoothness 160
Discontinuity, fractional-order 165
Discontinuity, infinite, at the origin 139
Discontinuity, of sign function (sgn  ) 65
Discontinuity, unit step function 61
Discrete cosine transforms (DCT) 301—304 306 327—328
Discrete Fourier transform (DFT) see also DFT
Discrete Fourier transform (DFT), accuracy 280—281
Discrete Fourier transform (DFT), and convolution 269 282
Discrete Fourier transform (DFT), and Fourier transform 262—263 288 291
Discrete Fourier transform (DFT), applications 281
Discrete Fourier transform (DFT), autocorrelation 263—264 270
Discrete Fourier transform (DFT), checking numerically 328
Discrete Fourier transform (DFT), cross-correlation 270
Discrete Fourier transform (DFT), error causes 280—281
Discrete Fourier transform (DFT), examples 265—266 272
Discrete Fourier transform (DFT), factorization 317
Discrete Fourier transform (DFT), FFT 275
Discrete Fourier transform (DFT), first value 270—271
Discrete Fourier transform (DFT), formula 258—264
Discrete Fourier transform (DFT), from DHT 295—296
Discrete Fourier transform (DFT), Hermitian property 298
Discrete Fourier transform (DFT), inverse 261—262 263
Discrete Fourier transform (DFT), MATLAB examples 272—275
Discrete Fourier transform (DFT), reversal property 268
Discrete Fourier transform (DFT), sum of sequence 270
Discrete Fourier transform (DFT), theorems 266—272
Discrete Fourier transform (DFT), timing 282
Discrete Fourier transform (DFT), two-dimensional 284—285 290
Discrete frequency 260—261
Discrete Hartley transform (DHT), and Hilbert transform 366—367
Discrete Hartley transform (DHT), checking numerically 328
Discrete Hartley transform (DHT), computing 305
Discrete Hartley transform (DHT), convolution using 298—299 320
Discrete Hartley transform (DHT), examples 297—298
Discrete Hartley transform (DHT), fast algorithm 309 322
Discrete Hartley transform (DHT), in two dimensions 299—300
Discrete Hartley transform (DHT), matrix formulation 317
Discrete Hartley transform (DHT), notation 294
Discrete Hartley transform (DHT), of a convolution 320
Discrete Hartley transform (DHT), theorems 300—301
Discrete Hartley transform (DHT), timing 314
Discrete samples 219—220 258
Discrete-time signals 203 204—205 218
Distribution function 428
Distribution function, of a sum 429
Distributions see also Generalized function
Distributions, multidimensional 89—92
Distributions, normal error, with zero mean 58
Distributions, of a sum 429—433
Distributions, of amplitude 450—455
Distributions, of size 437—438
Distributions, truncated exponential 436—438
Distributive law 27
Doetsch, G. 22 151 290 381 398
Dorsch, R. G. 370 371
Drift reduction 204
Driving function 392
Drunkard’s Walk 60
Duhamel integral 24
Duplicating property 84
Duplicating symbol 128
Duration 170—173
Dynamic power spectra 492
Dynamic power spectra, computing 494
D’Addario, L. R. 403
Ear 489—490
Echoes 20 54
Elastic capacitor 213
Electric charge distributions 91—92
Electric circuits 396—397
Electrical current, alternating 92 198 359
Electrical current, direct 170 198
Electrocardiograms 491
Electromagnetic radiator 92
Electromagnetics 148 203
Electrostatics 85
Elementary chirp signals (chirplets), frequency division 494
Elementary chirp signals (chirplets), interactive presentation 502
Elementary chirp signals (chirplets), spectrograph 491
Elementary chirp signals (chirplets), time division 496
Elliot, D. F. 283—284 289
End-fire arrays 407
Energy spectrum 47—48
Energy theorem 127 206
Energy, and Laplace transform 389 392—396
Energy, and power theorem 120—122
Energy, infinite 9
Energy, stored 392
entropy 478 486
Entropy, of image 567
Envelope and dynamic power spectra 408—409
envelope function 116
Envelope of a signal 363
Envelope of bandpass noise 465—466
Envelope, Gaussian 247
Epoch 155
Equalization 486 566
Equivalence theorem 497—498
Equivalent width 164 189
Equivalent width, and beamwidth 167
Equivalent width, for Hankel transform 339
Equivalent width, for two-dimensional Fourier transform 333
Equivalent width, in spectroscopy 165
Equivalent width, of distributions 166
Equivalent width, of function 166 167
Equivalent width, of functions 166
Equivalent width, of Gaussian function 59
Equivalent width, of various functions 168—169
Equivalent width, of waveforms and spectra 206
Equivalent width, reciprocal property 167
Erd lyi A. 22 329 371 381 398 573
Erdlyi’s tables 301
erf 58—59
Error integral 58
Errors and precision 140—141
Errors in convolution examples 29
Errors in discrete Fourier transform 280—281
Errors in sampling 234—235
Errors sign 142
Ersoy, O. K. 289 324
Euler, L. 236 256 594 596
Evanescent fields 410 418 421
Evans, D. M. 289 323 325
Even function 13 266
Even function, transform of 13 15 266—267
Even impulse pair 2—3 70 84
eye 424 447 553
Fabry — Perot interferometers 147
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