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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 |
Sequence, mean of 271
Sequence, of particularly well-behaved functions 95—96
Sequence, of pulses 75—78 88 93
Sequence, of rectangle functions 77—78 81 83
Sequence, reciprocal 34
Sequence, regular 94—95
Sequence, representable by polynomial 30—34 347
Sequence, semi-infinite 32 34
Sequence, sum of 34 270
Sequence, two-sided 33
Serial division 32 348
Serial division, asterisk notation 32
Serial division, in matrix notation 36—38
Serial division, in statistics 431—432
Serial division, inversion of 34—36
Serial division, numerical calculation 32
Serial division, of signal samples 250
Serial division, problems 49 250
Serial division, sequences in 38—39
SETI Institute 147
Seventh wave 194
sgn 22 65 71 72
Sgn, Fourier transform of 140 420
Shah function xx 577
Shannon, C. E. 248
Sharpening 162—163 174 194—195
Shear theorem 129 333 374
Sheng, Y. 500 506
Sheppard, C. J. 370 372
Shift theorem 207
Shift theorem, and antennas 412—413
Shift theorem, and discrete Fourier transform 268—269
Shift theorem, and waveforms 207
Shift theorem, for Fourier transform 111—112 111—113 114 129 130 131 207 268—269 332
Shift theorem, for fractional Fourier transform 369
Shift theorem, for Hankel transform 339
Shift theorem, for Hilbert transform 365
Shift theorem, for Laplace transform 385
Shift theorem, in two dimensions 332
Shift theorem, proof 129
Shockley, W. 476n
Shuffling 171 192 321
Si 66—67 241
Sifting 78—81 86 102
Sifting,  symbol 82
Sign function (sgn) 22 65 71 72
Sign function (sgn), Fourier transform of 140 583
Signal theory 203
Signal-to-noise ratio 469
Silver, S. 423
Similarity theorem 108—110
Similarity theorem, and DFT 272
Similarity theorem, and equivalent width 167
Similarity theorem, and FHT algorithm 310
Similarity theorem, for antennas 411—412
Similarity theorem, for Fourier transform 129—130
Similarity theorem, for Hankel transform 339
Similarity theorem, for Laplace transform 385
Similarity theorem, for waveforms 205—207
Similarity theorem, in two dimensions 332 335
Similarity theorem, proof 129
Similarity theorem, symmetrical version 111
Simple shear theorem 333
Sinc function 168
Sinc function,  66—68 105
Sinc function, and antennas 415
Sinc function, and central-limit theorem 195
Sinc function, and power spectrum 460
Sinc function, and running mean 185
Sinc function, and sampling 220 224
Sinc function, and smoothness 160
Sinc function, as continued product 195 525
Sinc function, derivatives 73
Sinc function, exercise 216
Sinc function, Fourier transform of 105 107 138
Sinc function, in slow Fourier transform example 144
Sinc function, interpolation 292
Sinc function, Maclaurin series 528
Sinc function, notation xx
Sinc function, pictorial 578
Sinc function, replicated 552
Sinc function, self-convolution 52
Sinc function, spectral nature 65—66
Sinc function, table 508—512
Sine function, and impulse pairs 84
Sine function, central ordinate of transform 153
Sine function, Hilbert transform 360—361
Sine integral 65
Sine transform 17 150
Sine transform, and Hankel’s theorem 340
Sine transform, discrete 301—304
Sine transform, graphic representation 18
Sinusoid 61 183—184 416
Sinusoidal response xx 3 39
Sinusoidal time variation 485
Size distributions 437—438
Slopes, sampling 230—232 249
Slopes, upper limits 174—176
Sloping step function 55
Slow Fourier transform 136 142—144
Smearing 24
Smith, Babington 462
Smoothness 160—163 476
Sneddon, I. N. 21
Software, for Fourier analysis 141—142
Soil temperature 487 488
Sonine functions 427
Sound tracks 3 53 162
Sound tracks, exercise 212
Sound, underwater 493
Space invariance 3 115 213
Spacing, of impulses 83
Spatial frequency 417
Spatial sinusoid diffusion 481—484
Special symbols 70 71
Specific heat 476
Spectral analysis 142 147—148
Spectral lines 48 164 239 287
Spectral window 288
Spectrograph, dynamic 491—494
Spectroheliograph 402
Spectroscopy, and equivalent width 165
Spectroscopy, Fourier transform 287
Spectrum see also Angular spectrum; Dynamic power spectra
Spectrum, and function width 167
Spectrum, and sharpness 174
Spectrum, and waveforms 1 198—200 206
Spectrum, angular 409—417 417—419
Spectrum, cutoff 66—67
Spectrum, energy 47—48
Spectrum, frequency increase effect 163—164 174
Spectrum, Hermitian 199
Spectrum, line to continuous 239
Spectrum, measurement of 147—148
Spectrum, of noise waveform 458 461
Spectrum, of X radiation 48
Spectrum, random input effect 458—462
Spectrum, resolution exercise 218
Speech 490 491 492—493
Spline interpolation 252—253
Square, equation of 537
Stability 214 215
Staircase function 138 400
standard deviations 43 59
Statics 155 428—445
Statics, mean-square abscissa 158
Statistics see also Random numbers
Statistics, for frequency distribution, and convolution 430—435
Statistics, for frequency distribution, distribution of a sum 429—433
Statistics, for frequency distribution, Gaussian distribution in 59
| Statistics, for frequency distribution, notation 429
Statistics, for frequency distribution, probability density 438—442
Statistics, for frequency distribution, truncated exponential distribution 436—438
Stegun, I. A. 190 195
Steiner symmetrization 192—193
Steiner, Jacob 192—193
Step function 61—65 70
Step response 201—202
Steward, E. G. 469
Stieltjes integral 4 5 48
Stirling formula 441
Stock market problem 378
Stored energy 392
Strang, G. 500 506
Streibl, Nv 370
Strength, absolute 287
Stress deflection 115
Stretching 272 276
Strip of convergence 382—383 384 385
Strip of convergence, exercises 398 400
Stripe diagram 315
Stutzman, W. L. 423
Subband Coding 502
Subsidiary equation 386
Sum of series 34
Sum, distribution of 429—433
Summary of symbols 70 71
Summary of theorems 130
Sunspots 191 254 366
Superposition 24 209 391—392
Surfing 194
Sutton, G. A. 308 325
Swartztrauber, P. N. 370 371
Swarup, G. 402 469
Swenson, G. W., Jr 423
Switching problems 396—397
Switching waveforms 145—146
symbols 2—3 (see also Notation)
Symbols, bed-of-nails 90
Symbols, definition 74n
Symbols, for generalized functions 96—98
Symbols, for transformation 7—8
Symbols, impulse 4
Symbols, sampling (replicating) 70 81—83
Symbols, summary of special 70 71
Symmetrization 193
Symmetry 11—14 267
Symmetry, exercises 22—23 51
System function 200
systems 1 6—7 199
Tables,  transform 350 351
Tables, Abel transform 354
Tables, Fourier transform 21—22 105
Tables, Gaussian function 508
Tables, Hankel transform 338
Tables, Hilbert transform 365
Tables, Laplace transform 388
Tables, Mellin transform 345
Tables, of sequences and inverses 37
Tables, sinc  ,  , exp( ) 508—512
Tables, special symbols 70—71
Tables, three-dimensional Fourier transform 342
Tables, two-dimensional Fourier transform 334—335
Tabular intervals 82 91 140
tabulation 2
Tangent, hyperbolic 539 584
Tanh, Fourier transform of 584
Tape recorders 3
Tapering factor 288 291
Telescopes 419—420 (see also Radio telescope antenna analogy)
Television camera 351
Temperature, sinusoidal 481 485 486 487
Temperature, subsurface 488
Temperature, subsurface, sinusoidal 487—488
Temple, G. 74n 93—94 99
Teukolsky, S. A. 21 141 149 289 302 304 321 325
Theorems, for Hilbert transform 372
Theorems, for two-dimensional Fourier transform 332—335
Theorems, for waveforms spectra 206
Theorems, for z transform 351
Theorems, Fourier transform 130
Theorems, Hankel transform 339
Theorems, Hartley transform 298 300—301 310 375—376
Theorems, Laplace transform 385
Theorems, Mellin transform 346
Theorems, transform generation by 145—147
Thermal radiation 486
Thermal units 476
Thermo-electric analogy 487 541
Thompson, A. R. 403 423
Three dimensional Fourier transform 340—343 375 378
Tic and toe 283
Time and autocorrelation 45—46
Time and similarity theorem 109
Time and spectral resolution 489—490 502
Time domain, and frequency domain 195
Time in heat conduction 476—480
Time invariance 39
Time invariance, and linearity 209—222 212—213
Time invariance, in switching problems 396—397
Time invariance, versus space invariance 3
Timing 282—283 292 314—317
Timing, diagram 316
Titchmarsh, E. C. 21 120 130
Tolerance 429—430 443
Tomography 356—358 405
TRAINS 255
transducers see Filters
Transfer factor 200 203 209
Transfer function 200 209 390 416
Transform pairs in the limit 75 139
Transforms in the limit, and Gaussian functions 60
Transforms in the limit, definition 10—11
Transforms in the limit, of sinc function 105
Transforms in the limit, reciprocal real 293—295
Transforms in the limit, squared modulus 47—48
Transient response 385—386
Translation 152
Transmission lines 545
Transmission lines, and Abel transform 351
Transmission lines, and sinusoidal time variation 485
Transmission lines, exercises 212 215 401 488
Transmission lines, heat diffusion 475—479
Trapezoidal 145 429—430
Triangle function 57 105 168 264
Triangle function, exercises 73
Triangle function, Fourier transform of 105 107
Triangular aperture 426
Triple correlation 45 46
Truncated exponential 384 388 581
Truncated exponential, and noise waveform detection 466
Truncated exponential, convolution 27—28
Truncated exponential, in statistics 436—438
Tukey, J. W. 141 149 248 275 288 289
Tuning capacitors 147
Two-dimensional autocorrelation 53 291 376
Two-dimensional convolution 53 290 331
Two-dimensional Fourier transform 284 332—335
Two-dimensional Fourier transform, exercises 374 375 377
Two-dimensional Fourier transform, theorems 332
Two-dimensional Hartley transform 299—300
Two-dimensional theory antennas 417—419
Two-port element 200
Two-sided sequences 33
Uffink, J. 190
Uncertainty principle 490
Uncertainty relation 172 177—180 189
Undersampling 229—230 249
Underwater sound 493
Unit step function and cyclic convolution 265
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