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Bracewell R.N. — The Fourier Transform and its applications
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Название: The Fourier Transform and its applicationsАвтор: Bracewell R.N. Аннотация: I ransform methods provide a unifying mathematical approach to the study of electrical networks, devices for energy conversion and control, antennas, and other components of electrical systems, as well as to complete linear systems and to many other physical systems and devices, whether electrical or not. These same methods apply equally to the subjects of electrical communication by wire or optical fiber, to wireless radio propagation, and to ionized media—which are all concerned with the interconnection of electrical systems—and to information theory which, among other things, relates to the acquisition, processing, and presentation of data. Other theoretical techniques are used in handling these basic fields of electrical engineering, but transform methods are virtually indispensable in all of them. Fourier analysis as applied to electrical engineering is sufficiently important to have earned a permanent place in the curriculum—indeed much of the mathematical development took place in connection with alternating current theory, signal analysis, and information theory as formulated in connection with electrical communication.
Язык: Рубрика: Математика /Статус предметного указателя: Готов указатель с номерами страниц ed2k: ed2k stats Издание: 3rd editionГод издания: 2000Количество страниц: 618Добавлена в каталог: 10.04.2011Операции: Положить на полку |
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Предметный указатель
Shift theorem for Laplace transform 385 Shift theorem in two dimensions 332 Shift theorem, proof 129 Shockley, W. 476 Shuffling 171 192 321 Sifting 78—81 86 102 Sifting, shah symbol 82 Sign function 22 65 71 72 Sign function, 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 Sine function 168 Sine function and antennas 415 Sine function and central-limit theorem 195 Sine function and impulse pairs 84 Sine function and power spectrum 460 Sine function and running mean 185 Sine function and sampling 220 224 Sine function and smoothness 160 Sine function as continued product 195 525 Sine function in slow Fourier transform example 144 Sine function, central ordinate of transform 153 Sine function, derivatives 73 Sine function, exercise 216 Sine function, Fourier transform of 105 107 138 Sine function, Hilbert transform 360—361 Sine function, interpolation 292 Sine function, Maclaurin series 528 Sine function, pictorial 578 Sine function, replicated 552 Sine function, self-convolution 52 Sine function, sine 2 66—68 105 Sine function, spectral nature 65—66 Sine function, table 508—512 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 and function width 167 Spectrum and sharpness 174 Spectrum and waveforms 1 198—200 206 Spectrum of noise waveform 458 461 Spectrum of X radiation 48 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, random input effect 458—462 Spectrum, resolution exercise 218 Speech 490 491 492—493 Spline interpolation 252—253 Square root of 159 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, distribution of a sum 429—433 Statistics, Gaussian distribution in 59 Statistics, notation 429 Statistics, probability density 438—442 Statistics, 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, N. 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. 308 315 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 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, Abel transform 354 Symmetry, exercises 22—23 51 Symmetry, Fourier transform 21—22 105 Symmetry, Gaussian function 508 Symmetry, Hankel transform 338 System function 200 systems 1 6—7 199 Tables of sequences and inverses 37 Tables, Hilbert transform 365 Tables, Laplace transform 388 Tables, Mellin transform 345 Tables, special symbols 70—71 Tables, three-dimensional Fourier transform 342 Tables, two-dimensional Fourier transform 334—335 Tables, z transform 350 351 Tabular intervals 82 91 140 tabulation 2 Tangent, hyperbolic 539 584 Tanh, Fourier transform of 584 Tape recorders 3 Tapering factor 288 291 Telescopes (see also Radio telescope) Telescopes, antenna analogy 419—420 Television camera 351 Temperature, sinusoidal 487—488 Temperature, subsurface 488 Temple, G. 74 Teukolsky, S. A. 21 141 149 289 302 304 321 325 Theorems 332 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 Three dimensional, lie 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 Time-invariant 200 209 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 of 13 15 266—267 Transform pairs in the limit 75 139 Transforms in the limit definition 10—11 Transforms in the limit definition and Gaussian functions 60 Transforms in the limit definition of sine function 105 Transforms in the limit definition, reciprocal real 293—295 Transforms in the limit definition, 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 in statistics 436—438 Truncated exponential, convolution 27—28 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 convolution, exercises 374 375 377 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 Unit step function and impulse symbol 75—78 Unit step function, symbol 70 Unit step function, uses of 61—65 Unity 68 Upcross 469—470 473 Upcross rate 469 473 Update operator 252 van der Merwe, A. 190 Van der Pol, B. 22 74 93 99 381 398 484 485 Van Duzer, T. 423 Variance 159—160 Variance of Gaussian function 188 Variance, additive under convolution 189 430—431 434 Vectors 38—39 Velocity/force 203 Vetterli, M. 501 506 Vetterling, W. T. 21 141 149 289 302 304 321 325 Villasenor, J. V. 300 307 323 325 Violin 194 302—303 VLA (Very Large Array) 404 Voelker, D. 22 Voice print 492 Voigt profile 135 Volcano 135 Voltage 61 185 397 Volterra, V. 25 Voltmeter 473 Walker, J. S. 21 289 323 325 Wang, S. 372 Wang, Y. — H. 333 Wang, Z. xix 325 Water waves 135 425 Watts, D. G. 248 Wave equations 92 476 waveforms 1 Waveforms and Laplace transform 389 Waveforms and sampling theorem 220 Waveforms and shift theorem 412 Waveforms and spectra 1 198—200 206 Waveforms, acoustical 47 Waveforms, analogy with antennas 410—411
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