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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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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 in heat conduction 481 482 Convolution theorem in statistics 434 435 Convolution, algorithm 298 299 Convolution, associative nature 27 117 214 Convolution, autocorrelation 40 45 53 54 Convolution, between truncated exponentials 27 28 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, integral of 118 Convolution, inversion 269 413 Convolution, moments of 118 Convolution, numerical evaluation 32 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 141 249 275 289 Cornu spiral 20 546 Correlation coefficient 45 46 455 470 Correlation diagrams 452 456 Correlation diagrams, summary 189 Correlation diagrams, 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 Hankers 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 in two dimensions 331 Cross correlation, exercise 51 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 A 446 447 D'Addario, L. R. 403 Dashed line notation 68 Data, compression 303 304 Data, density 143 144 Data, digital filtering 299 320 Data, sampling 82 347 Daubechies, I. 500 505 days of the week 150 DCT 328 502 DCT and DCT 2 301 304 Deans, S. R. 329 358 371 Decay product 28 Deconvolution 34 54 Deconvolution, exercises 51 250 Definite integral theorem for Hankel transform 339 Definite integral theorem for two-dimensional Fourier transform 333 Definite integral theorem for waveforms and spectra 206 Definite integral theorem, derivation 152 153 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 of a convolution 126 130 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 with constant coefficients 385 393 396 Differential equations, Schrodinger's 370 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 in two dimensions 92 374 377 417—419 Diffraction, antenna analogy 419—420 Diffraction, Fraunhofer 66 368 Diffraction, Fresnel 171 420—421 Diffraction, optical and radio 406 Diffraction, problem solutions 545 Diffraction, three dimensional 375 Diffraction, X-ray 340 375 Diffusion equation 475—480 481 Diffusion in two dimensions 426 Diffusion of a spatial sinusoid 481—485 Diffusion, cylindrical 486—487 Diffusion, exercise 487 Diffusion, Gaussian 480—481 Diffusion, notation 479 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, S 5 92 Dirac, P. A. M. 74—75 Direct Current 170 198 Direction cosines 417—418 Dirichlet's discontinuous factor 57 Dirichlet, P. G. L. 236 Discontinuity (see Gibbs phenomenon) Discontinuity and large slope in short interval 174 Discontinuity and smoothness 160 Discontinuity of sign function (sgn x) 65 Discontinuity, fractional-order 165 Discontinuity, Impulse symbol and central-limi t theorem 190 Discontinuity, infinite, at the origin 139 Discontinuity, unit step function 61 Discrete cosine transforms (DCT) 301—304 306 327—328 Discrete cosine transforms (DCT) and convolution 269 282 Discrete cosine transforms (DCT) and Fourier transform 262—263 288 291 Discrete cosine transforms (DCT) from DHT 295—296 Discrete cosine transforms (DCT), accuracy 280—281 Discrete cosine transforms (DCT), applications 281 Discrete cosine transforms (DCT), autocorrelation 263—264 270 Discrete cosine transforms (DCT), checking numerically 328 Discrete cosine transforms (DCT), cross-correlation 270 Discrete cosine transforms (DCT), error causes 280—281 Discrete cosine transforms (DCT), examples 265—266 272 Discrete cosine transforms (DCT), factorization 317 Discrete cosine transforms (DCT), FFT 275 Discrete cosine transforms (DCT), first value 270—271 Discrete cosine transforms (DCT), formula 258—264 Discrete cosine transforms (DCT), Hermitian property 298 Discrete cosine transforms (DCT), inverse 261—262 263 Discrete cosine transforms (DCT), MATLAB examples 272—275 Discrete cosine transforms (DCT), reversal property 268 Discrete cosine transforms (DCT), sum of sequence 270 Discrete cosine transforms (DCT), theorems 266—272 Discrete cosine transforms (DCT), timing 282 Discrete cosine transforms (DCT), two-dimensional 284—285 290 Discrete frequency 260—261 Discrete Hartley transform (DHT) and Hilbert transform 366—367 Discrete Hartley transform (DHT) in two dimensions 299—300 Discrete Hartley transform (DHT) of a convolution 320 Discrete Hartley transform (DHT) of a sum 429 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), matrix formulation 317 Discrete Hartley transform (DHT), notation 294 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 Distributions of a sum 429—433 Distributions of amplitude 450—455 (see also Generalized function) Distributions of size 437—438 Distributions, multidimensional 89—92 Distributions, normal error, with zero mean 58 Distributions, truncated exponential 436—438 Distributive law 27 Doetsch, G. 22 151 190 381 398 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 E(X) 27 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 Eneigy theorem 127 206 Energy and Laplace transform 389 392—396 Energy and power theorem 120—122 Energy spectrum 47—48 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 beam width 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 Erdelyi A. 22 329 372 381 398 573 Erdelyi'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 impulse pair 2—3 70 84 eye 424 447 553 Fabry — Perot interferometers 147 Faltung 24 26 27 Fast Fourier transform (FFT) (see also Cooley — Tukey algorithm) Fast Fourier transform (FFT) and critical spacing 149 Fast Fourier transform (FFT) and permutation 321 Fast Fourier transform (FFT) and shift theorem 276 Fast Fourier transform (FFT) and stretching theorem 276 Fast Fourier transform (FFT), applications 281—282 Fast Fourier transform (FFT), data values 283—284 Fast Fourier transform (FFT), factorization of transform matrix 275—276 Fast Fourier transform (FFT), power spectra 285—288 Fast Fourier transform (FFT), practical considerations 278—280 Fast Fourier transform (FFT), timing 283 292 Fast Fourier transform (FFT), versus FHT 305 315 Fast Hartley transform (FHT), algorithm 309—314 Fast Hartley transform (FHT), matrix formulation 317—320 Fast Hartley transform (FHT), subroutine 322—324 Fast Hartley transform (FHT), timing 308 314—317 Fast Hartley transform (FHT), versus FFT 308—309 315 FFT 141 275 281 FHT (see Fast Hartley transform) Filtering, numerical 224 225 Filters 198 Filters and Hilbert transform 359 Filters and random input 450—455 462 466 473 Filters of noise 45—46 171 Filters, analogue 250 495 Filters, analogy with antennas 416 Filters, bandpass 250—251 494 Filters, characteristic waveform 201—202 Filters, constant — Q 501—502 Filters, definition 200 Filters, digital 299
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