Авторизация
Поиск по указателям
Bracewell R.N. — The Fourier Transform and its applications
Обсудите книгу на научном форуме Нашли опечатку?
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 |
Скопировать ссылку для форума | Скопировать ID
Предметный указатель
Periodic functions and discreteness 258—259 Periodic functions and similarity theorem 109 Periodic functions as impulse trains 245—246 Periodic functions in pairs in the limit 10—11 75 Periodic functions, convergence 236—238 Periodic functions, exercise 217 Periodic functions, overshoot 240—242 250 Periodic functions, sum of 211 Periodic structures 82—83 periodicity 211 236 Periodicity of impulse trains 245—246 Perkins, M. G. 300 325 Permittivity 148 Permutation 276—278 309 321—323 PERMUTE 309 Pettit, R. H. 49 52 Phase angle (pha) 47 Phasor generalization, by Hilbert transform 361 Phasor representation, of Fourier integral 20 423 photography 281—282 422 Physical realizability 363 363 Pictorial Dictionary xx 2 142 573 Pictorial representation 68—70 Pierce, J. R. 370 372 493 506 Plancherel's Theorem (see Rayleigh's theorem) Plancherel, M. 120 Plasma devices 479 Plus-i Fourier transform 6 435 Point charge, mass 4 74 Point response function 416 Poisson distribution 428 434 438 441 444 Poisson's equation 92 Poisson, S. D. 74 595 Poker, heated 478 Polygonal functions 57 145—147 211—212 Polynomials 30 348 Power spectrum and autocorrelation 122 170 Power spectrum and DHT 314 Power spectrum and electromagnetic signal 148 Power spectrum and spectrograph 493 Power spectrum and upcross and peak rates 469—70 Power spectrum in slow Fourier transform program 142 Power spectrum of error component 140 Power spectrum of noise 459 466—468 Power spectrum of waveform 143 Power spectrum, angular 412 Power spectrum, definition 285—286 Power spectrum, positive frequency 180 Power spectrum, smoothing 287—288 Power theorem 120—122 Power theorem for generalized functions 129 Power theorem for Hankel transform 339 Power theorem for Hilbert transform 363—364 Power theorem in two dimensions 332 Precision resistor 443 Prediction 250 Press, W. H. 21 141 149 289 302 304 321 325 Pressure distribution 89 Pressure gauges 425 Price, K. M. 403 Principal solution 515 prisms 112 147—148 413 probability distribution 428 Probability distribution of reciprocal 444 Probability distribution of sum 329 444 Probability distribution, convolution of 430 433 Probability distribution, Fourier transform of 435 450—455 Probability integral 59 Probability ordinate 58—59 Probable error 59 Product for Laplace transform 385 Product for Mellin transform 346 Product moment 453 455 470 Product of impulses 103 Product, Fourier transform of 117 269 Projection 357—358 Prolate spheroidal wavefunctions 217 Proofs, of theorems 128—129 Pseudocode xix Pulse modulation 82 347 Pulse sequence 75—78 590—593 Pulse train 248 Quadratic content theorem 301 Quadrature function 361 Quadrupoles 92 Quasi-monochromatic pulse 361 Quatrefoil pattern 92 Quian, S. 506 Rabiner, L. R. 289 490 506 Radar and Abel transform 351 Radar and uncertainty relation 180 Radar mapping 351 Radar, echoes from planets 491 Radar, frequency determination 500 Radar, pulse generator 196 Radar, raster scanning 82 Radar, spectral analysis 147 Radial sampling 376 Radiator, electromagnetic 92 Radio image 404 Radio interferometry 45 281 Radio signal 363 Radio source 403 471 Radio telescope 403 446 447 Radio telescope, exercises 424 471 Radio waves 20 Radioactive atom 436 Radioactive decay 28 Radioactive isotope decay 28 Radiofrequency spectral analysis 147 Radiometry and equivalent width 165 Radius of gyration 159 344 Radon transform 329 356—358 Railroads 255 Rainfall 184—185 438 Ramo, S. 423 Ramp function 61—62 211 Ramp-step function 55 76—77 584 Random array 473 Random digits 447—450 Random input 450 Random noise 45—46 444 446 Random noise and linear detector 473—474 Random noise, artificial 447 471 Random numbers, sum of 450 Random phenomena 428 437 443—444 Random polarization 446—447 Random process 286 Random walk 60 Rao, K. R. 283—284 289 302 304 324 325 371 Raster scanning 426 Ratcliffe, J. A. xviii Rayleigh distribution 428 575 Rayleigh distribution of detector output 466 Rayleigh distribution of heat flow 480 Rayleigh distribution of noise envelope 465 Rayleigh distribution, definition 59—60 Rayleigh distribution, exercise 133 Rayleigh's theorem for Fourier transform 119—120 130 Rayleigh's theorem for Hankel transform 339 Rayleigh, Lord 119 130 Real transforms 293—295 301 305—306 Reciprocal sequences 34 348 Reciprocal sequences, calculation 35—36 Reciprocal sequences, exercises 51 250 Reciprocal transform 5 16 266 293 301 329 Rectangle function 4 Rectangle function and impulse symbol 75 77 83 Rectangle function and running means 57 Rectangle function and sampling 224—226 Rectangle function and segmentally built functions 138 Rectangle function and sine function 105 Rectangle function, defined 55—57 Rectangle function, evenness 80—81 101 Rectangle function, exercises 53 212 216 Rectangle function, Fourier transform of 105—107 137 Rectangle function, generator for 212 216 Rectangle function, Hilbert transform of 365 Rectangle function, inverse operator 528 Rectangle function, Laplace transform of 388 Rectangle function, notation 2 Rectangle function, sequences of 77 81 83 93 Rectangle function, widths 168 468 Rectified sinusoid 585 Reflection coefficient 148 Refractive index 148 368 Regular sequence 94—95 Repeated root 389 Replacement rule 274 Replication 81 83—84 91 Replication and sampling 172—174 221 237 Replication of sine function 552 Resistance, negative 215 Resistance-capacitance networks 478—479 Resistor tolerances 429—430 443 Resolution, finite 93 Resolving power 4 24 74 531 Resonance 78 Resonators 28 Response, to point source 4 74 Restoration, running mean 194—195 Retrodiction 485 Reversal property 17 268 Reversal theorem, for Laplace transform 385 Reversibility and diffusion versus wave propagation 476—480 Reversibility of autocorrelation 45 Reversibility, notation 6 8 Riddle, A. C. 357 371 Riemann integral 236 Ring impulse 104 338 Ripley, B. D. 447 469 River current 253 Road example 162—163 Roberts, G. E. 381 398 416 Root-mean-square value 469 Rotation theorem 129 332 Row of spikes 91—92 rule of thumb 469 Running mean and filtering 226—229 Running mean and rectangle function 57 Running mean for weekly data 33 Running mean in transform domain 184 189 Running mean in two dimensions 333 Running mean of sunspot number 191 Running mean of waveform 206 Running mean, exercises 194—195 runs 452 Sampling and replication 172—174 Sampling for data control 82 347 Sampling in presence of noise 234—235 Sampling rate 254 Sampling symbol 70 81—83 Sampling theorem 219 222 224 Sampling theorem, inverse 256 Sampling, critical 223 Sampling, interlaced 232—234 235 250 251 Sampling, intervals in 219 Sampling, ordinate and slope 230—232 249 Sampling, radial 376 Sampling, shah 81—82 221—223 236 251 Sampling, slopes 230—232 249 Satapathy, J. K. 325 Scanning (see Convolution) Schafer, R. W. 211 289 490 506 Schelkunoff, S. A. 423 Schrodinger's Equation 196—197 370 Schwartz, L. 93—94 99 Schwartz, M. 211 Schwarz's inequality 49 176 178 189 Schwarz's inequality and uncertainty relation 178 Scrambling 321 Sea spectra 286—287 Sech pulse 583 Second difference 184 206 Second moment 156—157 189 Second moment for Hankel transform 339 Second moment from Mellin transform 344 Second moment theorem in two dimensions 333 Second moment, infinite 157 Segmented functions 57 145—147 Seismograms 491 Self-convolution 189 438—439 Self-convolution and autocorrelation 40—41 Self-convolution and Gaussian form 187 Self-convolution, exercises 51 191 Self-convolution, formulas 119 Self-multiplication 187 Self-transforming functions 23 193 Semi-infinite sequence 32 34 Semicircular envelope 591 Semicircular pulse 585 Semiconductors 475 479 Separable product theorem 333 Sequence as vectors 38—39 Sequence in serial products 38—39 Sequence of Gaussian functions 60 Sequence of particularly well-behaved functions 95—96 Sequence of pulses 75—78 88 93 Sequence of rectangle functions 77—78 81 83 Sequence, inverses of 36 37 Sequence, mean of 271 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 in statistics 431—432 Serial division of signal samples 250 Serial division, asterisk notation 32 Serial division, in matrix notation 36—38 Serial division, inversion of 34—36 Serial division, numerical calculation 32 Serial division, problems 49 250 Serial division, sequences in 38—39 SETI Institute 147 Seventh wave 194 sgn 22 65 71 72 Shah function xx 577 Shah symbol xx 3 74—78 414 Shah symbol in Fourier series 237 Shah symbol in sampling 81—82 221 222 251 Shah symbol, Fourier transform 246—248 Shah symbol, notation 82 Shah symbol, replicating property 82—84 Shah symbol, sifting property 82 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
Реклама
|
|
О проекте