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Bracewell R.N. — The Fourier Transform and its applications
Bracewell R.N. — The Fourier Transform and its applications



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Название: The Fourier Transform and its applications

Автор: 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: en

Рубрика: Математика/

Статус предметного указателя: Готов указатель с номерами страниц

ed2k: ed2k stats

Издание: 3rd edition

Год издания: 2000

Количество страниц: 618

Добавлена в каталог: 10.04.2011

Операции: Положить на полку | Скопировать ссылку для форума | Скопировать ID
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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
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