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Marks R.J.II. — The Joy of Fourier
Marks R.J.II. — The Joy of Fourier



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Название: The Joy of Fourier

Автор: Marks R.J.II.

Аннотация:

The emphasis of this text is the broad field of Fourier analysis and some of its immediate outgrowths including convolution, systems theory, Shannon sampling theory and the modelling of random variables and stochastic processes. The contents of this book evolved from a set of lecture notes for courses in advanced engineering mathematics (Chapters 2, 3, 4, 12 and 13), multidimensional signal processing (Chapters 2, 9 and 11), signal reconstruction (Chapters 2, 10 and 11) and Shannon sampling and interpolation theory (Chapters 2, 5, 7, 6 and 7). Chapter 4 is useful as a supplement a graduate course on random variables and stochastic processes. The book is written at the level of the advanced senior or first year graduate student who has an introductory foundation in Fourier analysis and stochastic processes. Rudimentary familiarity with image processing is helpful but not necessary.


Язык: en

Рубрика: Математика/

Статус предметного указателя: Готов указатель с номерами страниц

ed2k: ed2k stats

Год издания: 2006

Количество страниц: 811

Добавлена в каталог: 27.03.2013

Операции: Положить на полку | Скопировать ссылку для форума | Скопировать ID
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Предметный указатель
Restoration noise      399
Revelry      673
Rice random variable      731
Riemann, Georg Friedrich Bernhard      552
Right dense      626 629
Rihaczek, A.W.      448 770
Ringing Laplace autocorrelation      187
ROLL      417
Roman Empire      434
Root      671 673 675 704
Rotation      6 340 346 348 350 368 775
Rotation matrix      347-350 416 417
Sad Man      614 615
Saint Joseph      3
Sample and hold      249 250
Sample mean      175
Sampled DTFT      56
Sampling density      234 335 389 392 400 403 408-411 413 745
Sampling matrix      391 395-397 403 421
Sampling rate      214 220 230 238 273 279 292 295 298 302-306 315 316 330 333 407 410 428 474 746 750 753 757 762 765
Sampling rate parameter      243 274
Sampling theorem      2 6 16 52 53 202 276 335 388 394 526 738 739 741-762 765-780
Savings accrual      8
Scalar optics      677
SCALE      340
Scaling      6
Scaling matrix      347
Scaling theorem      16 21 152 159 181 425 426
Scharz's inequality      181 714 715
Schrodinger's Equation      181 691 692
Schwarz's inequality      75 76 108 109 222 327 464
Sech random variable      155
Second characteristic function      151 158 160 166 170 175 205
Second moment      185
Second order aliasing      255
Semitone      670 672
Semitones      432 669 673
Separability      345
Separability theorem      344 345 368 410
Separable      344 345
Separable functions      152 345 420 427
Set subtraction      620
Sezan, M. Ibrahim      526 749 767 772
Shannon number      230 236 503 739
Shannon sampling theorem      214 387 741-744 749 753-756 762 769 772 773 776
Shannon, C.E.      306
Shannon, Claude E.      214-216 252 260 743 762 772 776
Shepp — Logan phantom      361
Shift invariant      342 678
Shift invariant systems      112 680 745
Shift theorem      16 55 62 207 208 339 341 342 351 694
Short term Fourier transform      457 460
Short time Fourier transform      129 433 434 436-440 443 444 457 460 464 465 469
Short-Time Fourier Transform      439
Shot noise      188
Sifting      21 24 119 120
Sifting property      20 33
Signal integral property      47 91 189
Signal level      183
Signal of samples      54
Signal processing      2 526 738 740 742 745 747 748 762 763 769 771
Signal recovery      7 129 470 526 738 741 745 748 749 759 763 768 778
Signal-to-noise ratio      376 503 573
Signum function      22 30
Simultaneous equations      7 545 608
Simultaneous weighted projections      530 534
Sin transform      68
Sine      472
Sine function      8 22 24 28-30 36 67 113 132 737 752 772 774
Sine integral      22 42 74 91 311
Sine transform      61
Sinogram      420
Sinusoid      34 438 641 739 755 780
Slab      540 613
Slepian, David      498 772
Sliding window      434 740 762 773
Sliding window Fourier transform      436
Sonar      2 129 760
Spectral support      389-391 393-396 407 409 411-413
Spectrogram      3 6 433 436-438 446 454-461 464 590 591 593 594
Spectrograms      456
Spectrometry      740 762
Spectroscopy      2 741 747 749 750 755 757 771 776 778
Spectrum      3 11 25 48 49 106 220 255 548 739 754 761 763 777
Speech recognition      129 770
Spherical Bessel function      137 142
Spherical Bessel functions      8 23 41 43 72 73 94 101 737
Spherical harmonic      355
Spherically symmetric      352
Spherically symmetric functions      420 427
Spinal cord      587
Splines      738 741 743-747 749 752 767 769 771 776
Stable system      114
Stable systems      6 114-116 118 137 441 464
Standard deviation      151 153
Stark, Henry      526 613 744 767-769 772-774 779 780
Stationarity      203 212
Stationary      184 297 307 400 421 480
Stationary in the wide sense      184
Stationary processes      184 185 741 751 752 757-765 768-770 773 778 780
Step response      125-127
Stirling's formula      65 80
Stochastic process      184 204 212
Stochastic processes      x 6 149 182 185 186 189 212 231 739 741 759-761 767 771
Stochastic resonance      6-8 176 177 190 192 212 213 738 750 762 764 769 780
Strictly convex sets      527 528
Strictly positive      239
Strong convergence      532
Structuring element      621 622
Student's t random variable      719 730 732
Student's t variable      731
Sub — Nyquist sampling      409 410
Subharmonic      676
Subharmonics      676 706 707
Subpixel resolution      7 573-576
subspace      539 545 547 548 745 774 777 780
Subspaces      534 535 537
Subtile      404-412
Subtiles      405
Super resolution      470 738
Superposition integral      119 132 138 416
Superposition sum      120 338 416
Superresolution      526 738 741 747-752 754 755 761 765 768 775 778
Support      616-618 661 745
Symmetric signals      12
System operator      110
System theory      753 761
Systems theory      x
Table — continuous time Fourier transform pairs      22 23
Table — continuous time Fourier transform theorems      16
Table — discrete time Fourier transform pairs      55
Table — even and odd function properties      13
TAPs      673
taxes      693 697 701
Taylor series      12 25 64 65 76 108 151 170 178 201 207 208 260 262 267 319 334 471 472 523 682
Taylor, Brook      552
Tayor series      25
Tchebycheff      153; see Chebyshev
Television      410
Tempered scale      667 669 672 675-677 705 707 712 713
Template matching      549
TFR      432-434 439 449 452 736 747 748 751 756 762 764 768 777
Thermal noise      186
Thermal resistors      112
Thermometer      2
Thesaurus      184
Thin lens approximation      687
Thomson, William (Lord Kelvin)      552
Three Dolls      620 631
Tic Tac Toe      337-339 341 416 424
Tile      365-368 370 387 388 390 391 394-396 398-401 403-407 409 410
Tiles      396
Time frequency representations      335
Time invariant      184 342
Time invariant systems      6
Time limited signals      736
Time marginal      450
Time resolution      460 580
Time resolution versus frequency resolution trade off      437 438
Time scale      8 616 624 626 646-648 658-660 665
Time scales      7 335 336 616 625-629 640 641 645 648 649 652-654 741 762
Time variant systems      112
Time-bandwidth product      229 230 236 499 502 503
Time-frequency distributions      766
Time-frequency representation      526
Time-frequency representations      3 6 7 432 736 746 747 751 756 766 768
Time-invariant systems      111 112 115-117 137 139 143 147
Time-variant systems      112
TL      736; see time limited signals
toeplitz      476
Tomographic projection      7 335 355 356 358 576 586 587
Tomography      2 7 355 363 526 736 740 757 762 770-772 774;
Tonal color      670
Topographic projections      6
Transcendental equation      601 612 614
Transcendental functions      5 10 749 766
Transfer function      62 442 443 464 466 739 768
Transformation function      377-380 383-386
Transpose theorem      16 357
Transposition      129 340 346 348 350 416
Trapezoidal integration      223-226 228
triangle      315 316 421 422 482
Triangle function      22 34 67
Triangle random variable      158
Trigonometric functions      25
Trigonometric geometric series      168 717
Trigonometric polynomial      267 330 476 477 479 480
Trigonometric polynomials      274
Tritone      676 707
Trombones      670
Truncation error      230 245 247 326-329 331 741-746 749 753 755-758 761 768 775 779
Tseng, Shiao — Min      304
TUBA      233
Ultrasound      129 740 762
Uncertainty relationship      181 201 693 754
uniform      320 330 400 485
Uniform convergence      52 222 223
Uniform difference random variable      158
Uniform jitter      325 326
Uniform product random variable      725 727
Uniform quotient random variable      726
Uniform random variable      9 154-156 158 163 173 179 203 212 725-727
Uniform ratio random variable      726 727
Unilateral Laplace transform      18
Unit step      32 226
Unit step function      22 32 118 625
Unit vector      542
Universal set      528
Upsampling      234
Vadermonde determinant      278
Vandermonde determinant      258 290
Variable      176 15
Variance      150-158 160 163 166-168 171 173- 179 181 201-203 207 209 719-732 734
Vector norm      336
Vector optics      677
Venn, John      552
Vibrating lips      673
Vibrating string      667 668
Video processing      526
Violas      670
Violins      670
Voltage      10 184
Von Mises random variable      202 726
Von Neumann's alternating projection theorem      545 548
von Neumann, J.      545 766
Walsh functions      53 280 757
Wang, C.      573 777
Watermarking      526 777
Wave equation      667 668 674 679 680 691
Wave equations      180
Wave function      181 691 692
Wave packet      692
Wavelets      9 740 742 746 747 752 772 774 778 780
Weak convergence      532
Webb, H.      526
Weibull random variable      719 720 722 723
Weighted fractional Fourier transform      130 132 140 146 148
Weighting function      45
Welch window      435
Well-posed      312 511 512
Western music      667
White Gaussian noise      550 551 750
White noise      9 186 297 483 550
Whittaker      27 29 216
Whittaker E.T.      216
Whittaker J.M.      216
Whittaker — Shannon sampling theorem      214
Whittaker, E.T.      215 777
Whittaker, Edmund Taylor      214
Whittaker, J.M.      215 741 743-745 749 755 774 777 778
Wide sense stationary      184 185 188 204 212 231 292 313 323 330
Wigner distribution      448 455 458 579 590 591 593 594 739 740 743 746 755 775
Williams, W.J.      448 746
Window      59 60 434 436 439 454 461 464
Windows      434 435 438 440 441 443 445 446 456 457 464 738 740 749 762 773 778
Yang, Y.      774 777 779
Yaw      417
Youla, Dante C.      526 546 547 779
Z transform      61-63 442 444 694
Zadeh, Lotfi A.      530 780
ZAM GTFR      457
Zero padding      235
Zero phase      335
Zero phase filter      376
Zero phase filters      127 376
Zhu, Q. F.      573 777
1 2 3 4
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