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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
$Description$ $de$ $l’Egypte$      4
$L_{1}$      10
$L_{2}$      10 52 531 532 751
$L_{n}$      336
$L_{n}$ signals      10 12
$L_{\infty}$      10
$z$ transform      694
a.k.a      736
Abel transform      224 356-358 420 427
Abel, Niels Henrik      552
Absolute convergence      107
Absolutely convergent      267
Absolutely convergent series      75 76
Absolutely convergent sum      65 77
Acoustics      2 771 778
Additive closure      658-663
Additive systems      9 110 111 114 116 117 120 137 143
Additively idempotent      648; see AITS
Additivity      680
Airy disc      685 710
Airy pattern      685 710 712
Airy, George Biddell      552
AITS      648-650 654 656 658-661 665 736
AITS hull      649
AITS hulls      650
Algebraic decay      726 733
Alias      474
Aliased sampling      388
Aliasing      3 8 9 220 236 253-255 315 389 397 474 475 479 480 482 483 485 486 488 511 741 742 746 749 753 756 762 764 772-775
Alternating projection onto convex sets      7
Alternating projections onto convex sets      526; see POCS
AM      269 736
Ambient temperature      112
Amortization      8 703
Analytic      229 267 334 523 740 754 755 760 765 768 771 772
Analytic signals      12 548
Angular Fourier transform      129 738
Annulus      352 617 618 658 662 663
Anti-derivative      626
Antiextensive      624 647 665
Aperture      712 713
Array function      34-37 717
Array imaging      2 773
Associative      621 628
Associative memory      7 549-553 555 562 563 587 746 762 772
Atmospheric gases      4
audio recording      233
Autoconvolution      178 203 211
Autocorrelation      183-187 203 204 212 231 293-296 315 316 318 322 331 399 449 482 485 487 488 513 751 757
Average      158 175 176
Average power      204 213 776
Baby Senator      192
Back projection      363
Band Pass Filter      128 138
Band pass filters      378 379
Band stop filter      127 128 138
Band stop filters      378 379
Bandlimited signal      412 548
Bandlimited signals      7 11 12 41 75 76 107 137 140 142 148 214 217 223 228 229 231 239 244 276 279 312 326 470 500 505 523 526 539 547 577 578 588 736 739 741-746 749 750 753 758-763 765 767 768 770 775 778-780
Bandpass      269 271 279 280 305
Bandpass filters      434 740 742
Bandpass sampling      271 776
Bandpass signal      270 271
Bandpass signals      269 271 272 275 742
Bandwidth      11 52 127 140 214 217 218 220 224 230 234 238 239 242 247 262 265 269 273 277 283 292 297 298 413 415 473 501 504 510 512 539 547 578 741 751 755 760 763 776 779
Bandwith      577
Bartlett window      435 440
Bastinadoed      434
Bayes, Rev. Thomas      552
Be      736; see bounded energy signals
Beam splitter      691
Beat frequency      452
Bel      434
Bell shaped curve      158
Bernoulli random variable      157 167 168 170
Bernoulli trial      168 169
Bernoulli, Daniel      552
Bernoulli, Jacob (Jacques)      552
Bernoulli, Nicolaus (II)      552
Bertrand paradox      576 609 611
Bessel function      5 43 67 137 142 202 264 353 355 435 737
Bessel functions      8 23 39 41 43-45 71-73 94 98 101 426 777
Bessel, Friedrich Wilhelm      552
beta function      39 40 737
Beta random variable      156 163 164 201 208
BIBO      114 116 118 736
Bilateral Laplace transform      67
Binomial coefficient      39 737
Binomial coefficients      715
Binomial random variable      157 168-172 180 182 199 200 203
Binomial series      715
Biomedical engineering      2 768
Bit packet      159
BL      736; see bandlimited signals
Black, H.S.      214 215
Blackman window      435 440 441 443
Bohner, M.      625 741
Boltzmann's constant      186 427
Borel, E.      216
Borel, Emile      215
Born — Jordon kernel      448 585
Bortfeld, Thomas      599 604 605 741
boundary conditions      668
Bounded energy signals      736
Bounded input — bounded output stability      114 143
Bounded signal      75
Bounded signals      10-12 75 76 106 107 116 249 526 543 736 739
Bow tie constraint      451 580 584 585
Boxcar window      434 435 440 441 443 445
Bracewell,Ronald N.      742
Brahme's butterfly tumor      599 602 603 742
Bravais lattice      335
Bregman, L.M.      526 742
Brother Ray      177 195
BS      736; see bounded signals
Bugles      670 673 674
Bunched      252 258
BYTE      573
CA      736; see constant area signals
capacitors      112
Cardinal series      52 214-217 221-223 225 227 229-231 233 240 242 243 245-249 263 268 273 275 276 280 287 288 292 293 299 306 320 321 324 326 327 331 511 742 744 754 758 774
Cartesian coordinates      16
Cartesian product      628 645
cat      335 736
Cauchy principle value      165 166
Cauchy random variable      156 164-167 174 179 733
Cauchy, A.L.      214 215 742 744 745 777
Causal      441
Causal comb      34 82
Causal signal      8
Causal signals      16 18 49 67 113 117 526 740
Causal system      113 114
Causal systems      6 112 115-117 120 137 143 144 441 463
Causal window      441
CD      2 113 736
Cellular radio      526 769
Center of mass      151 173
Central limit theorem      6 9 158 177 179 180 197-200 202 203 209
Central Slice Theorem      358
Cents      670 671 673 675 676 707 712 713
Chain rule      614
Characteristic      80
Characteristic function      149-151 154-157 159 160 162 163 166 167 169 170 172- 178 179 201-203 207-209 211 321 324
Characteristic functions      6 150 175
Chebyshev filters      113
Chebyshev polynomial      94
Chebyshev polynomials      23 44 45 47 53 72 73 101 102 377 380 386 737
Chebyshev polynomials of the second kind      73 102
Chebyshev's inequality      153 154 176
Chebyshev, Pafnuty Lvovich      552
Chemistry      2 749 762
Cheung, Kwan Fai      548 745 746 778
Chi random variable      156 721-723
Chi-square random variable      156 161 174 180 201 205 206
Chi-squared random variable      161 163 719 721 722 727 728
Chirp      455
Choi, H.I.      448 746
chords      432 675 676 706
Chromatic scale      9
Chromatic step      670
Chromatic steps      432 669
Circular      355 400 401 420
Circular convolution      55
Circular harmonic      355
Circular pupil      390
Circular support      394
Circularly symmetric      352-355
Circularly symmetric functions      353
City block metric      336
Clarinets      670
Closed convex sets      527
Closed under addition      627 665
Closing      624 665
Closure      527 528 627 628 645
Cochlea      3
Cohen, Leon      6 438 446 448 449 579 746
Column space      537 538
Comb      387
Comb function      23 33 34 36 37 74 366 369 410 737
Combettes, P.L.      526 747
Communications engineering      2 764
Commutative      621 628
complete      280 501
Compound interest      693 694 698 699
Computed axial tomography      335 736
Condition number      305
Cone      535 537
Cone constraint      451
Cone kernel      455-457 460-462 465 468 579 589 592-594 747 748 751 756 762 764 766 768 777
Confluent hypergeometric function      201 207 208 728 737
Conformal radiotherapy      7 587 599
Conjugate symmetry      48
Conjugately symmetric      234
Conjugately symmetric functions      48
Conservation of contours      378
Constant area signals      736
Constant phase signals      736
Content addressable memory      549
Continuous sampling      470 504 511
Continuous signals      5 739
Continuous time Fourier transform      48
Continuous time Fourier transforms      14 16 47 54
Continuous time signal      10
Continuous time signals      7 10-12 14 54 57 77 110 127 142 438 439 446 531 608 624 625 627 640
Continuous white noise      186
Contractive function      601 612 614
Contractive operator      600 601 607 612 614
Convergence factor      27 34
Convex cone      535
Convex cone hull      556
Convex cone hulls      536 537
Convex hulls      536
Convex set      528 529 540 546 600 613
Convex sets      526-528 530 531 533 534 536 544 575 577 609 665 769
Convex slab      540 613
Convolutio      656
Convolution      x 6 7 9 13 16 19 55 116-118 121-126 177 179 187 196-198 219 220 224 229 235 250 252 264 265 341-343 357 358 362 387 440 473 480 617 618 624 628 629 646-648 659 661 680 737 761 763 764 769 773 774
Convolution integral      121
Convolution sum      121
Convolution theorem      19 34 357
Convolutions      173
Correlation      16 55 188 224 296 741 747 750 753 758 761 769 770
Cosine transform      60 67 68 88 335 373 556 763 769
Cotangent      23 92
cp      736; see constant phase signals
Cramer's rule      258 290
Crystallography      746 751 757 773 778
CTFT      14 17 19 21 57 627 736;
CTS      736
Cumulative distribution function      150
Cumulative sum      55
Current      10 184
Cyclostationary stochastic processes      330
Davis, John M.      624 762
dB — decibels      11
DCT      3 6 60 76 372-375 382 383 556 736 738
de Broglie wavelength      692
de Broglie, Louis Victor Pierre Raymond duc      692
De Moivre, Abraham      552
Decade      56 57 776
Decibel      434 736
Decimate      434
Decimated      434 457 461
Decimation      402 403 407-410 412 413 422
Deconvolution      526 646 738 751 754 755 762 769 771 775
Degree of aliasing      254
Degrees Kelvin      186
DeMoivre — Laplace theorem      180
Derivative kernel      263 265-267 312
Derivative theorem      16 19 68 76 108 142 150 181 357 420
DeSantis      75
DeSantis, D.      748
DeSantis, P.      504 507
Detection theory      203 211 732 733
Deterministic random variable      157 166 176
DFT      14 56-60 76 109 128 129 370 371 376 736 738 777;
Diagonal matrix      347
Diamond kernel      454-456 766
Diapason      671
Diapente      671
Diatesseron      671
Dice      168
Difference equation      62 63 694 754
Difference equations      8
Diffraction      7 677 680 682 709 738 739
Diffraction integral      677 680 682
Digital Signal Processing      56
Dilation      616-622 627 628 634 665 737
Dilation duality      621 633 634
Dilation subset property      622
Dillard, G.M.      748
Dimple      620
Diodes      112
Dirac delta      21 24 67 126 127 146 218 220 230 286 366 387 452 468 480 482 583 613 629
Dirac delta function      21 22 24 25 33 34 57-59 87 119 120 166 188
Dirac delta functions      68
Dirichlet conditions      215
Discrete cosine transform      60 373;
Discrete dime signals      77
Discrete Fourier Transform      10 56
Discrete Fourier transforms      14
Discrete signals      5
Discrete time Fourier transform      10 53 57 58 157
Discrete time Fourier transforms      14 54 55 150
Discrete time signal      11
Discrete time signals      7 10 11 30 53 64 77 127 138 185 234 436 438 439 446 531 608 624 625 627 640
Discrete time systems      137 142
Discrete uniform random variable      168
Discriminant      715
dispersion      151 176
Dissipated power      10
Distributive      647 665
Double diamond kernel      455 456
Double factorial      38 65 206 737
Double Mersenne primes      716
Doublet      230
Dougherty, Edward R.      666 751
DTFT      13 14 62 87 370 624 627 736;
DTS      736
Duality      24
1 2 3 4
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