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Sundararajan D. — The discrete fourier transform: theory, algorithms and applications
Sundararajan D. — The discrete fourier transform: theory, algorithms and applications



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Название: The discrete fourier transform: theory, algorithms and applications

Автор: Sundararajan D.

Аннотация:

This book provides comprehensive coverage of practical Fourier analysis. It develops the concepts right from the basics and gradually guides the reader to the advanced topics. It presents the latest and practically efficient DFT algorithms, as well as the computation of discrete cosine and Walsh-Hadamard transforms. The large numbers of visual aids such as figures, flow graphs and flow charts makes the mathematical topic easy to understand. In addition, the numerous examples and the set of C-language programs (a supplement to the book) help greatly in understanding the theory and algorithms. Discrete Fourier analysis is covered first, followed by the continuous case, as the discrete case is easier to grasp and is very important in practice. This book should be useful as a text for regular or professional courses on Fourier analysis, and also as a supplementary text for courses on discrete signal processing, image processing, communications engineering and vibration analysis.


Язык: en

Рубрика: Математика/

Статус предметного указателя: Готов указатель с номерами страниц

ed2k: ed2k stats

Год издания: 2001

Количество страниц: 392

Добавлена в каталог: 23.10.2010

Операции: Положить на полку | Скопировать ссылку для форума | Скопировать ID
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Предметный указатель
Aliasing      197 226 254
Aliasing, folding frequency      227
Aliasing, folding of frequencies      229
Aliasing, highest frequency component      227
Aliasing, reducing the aliasing effect      231
Aliasing, sampling frequency      227
Aliasing, sampling rate      227
Aliasing, sampling theorem      227
Aliasing, time-domain      228
Antihermitian symmetry      71
Basis functions, DCT      304
Basis functions, DFT      40
Basis functions, DWT      314
Basis functions, NDHT      320
Basis functions, SDHT      326
Bit-reversal      343
Bit-reversal, algorithm      345
Bit-reversal, bit-reversed order      128 344
Bit-reversal, number system      343
Butterfly computation      123
Complete representation      58
Complex amplitude      22
Complex exponential function      22 46 199 337
complex numbers      333
Complex numbers, argument      335
Complex numbers, exponential form      335
Complex numbers, imaginary part      334
Complex numbers, imaginary unit      334
Complex numbers, magnitude      335
Complex numbers, operations, addition      334
Complex numbers, operations, conjugation      335
Complex numbers, operations, multiplication      335
Complex numbers, operations, subtraction      334
Complex numbers, polax form      335
Complex numbers, real part      334
Complex numbers, rectangular form      334
Complex numbers, roots      336
Complex plane      333
Computation of a single DFT coefficient      130
Computational complexity      341
Continuous-time signal      7
Convergence      251
Convolution 2—D, circular      296
Convolution 2—D, circular, spatial frequency-domain      209
Convolution 2—D, circular, spatial time-domain      208
Convolution 2—D, linear      295
Convolution 2—D, overlap-save method      296
Convolution, circular      289
Convolution, frequency-domain      84
Convolution, linear      288
Convolution, overlap-save method      292
Convolution, simulation by DFT      290
Convolution, time-domain      83
Correlation      298
Correlation, circular, auto      85 210
Correlation, circular, cross      85 209
Cosine function      8 12 47 200 337
DCT      (see Discrete cosine transform)
Decimation-in-frequency      114 132
Decimation-in-time      108 132
DFT      (see Discrete Fourier transform)
Digital signal      8
Dirichlet conditions      249
Discontinuity      251
Discrete cosine transform 2—D      309
Discrete cosine transform, basis functions      305
Discrete cosine transform, computation using the DFT      306
Discrete cosine transform, computational complexity      309
Discrete cosine transform, definition      305
Discrete cosine transform, orthogonality      304
Discrete Fourier transform 2—D, center-zero format      196
Discrete Fourier transform 2—D, complex exponential      199
Discrete Fourier transform 2—D, computation algorithms      212
Discrete Fourier transform 2—D, computation real data      217
Discrete Fourier transform 2—D, computation row-column method      202
Discrete Fourier transform 2—D, definition      195
Discrete Fourier transform 2—D, impulse      197
Discrete Fourier transform 2—D, properties      (see properties of the 2—D DFT)
Discrete Fourier transform 2—D, real sinusoid      199
Discrete Fourier transform, basis functions      40
Discrete Fourier transform, center-zero format      43
Discrete Fourier transform, complex exponential      46
Discrete Fourier transform, computation with vectors      101
Discrete Fourier transform, dc      45
Discrete Fourier transform, definition      37 38
Discrete Fourier transform, direct computation      51
Discrete Fourier transform, direct implementation      51
Discrete Fourier transform, frequency increment      40
Discrete Fourier transform, Hann function      49
Discrete Fourier transform, impulse      44
Discrete Fourier transform, kernel matrix      43
Discrete Fourier transform, properties      (see Properties of the DFT)
Discrete Fourier transform, real data, algorithm for complex data      163
Discrete Fourier transform, real data, single real data set      169
Discrete Fourier transform, real data, two real data sets      166
Discrete Fourier transform, real sinusoid      46
Discrete Fourier transform, rectangular waveform      49
Discrete Fourier transform, vector format      96 99 100
Discrete signal      7
Discrete Walsh transform      313
Discrete Walsh transform 2—D      318
Discrete Walsh transform, basis functions      314
Discrete Walsh transform, definition      313
Discrete Walsh transform, orthogonality      315
Discrete Walsh transform, PM DWT algorithm      316
Discrete Walsh transform, sequency      314
DWT      (see discrete Walsh transform)
Euler’s identity      337
Even function      15 71
Even half-wave symmetry      71
Finality of coefficients      57
Fourier analysis      32
Fourier Series, 1—D      249
Fourier Series, 1—D, aliasing effect      254
Fourier Series, 1—D, approximatation by DFT      253
Fourier Series, 1—D, continuous-time frequency      257 260
Fourier Series, 1—D, convergence      251
Fourier Series, 1—D, Dirichlet conditions      249
Fourier Series, 1—D, exponential form      250
Fourier Series, 1—D, Gibbs phenomenon      251 261
Fourier Series, 1—D, sample value at a discontinuity      257
Fourier Series, 1—D, trigonometric form      250
Fourier Series, 1—D, waveform reconstruction      259
Fourier Series, 2—D      262
Fourier synthesis      32 35
Fourier transform 2—D      282
Fourier transform, 1—D      273
Fourier transform, 1—D, approximation by DFT      277
Fourier transform, 1—D, complex exponential      276
Fourier transform, 1—D, dc signal      276
Fourier transform, 1—D, definition      276
Fourier transform, 1—D, impulse      276
Fourier transform, 1—D, limiting case of the FS      273
Fourier transform, 1—D, pulse      275 277
Fourier transform, 1—D, real sinusoid      276
Fourier transform, 1—D, relation between FS and FT      275 277
Fourier transform, 1—D, signal reconstruction      281
Frequency composition, 1—D real signals      37
Frequency composition, 2—D real signals      196
Frequency-domain      10
Gibbs phenomenon      251 261
Hamming window      240
Hann window      239
Hermitian symmetry      71
IDFT      (see Inverse discrete Fourier transform)
Impulse      9
Inverse discrete Fourier transform, center-zero format      196
Inverse discrete Fourier transform, computation using DFT      104 111
Inverse discrete Fourier transform, definition      195
Inverse discrete Fourier transform, direct computation      51
Inverse discrete Fourier transform, vector format      104
Inverse discrete Walsh transform, definition      316
Inverse naturally ordered discrete, Hadamaxd transform      322
Inverse sequency ordered discrete, Hadamaxd transform      326
Leakage effect      231
Leakage effect, frequency response, DFT      235
Leakage effect, frequency response, rectangular and Hann windows      240
Leakage effect, Multiplication of the signal with a rectangular window      233
Leakage effect, reduction of leakage      244
Leakage effect, spectral resolution      241
Leakage effect, windows      (see Windows)
Least squares error      55—57 257
L’Hopital’s Rule      263 356
Naturally ordered discrete Hadamard, basis functions      320
Naturally ordered discrete Hadamard, definition      320
Naturally ordered discrete Hadamard, kernel generation      321
Naturally ordered discrete Hadamard, PM NDHT algorithm      322
Naturally ordered discrete Hadamard, transform      320
Naturally ordered discrete Hadamard, transform 2—D      323
NDHT      (see Naturally ordered discrete)
Odd function      15 71
Odd half-wave symmetry      71
Orthogonality      24 26
Orthogonality, complex exponential      26
Orthogonality, cosines over half-cycles      304
Orthogonality, trigonometric functions      24
Orthogonality, Walsh function      315
Overlap-save method      292 296
Parseval’s theorem      90 212
periodicity      62
Phase shift      11 12
Picket-fence effect      244
Picket-fence effect, denser spectrum      245
PM DFT Algorithms, classification      114
PM DIF DFT algorithms, $2\times1$ PM DIF DFT algorithm      134
PM DIF DFT algorithms, $2\times1$ PM DIF DFT algorithm, butterfly      134
PM DIF DFT Algorithms, $2\times1$ PM DIF DFT algorithm, compression of data vectors      113
PM DIF DFT algorithms, $2\times1$ PM DIF DFT algorithm, computational stages      135
PM DIF DFT Algorithms, $2\times1$ PM DIF DFT algorithm, shift of transform vectors      112
PM DIF DFT algorithms, $2\times2$ PM DIF DFT algorithm      154
PM DIF DFT algorithms, $2\times2$ PM DIF DFT algorithm, butterfly      157
PM DIF DFT algorithms, $2\times2$ PM DIF DFT algorithm, computational stages      157
PM DIF DFT algorithms, $u\times1$ PM DIF DFT algorithms      132
PM DIF DFT algorithms, $u\times1$ PM DIF DFT algorithms, butterfly      133
PM DIF DFT algorithms, $u\times1$ PM DIF DFT algorithms, computational stages      134
PM DIF DFT Algorithms, fundamentals      112
PM DIF RIDFT algorithms, $2\times1$ PM DIF RIDFT algorithms      180
PM DIF RIDFT algorithms, $2\times1$ PM DIF RIDFT algorithms, butterfly      183
PM DIF RIDFT algorithms, $2\times1$ PM DIF RIDFT algorithms, computational stages      184
PM DIF RIDFT algorithms, $2\times1$ PM DIF RIDFT algorithms, special butterflies      184
PM DIF RIDFT algorithms, $2\times2$ PM DIF RIDFT algorithms      190
PM DIF RIDFT algorithms, $2\times2$ PM DIF RIDFT algorithms, butterfly      190
PM DIF RIDFT algorithms, $2\times2$ PM DIF RIDFT algorithms, computational stages      191
PM DIF RIDFT algorithms, $2\times2$ PM DIF RIDFT algorithms, special butterflies      192
PM DIF RIDFT algorithms, storage of data      176
PM DIT DFT algorithms, $2\times1$ PM DIT DFT algorithm      125
PM DIT DFT algorithms, $2\times1$ PM DIT DFT algorithm, butterfly      125
PM DIT DFT algorithms, $2\times1$ PM DIT DFT algorithm, computation of a single DFT coefficient      130
PM DIT DFT algorithms, $2\times1$ PM DIT DFT algorithm, computational complexity      135
PM DIT DFT algorithms, $2\times1$ PM DIT DFT algorithm, computational stages      126
PM DIT DFT algorithms, $2\times1$ PM DIT DFT algorithm, flow chart description      141
PM DIT DFT algorithms, $2\times1$ PM DIT DFT algorithm, implementation issues      148
PM DIT DFT algorithms, $2\times1$ PM DIT DFT algorithm, reordering of the input data      128
PM DIT DFT algorithms, $2\times2$ PM DIT DFT algorithm      151
PM DIT DFT algorithms, $2\times2$ PM DIT DFT algorithm, butterfly      153
PM DIT DFT algorithms, $2\times2$ PM DIT DFT algorithm, computational complexity      158
PM DIT DFT algorithms, $2\times2$ PM DIT DFT algorithm, computational stages      154 6
PM DIT DFT algorithms, $6\times1$ PM DIT DFT algorithm      138
PM DIT DFT algorithms, $6\times1$ PM DIT DFT algorithm, butterfly      139
PM DIT DFT algorithms, $6\times1$ PM DIT DFT algorithm, computational complexity      140
PM DIT DFT algorithms, $6\times1$ PM DIT DFT algorithm, computational stages      140
PM DIT DFT algorithms, $u\times1$ PM DIT DFT algorithm      122
PM DIT DFT algorithms, $u\times1$ PM DIT DFT algorithm, butterfly      123
PM DIT DFT algorithms, $u\times1$ PM DIT DFT algorithm, computational stages      124
PM DIT DFT Algorithms, fundamentals      106
PM DIT DFT Algorithms, shift of data vectors      106
PM DIT DFT Algorithms, zero padding of data vectors      107
PM DIT RDFT algorithms, $2\times1$ PM DIT RDFT algorithms      176
PM DIT RDFT algorithms, $2\times1$ PM DIT RDFT algorithms, butterfly      177
PM DIT RDFT algorithms, $2\times1$ PM DIT RDFT algorithms, computational stages      178
PM DIT RDFT algorithms, $2\times1$ PM DIT RDFT algorithms, special butterflies      178
PM DIT RDFT algorithms, $2\times2$ PM DIT RDFT algorithms      187
PM DIT RDFT algorithms, $2\times2$ PM DIT RDFT algorithms, butterfly      187
PM DIT RDFT algorithms, $2\times2$ PM DIT RDFT algorithms, computational stages      187
PM DIT RDFT algorithms, $2\times2$ PM DIT RDFT algorithms, special butterflies      189
PM DIT RDFT algorithms, comparison with DFT algorithms      193
PM DIT RDFT algorithms, storage of data      175
Prime-factor DFT algorithm      139 347
Properties of the 2—D DFT, complex conjugates      208
Properties of the 2—D DFT, convolution      (see Convolution)
Properties of the 2—D DFT, correlation      (see Correlation)
Properties of the 2—D DFT, difference      210
Properties of the 2—D DFT, image rotation      210
Properties of the 2—D DFT, linearity      205
Properties of the 2—D DFT, Parseval’s theorem      212
Properties of the 2—D DFT, periodicity      205
Properties of the 2—D DFT, reversal property      207
Properties of the 2—D DFT, separable signals      211
Properties of the 2—D DFT, spatial circular shift of a spectrum      206
Properties of the 2—D DFT, spatial circular shift of an image      206
Properties of the 2—D DFT, sum and difference of sequences      210
Properties of the 2—D DFT, symmetry      207
Properties of the DFT, circular shift of a spectrum      66
Properties of the DFT, circular shift of a time sequence      62
Properties of the DFT, complex conjugates      81
Properties of the DFT, DFT of overlapping segments      66
Properties of the DFT, DFT twice in succession      70
Properties of the DFT, duality      71
Properties of the DFT, linearity      61
Properties of the DFT, padding the data with zeros      86
Properties of the DFT, padding the data with zeros at the end      86
Properties of the DFT, padding the data with zeros in between the samples      89
Properties of the DFT, Parseval’s theorem      90
Properties of the DFT, periodicity      62
Properties of the DFT, signal defined over a finite range      80
Properties of the DFT, sum and difference of sequences      85
Properties of the DFT, symmetry, complex signal      78
Properties of the DFT, symmetry, complex signal, even      78
Properties of the DFT, symmetry, complex signal, even half-wave      80
Properties of the DFT, symmetry, complex signal, odd      80
Properties of the DFT, symmetry, complex signal, odd half-wave      80
Properties of the DFT, symmetry, imaginary signal      75
Properties of the DFT, symmetry, imaginary signal, even      76
Properties of the DFT, symmetry, imaginary signal, even half-wave      76
Properties of the DFT, symmetry, imaginary signal, odd      76
Properties of the DFT, symmetry, imaginary signal, odd half-wave      78
Properties of the DFT, symmetry, symmetry, real signal      72
Properties of the DFT, symmetry, symmetry, real signal, even      74
Properties of the DFT, symmetry, symmetry, real signal, even half-wave      75
Properties of the DFT, symmetry, symmetry, real signal, odd      74
Properties of the DFT, symmetry, symmetry, real signal, odd half-wave      75
Properties of the DFT, symmetry, time-reversal      69
Rectangular window      236
Roots of unity      40 336
Rotating vector      339
Row-column method      202 309
Sampling frequency      227
Sampling rate      227
Sampling theorem      227
SDHT      (see Sequency ordered discrete Hadamaxd transform)
Sequency      314
Sequency ordered discrete Hadamard, basis functions      326
Sequency ordered discrete Hadamard, definition      325
Sequency ordered discrete Hadamard, PM SDHT algorithm      327
Sequency ordered discrete Hadamard, transform      325
Sequency ordered discrete Hadamard, transform 2—D      328
Signal representation, frequency-domain      10 11
Signal representation, time-domain      7 10 11
Signal, continuous-time      7
Signal, digital      8
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