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D.E. Newland — An Introduction to Random Vibration, Spectral and Wavelet Analysis
D.E. Newland — An Introduction to Random Vibration, Spectral and Wavelet Analysis

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Название: An Introduction to Random Vibration, Spectral and Wavelet Analysis

Автор: D.E. Newland

Аннотация:

One of the first engineering books to cover wavelet analysis, this classic text describes and illustrates basic theory, with a detailed explanation of discrete wavelet transforms. It examines joint probability distributions, ensemble averages, and correlation, Fourier analysis, spectral density and excitation response relations for linear systems, more. 1993 edition.


Язык: en

Рубрика: Физика/

Статус предметного указателя: Готов указатель с номерами страниц

ed2k: ed2k stats

Год издания: 1993

Количество страниц: 503

Добавлена в каталог: 05.05.2013

Операции: Положить на полку | Скопировать ссылку для форума | Скопировать ID
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Предметный указатель
Accuracy of measurements      95
Accuracy of spectral analysis, example calculation      102
Accuracy of spectral estimates      138
Addition of zeros to sample record      139
Alias spectra      120
Aliased spectral window      251 427
Aliasing      118
Aliasing distortion      120
Analogue, digital conversion      149
Analogue, digital conversion, error analysis      149
Analogue, spectrum analysis      95
Analogue, spectrum analyzer      95
Analysing wavelet      298
Aperiodic functions, Fourier transform of a train of      129
Artificial generation of isotropic surface      258 263
Artificial generation random process      167
Artificial generation two-dimensional random process      256
Autocorrelation      25
Autocorrelation function for a pseudo random binary signal      173
Autocorrelation function for a random binary process      168
Autocorrelation function for white noise      46
Autocorrelation function, definition of      25
Autocorrelation function, properties of      26 27
Autocorrelation function, spatial      198
Autocorrelation input-output relation for a linear system      69
Average frequency of crossings      86
Average value of a function of random variables      14
Averages, second order      14
Averaging spectral estimates      138
Averaging time of a spectrum analyzer      95
Bandwidth of analogue spectrum analyzer      96
Bandwidth of spectral window      108
Bandwidth, half-power      191
Bandwidth, mean square      191
Beam, response to random excitation      281 285
Bias error of spectral measurement      103
Binary random process      168
Binary sequence, full length      433
Bingham window      146
Binomial probability distribution      175
Broad band random process      44
Calculation of averages      7
Calculation of spectral estimates from discrete data      120
Central limit theorem      80
Chain code      183
Chi-square, probability density function      417
Chi-square, probability distribution, application to spectral analysis      138
Chi-square, probability distribution, dependence on degrees-of-freedom      110
Chi-square, random variable      109
Chi-square, random variable, distribution of      110 417
Chi-square, tabulated values of distribution      381
Circular correlation function      122
Circular correlation function, interpretation in terms of linear correlation function estimate      129
Circular correlation function, relationship with linear correlation function      128 129
Circular correlation function, two-dimensional      241 243 261
Circular wavelet transforms      322
Clock frequency of random binary process      170
Coherence functions      207
Coherence functions, digital calculation of      210
Coherence functions, multiple      207 209
Coherence functions, ordinary      209
Coherence functions, partial      438
Complex frequency, response function      56
Complex frequency, response function, measurement of      206
Computer programs, FFT in Basic      374
Computer programs, FFT in Fortran      373
Computer programs, Two-dimensional DFT      376
Computer programs, wavelet      387
Conditional probability      17
Confidence limits of spectral measurements      108
Confidence limits, sample calculation      112
Continuous time series      113
Convolution      64 412
Convolution by wavelets      353
Convolution, integral      64
Correction for slow trend in spectral analysis      147
Correlated random noise, synthesis of      185
Correlation      21
Correlation calculation from data extended by additional zeros      139
Correlation coefficient      23 241
Correlation function      see also "Autocorrelation" "Cross-correlation" "Circular
Correlation, circular      122
Correlation, consistent estimate for      127
Correlation, error due to "wrap around"      125
Correlation, sample average      126
Correlation, separation of overlapping parts by added zeros      142
Cosine data taper function      147
Covariance      23
Cross-correlation      29
Cross-correlation function, definition of      29
Cross-correlation function, properties of      30
Cross-correlation input-output relation for a linear system      77
Cross-spectral density between parallel tracks on a random surface      263
Cross-spectral density from multi-dimensional spectral density      279
Cross-spectral density from two-dimensional spectral density      237
Cross-spectral density, definition of      48
Cross-spectral density, input-output relations for a linear system      79 414
Cross-spectral density, properties of      49
Crossing analysis      85
Data, taper function      147
Data, window      147
Data, window, cosine taper      146 425
Degrees-of-freedom, for chi-square distribution      110
Delta function, units of      46
Derived process      46
Derived process, spectral density of      46
Digital filtering      182
Digital simulation of random processes      186
Digital spectral analysis      113
Digital spectral analysis, correction for slow trend      147
Digital spectral analysis, data weighting      146
Digital spectral analysis, data weighting, advantage of      148
Digital spectral analysis, example showing choice of parameters      145
Digital spectral analysis, practical considerations      146
Digital spectral analysis, quantization error      148
Digital spectral analysis, summary of method      142
Digital spectral analysis, windows and smoothing      125
Dilation equations      300
Dilation wavelets      303
Dirac's delta function      46
Direct method of spectral analysis      135
Discrete Fourier Transform      114
Discrete Fourier transform, definition      116
Discrete Fourier transform, Parseval's theorem for, one-dimensional      420
Discrete Fourier transform, Parseval's theorem for, two-dimensional      233
Discrete Fourier transform, properties of      118
Discrete Fourier transform, properties of two-dimensional      229
Discrete Fourier transform, two-dimensional      226
Discrete harmonic wavelet transform      364 398
Discrete spectral density      122
Discrete spectral density, two-dimensional      239 262
Discrete time series      113
Discrete wavelet analysis      295
Discrete wavelet transform      326
Discrete wavelet transform, properties of      339
Distribution of peaks      90
Distribution of reverse arrangements for a random series, table of values      385
Double-sided function of frequency      52 199
Duality theorem of Fourier analysis      407
DWT      326 see
Dynamic characteristics, measurement of      167 206
Effective bandwidth of spectral window      108 141
Ensemble averaging      19
Ensemble averaging, concept for a linear system subjected to random excitation      67
Envelope distribution for a narrow band random process      417
Environmental vibration simulation      201
Environmental vibration simulation, number of separate inputs required      205
Ergodic random process      20 211
Ergodicity, discussion of      211
Excitation by random surface irregularities      196
Excitation-response relations      53
Extending record length by adding zeros      139
Extending record length by adding zeros to separate overlapping parts of linear correlation function      142
Failure due to random vibration      191
Failure due to random vibration, mechanisms of      192 193
Fast Fourier Transform      114 150
Fast Fourier transform, algorithm      155
Fast Fourier transform, alternative algorithms      165
Fast Fourier transform, basic theory      150
Fast Fourier transform, bit-reversed counter      162
Fast Fourier transform, butterfly calculation      152
Fast Fourier transform, computer program      373
Fast Fourier transform, decimation in frequency algorithm      166 431
Fast Fourier transform, decimation in time algorithm      166
Fast Fourier transform, flow chart for bit-reversed counter      163
Fast Fourier transform, flow chart for re-ordering data sequence      164
Fast Fourier transform, practical value      162
Fast Fourier transform, programming flow chart      155 156 159
Fast Fourier transform, sample calculation      152
Fast Fourier transform, signal flow graphs      155 157
Fast Fourier transform, twiddle factor      155
Fatigue failure, fractional damage      192
Fatigue failure, Palmgren — Miner hypothesis      192
Fatigue failure, prediction of mean lifetime      193
Fatigue law of a material      192
FFT      150 see
FFT computer program      373
Finite length records, analysis of      103
First crossing problem      194
First crossing problem, mean time to failure      196
First crossing problem, standard deviation of time to failure      196
First passage probability density      196
Folding frequency      120
Fourier analysis      33
Fourier analysis, duality theorem      407
Fourier integral and Fourier series, relationship between      36
Fourier series      33
Fourier series, calculation of coefficients      34
Fourier series, graphical representation of coefficients      34
Fourier series, multi-dimensional      226
Fourier series, two-dimensional      225
Fourier transform      35
Fourier transform of a train of aperiodic functions      129
Fourier transform of periodic function      116
Fourier transform, complex form of      38
Fourier transform, fast      150
Fourier transform, pair      39
Fourier transform, short-time      218
Fourth-order average for a Gaussian process      98
Frequency of crossings      86
Frequency of crossings for a Gaussian process      88
Frequency of maxima      92
Frequency of maxima, comparison with frequency of zero crossings      93
Frequency of zero crossings      89
Frequency of zero crossings, comparison with frequency of maxima      93
Frequency, negative      39
Frequency, response function      55
Frequency, response function, measurement of      206
Frequency, response function, relation to impulse response function      60
Frequency, response method      55
Full-length binary sequence      433
Gamma function, definition of      417
Gaussian distribution, tabulated values      379
Gaussian probability distribution      7
Gaussian probability distribution, second-order      18
Gaussian probability integral, table of      379
Gaussian random process      20
Generalized function      46 408
Generation of random numbers      183
Haar wavelet      321 322 450
Half-power bandwidth      191
Harmonic wavelet      359 398
Harmonic wavelet transform, FFT algorithm for      367
Impulse response, function      58
Impulse response, method      58
Inverse discrete Fourier transform      116
Inverse Fourier transform      35
Isotropic random process      239 258
Joint probability      12
Joint probability, density function      12
Lag window      131
Lag window, basic form of, for digital spectral analysis      136
Lag window, relationship with spectral window      136
Line of regression      22
Linear superposition, principle of      53
Linear system, equations of      53
Linear system, excitation-response relations      53
Linear system, principle of superposition      53
Linear system, response to an arbitrary input      62
Linear system, transmission of random vibration      67
Locally stationary process      217
Mallat's algorithm, tree (pyramid)      326 389
Matlab information      477
Mean level, input-output relation for a linear system      68
Mean square bandwidth      191
Mean square response, approximate calculation of      189
Mean square response, exact calculation of      73 371
Mean square response, input-output relation for a linear system      73
Mean square response, list of integrals      371
Mean square spectral density      42
Mean square wavelet maps      348 393 399
Measurement accuracy      95
Modal mean square bandwidth      191
MODULO      187
Multiple coherence function      207 209
Narrow band random process      44
Narrow band random process, crossing analysis      85
Narrow band random process, description of      82
Narrow band random process, distribution of peaks      90
Narrow band random process, envelope distribution      417
Narrow band random process, frequency of maxima      92
Narrow band random process, peak distribution      90
Narrow band random process, statistics of      82
Negative frequency      39
Non-stationary random process      211
Non-stationary random process, analysis of locally stationary process      217
Non-stationary random process, short-sample average      212
Non-stationary random process, spectral density of      214
Non-stationary random process, testing for      212
Non-stationary trend, testing for      212
Normal mode analysis      280
Normalized covariance      23
Nyquist frequency      120
Ordinary coherence function      209
P.r.b.s.      172 see
Parseval's theorem      233 407 420 442
Parseval's theorem for a two-dimensional series      233
Partial coherence function      438
Pascal's triangle      177
Peak distribution, Rayleigh      91
Peak distribution, Weibull      219
Periodic function, Fourier transform of      116
Periodogram      429
Plate, response to random excitation      283 290 292
Pre-whitening before spectral analysis      148
Principle of linear superposition      53
Probability analyzer      6
Probability density function, calculation of first-order from second-order      13
Probability density function, chi-square      417
Probability density function, conditional      17
Probability density function, first-order      2 4
Probability density function, Gaussian (normal)      7 18
Probability density function, second-order      12 17
Probability distribution, binomial      175
Probability distribution, chi-square      110 381 417
Probability distribution, function      10
Probability distribution, Gaussian (normal)      7 18 379
Probability integral, tabulated values of Gaussian      379
Probability of a first crossing in time T      195
Pseudo random binary sequence      172 183 433
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