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| Авторизация |
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| Поиск по указателям |
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| D.E. Newland — An Introduction to Random Vibration, Spectral and Wavelet Analysis |
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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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