Có 120+ tài liệu thuộc chủ đề "tư liệu lập trình"
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13.0 Introduction. In this chapter, we present some of the basic applications of Fourier and spectral methods that have made these revolutions possible.. Say the word “Fourier” to a numericist, and the response, as if by Pavlovian conditioning, will likely be “FFT.” Indeed, the wide application of Fourier methods must be credited principally to the existence of the fast Fourier...
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Sample page from NUMERICAL RECIPES IN C: THE ART OF SCIENTIFIC COMPUTING (ISBN Copyright (C by Cambridge University Press.Programs Copyright (C by Numerical Recipes Software. We have defined the convolution of two functions for the continuous case in equation (12.0.8), and have given the convolution theorem as equation (12.0.9). The theorem says that the Fourier transform of the convolution of...
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1928, Proceedings of the Royal Society of Edinburgh , vol. 13.10 Wavelet Transforms. Like the fast Fourier transform (FFT), the discrete wavelet transform (DWT) is a fast, linear operation that operates on a data vector whose length is an integer power of two, transforming it into a numerically different vector of the same length. Also like the FFT, the wavelet...
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The number of nonnegligible elements in a matrix like that in Figure 13.10.5 scales only as N , the linear size of the matrix. where is the truncation level, e.g., 10 − 6 . Beylkin, G., Coifman, R., and Rokhlin, V. 1990, Proceedings of the IEEE , vol. Freedman, M.H., and Press, W.H. 13.11 Numerical Use of the Sampling Theorem....
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13.2 Correlation and Autocorrelation Using the FFT 545. Sample page from NUMERICAL RECIPES IN C: THE ART OF SCIENTIFIC COMPUTING (ISBN Copyright (C by Cambridge University Press.Programs Copyright (C by Numerical Recipes Software. 13.2 Correlation and Autocorrelation Using the FFT. The correlation will be large at some value of t if the first function (g) is a close copy of...
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13.3 Optimal (Wiener) Filtering with the FFT 547. 13.3 Optimal (Wiener) Filtering with the FFT. Our task is to find the optimal filter, φ(t) or Φ(f. Substituting equations (13.3.3) and (13.3.2), the right-hand side of (13.3.4) becomes Z. (This is practically the definition of what we mean by noise!) Obviously (13.3.5) will be a minimum if and only if the...
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Sample page from NUMERICAL RECIPES IN C: THE ART OF SCIENTIFIC COMPUTING (ISBN Copyright (C by Cambridge University Press.Programs Copyright (C by Numerical Recipes Software. The tail is extrapolated back into the signal region as a “noise model.” Subtracting gives the “signal model.” The models need not be accurate for the method to be useful. A simple algebraic combination of...
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Sample page from NUMERICAL RECIPES IN C: THE ART OF SCIENTIFIC COMPUTING (ISBN Copyright (C by Cambridge University Press.Programs Copyright (C by Numerical Recipes Software. Oppenheim, A.V., and Schafer, R.W. 1978, Proceedings of the IEEE , vol. Elliott, D.F., and Rao, K.R. Rabiner, L.R., and Gold, B. 13.5 Digital Filtering in the Time Domain. This section speaks particularly about the...
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13.6 Linear Prediction and Linear Predictive Coding. (compare equation 13.3.2, with a somewhat different notation). Our use of a Greek subscript to index the members of the set is meant to indicate that the data points are not necessarily equally spaced along a line, or even ordered: they might be. Now, suppose we want to construct the “best” estimate of...
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Sample page from NUMERICAL RECIPES IN C: THE ART OF SCIENTIFIC COMPUTING (ISBN Copyright (C by Cambridge University Press.Programs Copyright (C by Numerical Recipes Software. If the spectral character of the data is time-variable, then it is best not to use a single set of LP coefficients for the whole data set, but rather to partition the data into segments,...
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Here is a function which, given the coefficients already computed, evaluates (13.7.4) and returns the estimated power spectrum as a function of f∆ (the frequency times the sampling interval). Of course, f∆ should lie in the Nyquist range between − 1/2 and 1/2.. Loop over the terms in the sum.. Equation (13.7.4).. Be sure to evaluate P (f ) on...
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Sample page from NUMERICAL RECIPES IN C: THE ART OF SCIENTIFIC COMPUTING (ISBN Copyright (C by Cambridge University Press.Programs Copyright (C by Numerical Recipes Software. 1963, Bulletin of the Astronomical Institutes of the Netherlands , vol. Horne, J.H., and Baliunas, S.L. 13.9 Computing Fourier Integrals Using the FFT. Not uncommonly, one wants to calculate accurate numerical values for integrals of...
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14.0 Introduction. Section 14.1 deals with so-called measures of central tendency, the moments of a distribution, the median and mode. In § 14.2 we learn to test whether different data sets are drawn from distributions with different values of these measures of central tendency. This leads naturally, in § 14.3, to the more general question of whether two distributions can...
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Section 14.1 deals with so-called measures of central tendency, the moments of a distribution, the median and mode. In § 14.2 we learn to test whether different data sets are drawn from distributions with different values of these measures of central tendency. This leads naturally, in § 14.3, to the more general question of whether two distributions can be shown...
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Sample page from NUMERICAL RECIPES IN C: THE ART OF SCIENTIFIC COMPUTING (ISBN Copyright (C by Cambridge University Press.Programs Copyright (C by Numerical Recipes Software. that this is wasteful, since it yields much more information than just the median (e.g., the upper and lower quartile points, the deciles, etc. 8.5 that the element x (N+1)/2 can be located in of...
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Sample page from NUMERICAL RECIPES IN C: THE ART OF SCIENTIFIC COMPUTING (ISBN Copyright (C by Cambridge University Press.Programs Copyright (C by Numerical Recipes Software. 14.3 Are Two Distributions Different?. Given two sets of data, we can generalize the questions asked in the previous section and ask the single question: Are the two sets drawn from the same distribution function,...
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Sample page from NUMERICAL RECIPES IN C: THE ART OF SCIENTIFIC COMPUTING (ISBN Copyright (C by Cambridge University Press.Programs Copyright (C by Numerical Recipes Software. 1970, Journal of the Royal Statistical Society , ser. Anderson, T.W., and Darling, D.A. 1962, Proceedings of the Koninklijke Nederlandse Akademie van Wetenschappen , ser. Fisher, N.I., Lewis, T., and Embleton, B.J.J. 14.4 Contingency Table...
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Sample page from NUMERICAL RECIPES IN C: THE ART OF SCIENTIFIC COMPUTING (ISBN Copyright (C by Cambridge University Press.Programs Copyright (C by Numerical Recipes Software. 14.5 Linear Correlation. where, as usual, x is the mean of the x i ’s, y is the mean of the y i ’s.. The value of r lies between − 1 and 1, inclusive....
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Sample page from NUMERICAL RECIPES IN C: THE ART OF SCIENTIFIC COMPUTING (ISBN Copyright (C by Cambridge University Press.Programs Copyright (C by Numerical Recipes Software. Equation (14.5.5).. For large n, this easier computation of prob, using the short routine erfcc, would give approx- imately the same value.. Dunn, O.J., and Clark, V.A. Korn, G.A., and Korn, T.M. 14.6 Nonparametric or...
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Sample page from NUMERICAL RECIPES IN C: THE ART OF SCIENTIFIC COMPUTING (ISBN Copyright (C by Cambridge University Press.Programs Copyright (C by Numerical Recipes Software. Downie, N.M., and Heath, R.W. 14.7 Do Two-Dimensional Distributions Differ?. We here discuss a useful generalization of the K–S test. 14.3) to two-dimensional distributions. In a two-dimensional distribution, each data point is characterized by an...