Tài liệu Fourier and Spectral Applications part 12 doc

... 606 Chapter 13. Fourier and Spectral Applications Sample page from NUMERICAL RECIPES IN C: THE ART OF SCIENTIFIC COMPUTING ... values of N. For example, |e(t)| < 5 × 10 −5 for h =1/ 2and N =7;|e(t)|<2×10 −10 for h =1/ 3and N =15; and |e(t)| < 7 × 10 −18 for h =1/ 4and N =25. One may ask, what is the point of such a numerical ... 614–627. Beylkin, G., Coifman, R., and R...

Ngày tải lên: 26/01/2014, 14:20

... Analogously with the Fourier domain, where a class of computations, like convolutions, become computationally fast, there is a large class of computations 592 Chapter 13. Fourier and Spectral Applications Sample ... a small number of Fourier components, guaranteeing that there will be only a small number of nonzero c j ’s. On the other hand, there is sometimes no particular reason...

Ngày tải lên: 26/01/2014, 14:20

... write the function as a rational function in z, and compare with equation (13.5.2) to read off the c’s and d’s. 562 Chapter 13. Fourier and Spectral Applications Sample page from NUMERICAL RECIPES ... [3] Champeney, D.C. 1973, Fourier Transforms and Their Physical Applications (New York: Aca- demic Press). Elliott, D.F., and Rao, K.R. 1982, Fast Transforms: Algorithms, Ana...

Ngày tải lên: 26/01/2014, 14:20

... 572 Chapter 13. Fourier and Spectral Applications Sample page from NUMERICAL RECIPES IN C: THE ART OF SCIENTIFIC COMPUTING ... nature of the filter and theparticular inputthatis driving it. We are skeptical of these applications; the literature, however, is full of extravagant claims. CITED REFERENCES AND FURTHER READING: Childers, ... |H(f)| 2 . Now let us think about what the s...

Ngày tải lên: 26/01/2014, 15:20

... trade@cup.cam.ac.uk (outside North America). Chapter 13. Fourier and Spectral Applications 13.0 Introduction Fourier methods have revolutionized fields of science and engineering, from radio astronomy to medical ... 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 num...

Ngày tải lên: 21/01/2014, 18:20

... responsefunction fornegative times is wrapped around and stored at the extreme right end of the array r k . 540 Chapter 13. Fourier and Spectral Applications Sample page from NUMERICAL RECIPES IN ... disturb the true convolution; and while the original function wraps around onto the zero region, that region can be discarded. 542 Chapter 13. Fourier and Spectral Applications...

Ngày tải lên: 26/01/2014, 14:20

... h is one member of the discrete Fourier transform pair Corr(g, h) j ⇐⇒ G k H k *(13.2.3) where G k and H k are the discrete Fourier transforms of g j and h j , and the asterisk denotes complex ... superposed, and with one of them shifted left or right. We have already defined in equation (12. 0.10) the correlation between two continuous functions g(t) and h(t), which is denoted C...

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... what we mean by noise!) Obviously (13.3.5) will be a minimum if and only if the integrand 548 Chapter 13. Fourier and Spectral Applications Sample page from NUMERICAL RECIPES IN C: THE ART OF ... obtain. For example, we can sample a long stretch of data c(t) and plot its power spectral density using equations (12. 0.14), (12. 1.8), and (12. 1.5). This quantity is proportional...

Ngày tải lên: 26/01/2014, 14:20

... FFT Intheprevioussectionwe“informally”estimated thepowerspectral densityofa functionc(t) bytaking themodulus-squaredof the discrete Fouriertransformof some 550 Chapter 13. Fourier and Spectral Applications Sample page from ... ,  N 2 −1  P(f c )=P(f N/2 )= 1 W ss   D N/2   2 (13.4.10) where W ss stands for “window squared and summed,” W ss ≡ N N−1  j=0 w 2 j (13.4.11) 554 Cha...

Ngày tải lên: 26/01/2014, 14:20

... equally spaced data points, and in the Fourier domain, autocorrelations become simply squares of Fourier amplitudes (Wiener- Khinchin theorem, equation 12. 0 .12) , and the optimal filter can be ... set of x i ’s. It assumes that (13.6 .12) has correctly identified the spectral width of a resonance, but only slipped up on 568 Chapter 13. Fourier and Spectral Applications Sam...

Ngày tải lên: 26/01/2014, 14:20