Tài liệu Fourier and Spectral Applications part 12 doc
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...
Tài liệu Fourier and Spectral Applications part 11 docx
... 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...
Tài liệu Fourier and Spectral Applications part 6 doc
... 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...
Tài liệu Fourier and Spectral Applications part 8 docx
... 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...
Tài liệu Fourier and Spectral Applications part 1 ppt
... 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...
Tài liệu Fourier and Spectral Applications part docx
... 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...
Tài liệu Fourier and Spectral Applications part 3 ppt
... 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...
Tài liệu Fourier and Spectral Applications part 4 pptx
... 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...
Tài liệu Fourier and Spectral Applications part 5 pptx
... 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...
Tài liệu Fourier and Spectral Applications part 7 pptx
... 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...