Engineering Applications of Noncommutative Harmonic Analysis: With Emphasis on Rotation and Motion GroupsCRC Press, 2021 M02 25 - 674 páginas First published in 2001. The classical Fourier transform is one of the most widely used mathematical tools in engineering. However, few engineers know that extensions of harmonic analysis to functions on groups holds great potential for solving problems in robotics, image analysis, mechanics, and other areas. For those that may be aware of its potential value, there is still no place they can turn to for a clear presentation of the background they need to apply the concept to engineering problems. |
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... sample points are xj = jL / N , fj = f(x j)9 and dx is approximated as Ax = L /N . Or it can simply be viewed as the definition of the Fourier transform of a function whose arguments take values in a discrete set. As with the Fourier ...
... samples. Any attempt to do so leads to a phenomenon known as aliasing. One physical example of aliasing is when the wheels ... sample values of f*. In principle, all that is then required to calculate the 2B + 1 independent Fourier ...
... sample at a rate above the minimal rate to obtain a more robust estimate of a filtered signal. Sampling and Reconstruction of Functions on the Line Similar ideas apply for functions on the line. In this context a band-limited function ...
... sample at N> 2B +1 points, enough information exists to reconstruct the function from its samples. We denote the set of sampled values as S[f], with S[f]n denoting the single sample f(2nn/N). The convolution of two band-limited ...
... rules are both based on evenly spaced samples and are respectively In the case of Simpson's rule, n is assumed even. STURM-LIOUVILLE EXPANSIONS AND RELATED TRANSFORMS 49 3.5 Quadrature Rules and Discrete Polynomial Transforms.
Contenido
| 1 | |
| 15 | |
| 39 | |
4 Orthogonal Expansions in Curvilinear Coordinates | 81 |
5 Rotations in Three Dimensions | 111 |
6 RigidBody Motion | 149 |
7 Group Theory | 187 |
8 Harmonic Analysis on Groups | 239 |
15 Stochastic Processes Estimation and Control | 485 |
16 Rotational Brownian Motion and Diffusion | 515 |
17 Statistical Mechanics of Macromolecules | 545 |
18 Mechanics and Texture Analysis | 579 |
A Computational Complexity Matrices and Polynomials | 607 |
B Set Theory | 615 |
C Vector Spaces and Algebras | 623 |
D Matrices | 627 |
9 Representation Theory and Operational Calculus for SU2 and SO3 | 281 |
10 Harmonic Analysis on the Euclidean Motion Groups | 321 |
11 Fast Fourier Transforms for Motion Groups | 353 |
12 Robotics | 379 |
13 Image Analysis and Tomography | 419 |
14 Statistical Pose Determination and Cam era Calibration | 455 |
E Techniques from Mathematical Physics | 635 |
F Variational Calculus | 645 |
G Manifolds and Riemannian Metrics | 651 |
References | 655 |
Index | 659 |
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Engineering Applications of Noncommutative Harmonic Analysis: With Emphasis ... Gregory S. Chirikjian,Alexander B. Kyatkin Sin vista previa disponible - 2021 |