By John R. Pierce
Книга just about all approximately Waves just about all approximately WavesКниги Физика Автор: John R. Pierce Год издания: 2006 Формат: djvu Издат.:Dover courses Страниц: 224 Размер: 1,1 ISBN: 0486453022 Язык: Английский0 (голосов: zero) Оценка:This textual content considers waves the nice unifying suggestion of physics. With minimum arithmetic, it emphasizes the habit universal to phenomena akin to earthquake waves, ocean waves, sound waves, and mechanical waves. themes comprise speed, vector and complicated illustration, strength and momentum, coupled modes, polarization, diffraction, and radiation. 1974 variation.
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Extra resources for Almost All About Waves
79) j =1 where aij , j = 1 : : : m, are constant mixing coefficients and sj , j = 1 : : : m, are the m unknown source signals. Even for a fairly small number of sources (say, m = 10) the distribution of the mixture xk is usually close to gaussian. This seems to hold in practice even though the densities of the different sources are far from each other and far from gaussianity. Examples of this property can be found in Chapter 8, as well as in . 81) for which the inverse mapping y) of y is obtained from the exists and is unique.
9. Both the uniform and Laplacian density can be obtained as special cases of the generalized gaussian or exponential power family of pdf’s [53, 256]. 97) The positive real-valued power determines the type of distribution, and C is a scaling constant which normalizes the distribution to unit area (see ). ) If the parameter = 2, the usual gaussian density is obtained. The choice = 1 yields the Laplacian the uniform density. 97) density, and give rise to supergaussian densities, and > 2 to subgaussian ones.
Thus, the principle can be stated as follows P =P ICA estimation principle 2: Maximum nongaussianity. Find the local maxima of nongaussianity of a linear combination y b x under the constraint i i i that the variance of y is constant. Each local maximum gives one independent component. To measure nongaussianity in practice, we could use, for example, the kurtosis. Kurtosis is a higher-order cumulant, which are some kind of generalizations of variance using higher-order polynomials. Cumulants have interesting algebraic and statistical properties which is why they have an important part in the theory of ICA.
Almost All About Waves by John R. Pierce