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William H. Kautz
In signal processing, the Kautz filter, named after William H. Kautz, is a fixed-Pole (complex analysis), pole traversal filter (signal processing), filter, published in 1954. Like Laguerre filters, Kautz filters can be implemented using a cascade of all-pass filters, with a one-pole lowpass filter at each tap between the all-pass sections. Orthogonal set Given a set of real poles \, the Laplace transform of the Kautz orthonormal basis is defined as the product of a one-pole lowpass factor with an increasing-order allpass factor: :\Phi_1(s) = \frac :\Phi_2(s) = \frac \cdot \frac :\Phi_n(s) = \frac \cdot \frac . In the time domain, this is equivalent to :\phi_n(t) = a_e^ + a_e^ + \cdots + a_e^, where ''ani'' are the coefficients of the Partial fraction, partial fraction expansion as, :\Phi_n(s) = \sum_^ \frac For discrete-time Kautz filters, the same formulas are used, with ''z'' in place of ''s''. ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
William H
William is a male given name of Germanic origin.Hanks, Hardcastle and Hodges, ''Oxford Dictionary of First Names'', Oxford University Press, 2nd edition, , p. 276. It became very popular in the English language after the Norman conquest of England in 1066,All Things William"Meaning & Origin of the Name"/ref> and remained so throughout the Middle Ages and into the modern era. It is sometimes abbreviated "Wm." Shortened familiar versions in English include Will, Wills, Willy, Willie, Bill, and Billy. A common Irish form is Liam. Scottish diminutives include Wull, Willie or Wullie (as in Oor Wullie or the play ''Douglas''). Female forms are Willa, Willemina, Wilma and Wilhelmina. Etymology William is related to the given name ''Wilhelm'' (cf. Proto-Germanic ᚹᛁᛚᛃᚨᚺᛖᛚᛗᚨᛉ, ''*Wiljahelmaz'' > German ''Wilhelm'' and Old Norse ᚢᛁᛚᛋᛅᚼᛅᛚᛘᛅᛋ, ''Vilhjálmr''). By regular sound changes, the native, inherited English form of the name shoul ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |