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Kautz filter : ウィキペディア英語版
Kautz filter

In signal processing, the Kautz filter, named after William H. Kautz, is a fixed-pole traversal 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 expansion as,

:\Phi_n(s) = \sum_^ \frac
For discrete-time Kautz filters, the same formulas are used, with ''z'' in place of ''s''.〔


抄文引用元・出典: フリー百科事典『 ウィキペディア(Wikipedia)
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