Kautz filter

In signal processing, the Kautz filter, named after William H. Kautz, is a fixed-pole traversal filter, published in 1954.

[1][2] 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.

[citation needed] 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: In the time domain, this is equivalent to where ani are the coefficients of the partial fraction expansion as, For discrete-time Kautz filters, the same formulas are used, with z in place of s.[3] If all poles coincide at s = -a, then Kautz series can be written as,

, where Lk denotes Laguerre polynomials.