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.
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 a<sub>ni</sub> 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.
If all poles coincide at s = -a, then Kautz series can be written as, <br /> ,<br /> where L<sub>k</sub> denotes Laguerre polynomials.