Kautz filters and generalized frequency resolution: Theory and audio applications

Frequency-warped filters have recently been applied successfully to a number of audio applications. The idea of all-pass delay elements replacing unit delays in digital filters allows for focusing enhanced frequency resolution on the lowest (or highest) frequencies and enables a good match to the psychoacoustical Bark scale. Kautz filters can be seen as a further generalization, where each all-pass element may be different, allowing also complex-conjugate poles. This enables an arbitrary allocation of frequency resolution to filter design, such as modeling and equalization (inverse modeling) of linear systems. Strategies for using Kautz filters in audio applications are formulated. Case studies of loudspeaker equalization, room response modeling, and guitar body modeling for sound synthesis are presented.