Models for room responses, that is, transfer function or
impulse response representations from sound sources to observation
locations in a room, are used in various configurations of sound field
reproduction and control. Measured room (impulse) responses are
conventionally utilized directly as the modeling device: linear
timeinvariant (LTI) filtering is implemented using convolution,
corresponding to a finite impulse response (FIR) model or filter
representation of the response. Similarly, most
equalization schemes are based on constructing an inverse filter, more
or less directly, by inverting the identified (measured)
response, and by implementing the equalizer as an FIR filter. It is
however apparent that room responses are inherently recursive, implying
that an infinite impulse response (IIR) model or filter structure would
provide a more efficient representation, at least in principle.
The concept of Kautz filters can be seen as a
way to overcome some (most) problems associated to highorder IIR
filter design for long and complicated target responses,
such as room responses. Kautz filters, or more
suggestively, generalized transversal filters, are fixedpole IIR
filters that
inherit many favorable properties from FIR filters, such as,
unconditional
stability and robustness of design and implementation. In addition, the
Kautz
filter has a tapped transversal structure comprised of an allpass
filter
backbone and related tapoutput allpole filters that together enforce
the
tapoutput impulse responses to be mutually orthonormal for any choice
of
desired stable poles. (The FIR filter is a Kautz filter with respect to
the
choice of poles at the origin.) The essential design task is thus
how to generate the Kautz filter poles with respect to a given room
response, to which we have proposed an efficient procedure and various
modifications that utilize combined warping, subband, and multirate
techniques.
There are at
least three reasons why IIR filter or polezero modeling of
room responses using Kautz filters should be attractive from the
perspective of spatial sound reproduction and control:

relatively loworder models (parametrizations) of room
responses are attained, typically with 1020% of the complexity of a
direct FIR filter implementation

considerably lowerorder approximations with respect to a
desired allocation of spectral resolution can be constructed using
zooming/warping/resampling techniques
 the Kautz filter configuration provides an efficient
parametrization scheme for processing large collections of room
responses: the "room" can be characterized by a fixed set of poles
(resonances), whereas variations in the responses (e.g. due to
different source/receiver locations) are parametrized compactly
by the filter weights
Publications related to room response modeling and
equalization using specialized digital filtering methods, such as,
warping and Kautz filter techniques:
Publication

Short
description 
poster

Paatero,
T., Karjalainen,
M., and Härmä,
A., ''Modeling and Equalization of Audio Systems Using Kautz
Filters,'' in Proceedings of the International
Conference on Acoustics, Speech and Signal Processing
(ICASSP'01), vol. 5, pp. 33133316, Salt Lake City, Utah, USA, May
711, 2001. 
An introduction to Kautz filters for
modeling audio systems. Application cases: loudspeaker equalization
and instrument body modeling.

N/A 
Paatero, T.,
and Karjalainen, M.,
''New digital filter techniques for room response modeling,'' in Proceedings
of the AES 21st
International Conference on Architectural Acoustics and Sound
Reinforcement (AES21), St. Petersburg, Russia, June 13, 2002. 
Modeling of measured room responses using Kautz
filters. Particular emphasis on lowfrequency modeling.

paper
poster

Paatero, T.,
''An audio motivated hybrid of warping and Kautz filter techniques,''
in Proceedings of XI
European Signal Processing Conference (EUSIPCO 2002), Toulouse,
France, September 36, 2002. 
Presents a method for optimizing Kautz
filter poles (model resonances) with respect to warped (unequal)
frequency resolution.

N/A

Paatero, T.,
and Karjalainen, M.,
''Kautz Filters and Generalized Frequency Resolution  Theory and Audio
Applications,'' Journal of
the Audio Engineering Society, vol. 51, no. 1/2,
pp. 2744, January/February 2003. 
A tutorial on Kautz filters and a
review of our proposals for audio signal processing applications,
including room response modeling.

N/A

Paatero, T.,
''Efficient Polezero Modeling of Resonant Systems using Complex
Warping and Kautz Filter Techniques,'' in Proceedings of IEEE Workshop on
Applications of Signal Processing to Audio and Acoustics
(WASPAA'03), pp. 912, New Paltz, New York, USA, October 1922,
2003. 
Utilization of complex warping for
focusing frequency resolution of polezero modeling (in the form
of Kautz filters).

paper
poster

Paatero, T.,
''Modeling of Long and Complex Responses Using Kautz Filters and
TimeDomain Partitions,'' in Proceedings of 12th European Signal
Processing Conference (EUSIPCO 2004), pp. 313316, Vienna,
Austria, September 610, 2004. 
Strategies for partitioned
modeling of complex room responses using Kautz filters.

N/A

Karjalainen,
M., Paatero,
T., Mourjopoulos, J. N., and Hatziantoniou, P. D.,
''About Room Response Equalization and Dereverberation,'' in Proceedings
of IEEE
Workshop on
Applications of Signal Processing to Audio and Acoustics
(WASPAA'05), pp. 183186, New Paltz, NY, USA, October 1619, 2005. 
An overview on room response
equalization and dereverberation. A comparison of methods for room
response inversion, including smoothing and warping techniques.


