Room response modeling and equalization using specialized digital filter techniques

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 time-invariant (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 high-order IIR filter design  for long and complicated  target responses, such as room responses. Kautz filters, or more suggestively, generalized transversal filters, are fixed-pole 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 tap-output all-pole filters that together enforce the tap-output 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 pole-zero modeling of room responses using Kautz filters should be attractive from the perspective of spatial sound reproduction and control:

  • relatively low-order models (parametrizations) of room responses are attained, typically with 10-20% of the complexity of a direct FIR filter implementation   

  • considerably lower-order 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

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. 3313-3316, Salt Lake City, Utah, USA, May 7-11, 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 1-3, 2002. Modeling of measured room responses using Kautz filters. Particular emphasis on low-frequency modeling.

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 3-6, 2002. Presents a method for optimizing Kautz filter poles (model resonances) with respect to warped  (unequal) frequency resolution.
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. 27-44, January/February 2003. A tutorial on Kautz filters and a review of our proposals for audio signal processing applications, including room response modeling.
Paatero, T., ''Efficient Pole-zero 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. 9-12, New Paltz, New York, USA, October 19-22, 2003. Utilization of complex warping for focusing frequency resolution of  pole-zero modeling (in the form of Kautz filters).

Paatero, T., ''Modeling of Long and Complex Responses Using Kautz Filters and Time-Domain Partitions,'' in Proceedings of 12th European Signal Processing Conference (EUSIPCO 2004), pp. 313-316, Vienna, Austria, September 6-10, 2004. Strategies for partitioned  modeling of complex room responses using Kautz filters.
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. 183-186, New Paltz, NY, USA, October 16-19, 2005. An overview on room response equalization and dereverberation. A comparison of methods for room response inversion, including smoothing and warping techniques.

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Modified: 18.1.2006
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