The doctoral dissertations of the former Helsinki University of Technology (TKK) and Aalto University Schools of Technology (CHEM, ELEC, ENG, SCI) published in electronic format are available in the electronic publications archive of Aalto University - Aaltodoc.

Generalized Linear-in-Parameter Models – Theory and Audio Signal Processing Applications

Tuomas Paatero

Dissertation for the degree of Doctor of Science in Technology to be presented with due permission of the Department of Electrical and Communications Engineering for public examination and debate in Auditorium S1 at Helsinki University of Technology (Espoo, Finland) on the 25th of November, 2005, at 12 o'clock noon.

Dissertation in PDF format (ISBN 951-22-7964-9)   [5145 KB]
Dissertation is also available in print (ISBN 951-22-7936-3)


This thesis presents a mathematically oriented perspective to some basic concepts of digital signal processing. A general framework for the development of alternative signal and system representations is attained by defining a generalized linear-in-parameter model (GLM) configuration. The GLM provides a direct view into the origins of many familiar methods in signal processing, implying a variety of generalizations, and it serves as a natural introduction to rational orthonormal model structures. In particular, the conventional division between finite impulse response (FIR) and infinite impulse response (IIR) filtering methods is reconsidered. The latter part of the thesis consists of audio oriented case studies, including loudspeaker equalization, musical instrument body modeling, and room response modeling. The proposed collection of IIR filter design techniques is submitted to challenging modeling tasks. The most important practical contribution of this thesis is the introduction of a procedure for the optimization of rational orthonormal filter structures, called the BU-method. More generally, the BU-method and its variants, including the (complex) warped extension, the (C)WBU-method, can be consider as entirely new IIR filter design strategies.

Keywords: Hilbert spaces, conformal mappings, Kautz filters, frequency warping, pole-zero modeling

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© 2005 Helsinki University of Technology

Last update 2011-05-26