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Simulation Of Room Transfer Functions With Directivity Patterns On The Basis Of Modes

Authors Ureta Staackmann, A.
Year 2014
Thesis Type Master's thesis
Topic Audio Signal Processing
Keywords modes of rectangular room, source and receiver directivity, spherical harmonic directivities, multipole directivities, room transfer function, Moden des Rechteckraums, Quell- und Empfangsrichtwirkung, Richtwirkung in Kugelflächenfunktionen, Richtwirkung in Multipolen, Raumübertragungsfunktion, Akustik
Abstract The study presented here intends to provide ideas and theoretical principles required to simulate room transfer functions with directivities on the basis of modes, via the so-called Room Modes Method (RMM). The lossless Helmholtz equation in the Cartesian coordinate system is the starting point for the considerations made here. It provides the transfer function between source and receiver as the infinite sum of room modes and their individual resonant behavior. Simulation to infinity is only possible in theory and must therefore be band limited. It becomes possible to describe the point-to-point transmission by a limited number of room modes. The well-known Image Source Method (ISM) is used as a reference in order to compare the performance achieved and accuracy of the RMM. Both methods deliver the perfect solution when summed over infinitely many room modes and image sources, respectively. A direct comparison between the two methods is for this very reason of great interest. The main focus of this thesis lies in employing sources and receivers having arbitrary directivity patterns, which yields directional room transfer functions. This can be done by weighting the Green's function with the spherical harmonics for the ISM or by employing the multipole characteristics in the RMM. The first ones can be directly evaluated and applied, while the multipole characteristics imply directional derivatives on the series representation of the Green's function. Ultimately both variants are compared in the spherical harmonic domain, by conversion from multipole to spherical harmonic farfield directivity patterns. General directivity patterns are created by a linear combination of multipoles or spherical harmonics. Finally, simulations of directional room transfer functions are carried out for both methods and are made available for a comparison and evaluation of their performance. The accuracy of both methods is likely to stand in direct relationship to their truncation in space or the modal domain, respectively. The influence of this truncation constitutes the main problem studied in this work.
Supervisors Zotter, F., Heusdens, R.