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IEEE International Conference on Acoustics, Speech, and Signal Processing
May 14-19, Toulouse, France
Title
Wave Field Simulation with the Functional Transformation Method
Authors
Stefan Petrausch and Rudolf Rabenstein
Abstract
The Functional Transformation Method (FTM) provides a frequency domain based analytic solution of arbitrary linear partial differential equation.
For wave field simulations however, its application was so far restricted to simple geometries as the FTM involves a search for the eigenmodes of the model.
Recently so called block based modeling algorithms were introduced, that follow a divide-and-conquer approach. A complex geometry is split into several simple elementary blocks.
These blocks are solved and discretized separately, while their connection is realized in the discrete system during run-time.
In this paper a 2D wave field simulation program based on block based modeling is demonstrated.
Elementary block models are solved with the FTM and can be connected together to create complex 2D geometries.
The complete system benefits from the advantages of the FTM (e.g. dispersion-free simulations), while the complexity of the geometry fits the needs of typical CAD drawings.
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Additional Multimedia Content
Several example videos can be downloaded in the sequel. All videos were generated by the simulation tool "Wave2D" frame by frame.
These frames were afterwards encoded using the DivX-format version 5.
A simplified version of "Wave2D" without block-based modeling can be downloaded here.
Church-Example
The first example models the room acoustics of the church St. Johannis located in Ansbach, Germany.
The church is a Gothic hall church with a relatively big sanctuary. The acoustics are modeled in 2D according to the ground plan below on the left.
The abstraction of this ground plan used in the simulation can be seen on the right.
The simplified ground plan was split into rectangular and triangular blocks. The resulting interaction topology was written down in a script-file for the program "Wave2D" and loaded within the program. The ground plan itself is about 169m² in size, the temporal sample rate of the simulation is 22.05kHz. The simulation was performed on a Pentium IV at 2.8GHz, which produced about 4-5 frames per second. Two examples can be seen below: the left one is excited by a smoothed impulse in the sanctuary, the right one is excited by a sine function at the same location.
Wave Field Synthesis
The second example is a simulation of a new multichannel reproduction system called Wave Field Synthesis (WFS).
The aim of WFS is to exactly reproduce a given soundfield within an array of loudspeakers.
In doing so, enhanced signal processing algorithms are applied to for instance eliminate the influence of the listening room.
These algorithms require exact impulse responses of the listening room, which are simulated here with the program "Wave2D".
With these impulse responses it is possible to calculate compensation filters to create the appropriate driving signals for the loudspeakers.
These driving signals are again fed into the program "Wave2D" to simulate WFS with active room compensation.
More details about these simulations can be found here.
The next two videos demonstrate WFS with adjusted compensation filters on the left side and WFS with mismatched compensation filters due to an obstacle (for instance a human being) in the room.
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