Dr Damian Murphy

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Abstract

Diffuse reflection has a significant effect on an acoustic environment, and is an important consideration in any acoustic modelling application. The focus of this work is on the simulation of diffuse reflection in a Digital Waveguide Mesh. Diffusion models, based on both physical mapping and statistical approaches, have been implemented and compared, the results of which are presented in my thesis. The diffusion coefficient was found to be a useful method to analyse and quantify the scattering characteristics of these models. A new diffusion boundary diffusion model, referred to as the diffusing layer technique is also presented and discussed. This web page contains sound files that have been designed to demonstrate the auditory effect of the implementation of the diffusing layer diffusing boundary model.

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Audio Examples in the 2-D Digital Waveguide Mesh

A 2-D DWM structure, rectangular in shape and with a triangular mesh topology, is used to create a series of impulse responses designed to demonstrate the auditory effect of the diffusing layer model implementations. The structure has a length of 6.60 m and a width of 3.81 m and the update frequency of the mesh is 44.1 kHz. The dimensions and geometry of the mesh are illustrated in Figure 1. The diffusing layer diffusion model is applied at all boundaries of the structure and a reflection coefficient r is also applied at all boundaries. Two sets of tests are performed. The first is designed to investigate the auditory effect of the diffusing layer model on the impulse response with a relatively high reflection coefficient (r = 0.95) and the second is designed to investigate the auditory effect of the diffusion model with a relative low coefficient (r = 0.4). In each set of tests seven impulse responses are obtained, with different implementations of the diffusing layer model applied at the boundaries. The diffusing layer boundary model implementations are named MA00, MA15, MA30, MA45, MA60, MA75 and MA90. In each test an impulse response is created by applying a low-pass filtered impulse near one corner of the mesh and taking an output from a point near the opposite corner.

Fig. 1 Diagram showing the mesh geometry used to create the 2-D auditory examples.

The following are the resulting impulse responses from the simulation for r = 0.95. The impulse responses have also been used to process a selection of auditory samples, recorded in anechoic conditions, using the process of convolution:

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Publications and Presentations from the Project:

Shelley, S., "Diffuse Boundary Modelling in the Digital Waveguide Mesh" A thesis submitted in partial fulfilment of the requirements for the degree of Doctor of Philosophy in Electronics, University of York, November 2007. Download - 5Mb

Shelley, S., and Murphy, D.T., "Modeling Diffuse Boundaries in the 2-D Digital Waveguide Mesh", IEEE Transactions on Audio, Speech and Language Processing, vol. 16, no. 3, pp. 651-665, March 2008.

Murphy, D.T., Shelley, S., and Southern, A., "Diffusing Boundaries in the Digital Waveguide Mesh and their Effect on Reverberation Time", to be presented at the 3rd Int. Symposium on Communications, Control and Signal Processing (ISCCSP 2008), Le Méridien Hotel, St. Julians, Malta, March 12?14, 2008 [Invited Paper].

Shelley, S., and Murphy, D. T., "Measuring Diffus?on in a 2D D?g?tal Wavegu?de Mesh", Proc. of 8th International Conference on Digital Audio Effects (DAFx-05), pp. 249-253, Madrid, Spain 4-8 Sept. 2005.

Shelley, S., and Murphy, D.T., "Diffus?on Modell?ng at the Boundary of a D?g?tal Wavegu?de Mesh", Proc. of 13th European Signal Processing Conference, EUSIPCO2005, Antalya, Turkey, 4-8 Sept. 2005. [Awarded Best Student Paper, 2nd Place].

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Additional Contact Details:

Simon Shelley
e: s.b.shelley[@]tue.nl

This work has been conducted under the supervision of:

Dr. Damian T. Murphy
who is maintaining this website and can be contacted above.

sbs/dtm, Oct 2008