SELECTED PUBLICATIONS RELATED TO NUMERICAL MODELLING OF ACOUSTIC SPACES
Kowalczyk, K., van Walstijn, M. & Murphy, D. (2011), "A Phase Grating Approach to Modeling Surface Diffusion in FDTD Room Acoustics Simulations", IEEE Transactions on Audio, Speech, and Language Processing. Vol. 19(3), pp. 528 - 537.
Abstract: In this paper, a method for modeling diffusive boundaries in finite-difference time-domain (FDTD) room acoustics simulations with the use of impedance filters is presented. The proposed technique is based on the concept of phase grating diffusers, and realized by designing boundary impedance filters from normal-incidence reflection filters with added delay. These added delays, that correspond to the diffuser well depths, are varied across the boundary surface, and implemented using Thiran allpass filters. The proposed method for simulating sound scattering is suitable for modeling high frequency diffusion caused by small variations in surface roughness and, more generally, diffusers characterized by narrow wells with infinitely thin separators. This concept is also applicable to other wave-based modeling techniques. The approach is validated by comparing numerical results for Schroeder diffusers to measured data. In addition, it is proposed that irregular surfaces are modeled by shaping them with Brownian noise, giving good control over the sound scattering properties of the simulated boundary through two parameters, namely the spectral density exponent and the maximum well depth.
BibTeX:
@article{tasl11b,
  author = {Konrad Kowalczyk and Maarten van Walstijn and Damian Murphy},
  title = {A Phase Grating Approach to Modeling Surface Diffusion in FDTD Room Acoustics Simulations},
  journal = {IEEE Transactions on Audio, Speech, and Language Processing},
  year = {2011},
  volume = {19},
  number = {3},
  pages = {528 - 537},
  doi = {http://dx.doi.org/10.1109/TASL.2010.2051830}
}
Kowalczyk, K. & van Walstijn, M. (2011), "Room acoustics simulation using 3-D compact explicit FDTD schemes", IEEE Transactions on Audio, Speech, and Language Processing. Vol. 19(1), pp. 34-46.
Abstract: This paper presents methods for simulating room acoustics using the finite-difference time-domain (FDTD) technique, focusing on boundary and medium modeling. A family of nonstaggered 3-D compact explicit FDTD schemes is analyzed in terms of stability, accuracy, and computational efficiency, and the most accurate and isotropic schemes based on a rectilinear grid are identified. A frequency-dependent boundary model that is consistent with locally reacting surface theory is also presented, in which the wall impedance is represented with a digital filter. For boundaries, accuracy in numerical reflection is analyzed and a stability proof is provided. The results indicate that the proposed 3-D interpolated wideband and isotropic schemes outperform directly related techniques based on Yee's staggered grid and standard digital waveguide mesh, and that the boundary formulations generally have properties that are similar to that of the basic scheme used.
BibTeX:
@article{tasl11a,
  author = {Konrad Kowalczyk and Maarten van Walstijn},
  title = {Room acoustics simulation using 3-D compact explicit FDTD schemes},
  journal = {IEEE Transactions on Audio, Speech, and Language Processing},
  year = {2011},
  volume = {19},
  number = {1},
  pages = {34-46},
  doi = {http://dx.doi.org/10.1109/TASL.2010.2045179}
}
Kowalczyk, K. & van Walstijn, M. (2010), "A comparison of nonstaggered compact FDTD schemes for the 3D wave equation", In IEEE International Conference on Acoustics, Speech and Signal Processing (ICASSP 2010).
Abstract: This paper aims at providing a better insight into the 3D approximations of the wave equation using compact finite-difference time-domain (FDTD) schemes in the context of room acoustic simulations. A general family of 3D compact explicit and implicit schemes based on a nonstaggered rectilinear grid is analyzed in terms of stability, numerical error, and accuracy. Various special cases are compared and the most accurate explicit and implicit schemes are identified. Further considerations presented in the paper include the direct relationship with other numerical approaches found in the literature on room acoustic modeling such as the 3D digital waveguide mesh and Yee's staggered grid technique.
BibTeX:
@inproceedings{icassp10,
  author = {Kowalczyk, K. and van Walstijn, M.},
  title = {A comparison of nonstaggered compact FDTD schemes for the 3D wave equation},
  booktitle = {IEEE International Conference on Acoustics, Speech and Signal Processing (ICASSP 2010)},
  year = {2010},
  url = {http:\sarc.qub.ac.ukvanwalstijnpubspapers0.pdf}
}
Kowalczyk, K. & van Walstijn, M. (2010), "Finite difference time domain modeling of phase grating diffusion", In 4th International Symposium on Communications, Control and Signal Processing (ISCCSP 2010)., pp. 1 -4.
Abstract: In this paper, a method for modeling diffusion caused by non-smooth boundary surfaces in simulations of room acoustics using finite difference time domain (FDTD) technique is investigated. The proposed approach adopts the well-known theory of phase grating diffusers to efficiently model sound scattering from rough surfaces. The variation of diffuser well-depths is attained by nesting allpass filters within the reflection filters from which the digital impedance filters used in the boundary implementation are obtained. The presented technique is appropriate for modeling diffusion at high frequencies caused by small surface roughness and generally diffusers that have narrow wells and infinitely thin separators. The diffusion coefficient was measured with numerical experiments for a range of fractional Brownian diffusers.
BibTeX:
@inproceedings{isccsp10,
  author = {Kowalczyk, Konrad and van Walstijn, Maarten},
  title = {Finite difference time domain modeling of phase grating diffusion},
  booktitle = {4th International Symposium on Communications, Control and Signal Processing (ISCCSP 2010)},
  year = {2010},
  pages = {1 -4},
  doi = {http://dx.doi.org/10.1109/ISCCSP.2010.5463366}
}
Kowalczyk, K. & van Walstijn, M. (2010), "Wideband and Isotropic Room Acoustics Simulation Using 2-D Interpolated FDTD Schemes", IEEE Transactions on Audio, Speech, and Language Processing. Vol. 18(1), pp. 78 -89.
Abstract: In this paper, a complete method for finite-difference time-domain modeling of rooms in 2-D using compact explicit schemes is presented. A family of interpolated schemes using a rectilinear, nonstaggered grid is reviewed, and the most accurate and isotropic schemes are identified. Frequency-dependent boundaries are modeled using a digital impedance filter formulation that is consistent with locally reacting surface theory. A structurally stable and efficient boundary formulation is constructed by carefully combining the boundary condition with the interpolated scheme. An analytic prediction formula for the effective numerical reflectance is given, and a stability proof provided. The results indicate that the identified accurate and isotropic schemes are also very accurate in terms of numerical boundary reflectance, and outperform directly related methods such as Yee's scheme and the standard digital waveguide mesh. In addition, one particular scheme-referred to here as the interpolated wideband scheme-is suggested as the best scheme for most applications.
BibTeX:
@article{tasl10,
  author = {Konrad Kowalczyk and Maarten van Walstijn},
  title = {Wideband and Isotropic Room Acoustics Simulation Using 2-D Interpolated FDTD Schemes},
  journal = {IEEE Transactions on Audio, Speech, and Language Processing},
  year = {2010},
  volume = {18},
  number = {1},
  pages = {78 -89},
  doi = {http://dx.doi.org/10.1109/TASL.2009.2023645}
}
Kowalczyk, K. & van Walstijn, M. (2008), "Virtual room acoustics using finite difference methods. How to model and analyse frequency-dependent boundaries?", In 3rd International Symposium on Communications, Control and Signal Processing (ISCCSP 2008). 12-14 2008., pp. 1504 -1509.
Abstract: In this paper, we present new methods for constructing and analysing frequency-dependent boundaries in room acoustic modelling with the use of finite difference time domain (FDTD) techniques. Novel FDTD formulations of simple locally reacting wall models with complex impedance are proposed and analysed in terms of pressure wave reflectance for different wall impedances and angles of incidence. The analysis is done using both numerical experiments and analytic evaluation. For the numerical experiments, a compact implicit scheme of 4th-order accuracy is used for updating the room interior grid points, the results of which are analysed in both time and frequency domains. The simulation results show that the 2D frequency-dependent locally reacting wall models adhere well to their theoretical counterparts, particularly at low frequencies. Furthermore, they validate the analytic evaluation method, which paves the way for using either method as a tool for analysis of numerical reflectance.
BibTeX:
@inproceedings{isccsp08a,
  author = {Kowalczyk, K. and van Walstijn, M.},
  title = {Virtual room acoustics using finite difference methods. How to model and analyse frequency-dependent boundaries?},
  booktitle = {3rd International Symposium on Communications, Control and Signal Processing (ISCCSP 2008)},
  year = {2008},
  pages = {1504 -1509},
  doi = {http://dx.doi.org/10.1109/ISCCSP.2008.4537465}
}
Kowalczyk, K. & van Walstijn, M. (2008), "Modelling Frequency-Dependent Boundaries as Digital Impedance Filters in FDTD and K-DWM Room Acoustics Simulations", Journal of the Audio Engineering Society. Vol. 56, pp. 569-583.
Abstract: A novel method for modeling frequency-dependent boundaries in finite-difference time-domain (FDTD) room acoustic simulations offers a significant improvement over the conventional one-dimensional approach. The method incorporates a digital impedance filter resulting in multidimensional formulation. Reflecting sound waves approximate the theoretical reflectance for any value of wall impedance and angle of incidence, especially at low frequencies. Both phase and amplitude are preserved. Results obtained from numerical experiments confirm the validity of the approach.
BibTeX:
@article{jaes08,
  author = {Konrad Kowalczyk and Maarten van Walstijn},
  title = {Modelling Frequency-Dependent Boundaries as Digital Impedance Filters in FDTD and K-DWM Room Acoustics Simulations},
  journal = {Journal of the Audio Engineering Society},
  year = {2008},
  volume = {56},
  pages = {569-583},
  url = {http://www.sarc.qub.ac.uk/~mvanwalstijn/pubs/papers/jaes08.pdf}
}
Kowalczyk, K. & van Walstijn, M. (2008), "Modelling Frequency-Dependent Boundaries as Digital Impedance Filters in FDTD and K-DWM Room Acoustics Simulations", In 124th Audio Engineering (AES) Convention, Amsterdam.
Abstract: This paper presents a new method for modelling frequency-dependent boundaries in finite difference time domain (FDTD) and Kirchhff variable digital waveguide mesh (K-DWM) room acoustics simulations. The proposed approach allows direct incorporation of a digital impedance filter (DIF) in the multi-dimensional (i.e. 2D or 3D) FDTD boundary model of a locally reacting surface. An explicit boundary update equation is obtained by carefully constructing a suitable recursive formulation. The method is analysed in terms of pressure wave reflectance for different wall impedance filters and angles of incidence. Results obtained from numerical experiments confirm the high accuracy of the proposed digital impedance fillter boundary model, the reflectance of which closely matches locally reacting surface (LRS) theory. Furthermore, a numerical boundary analysis (NBA) formula is provided as a technique for analytic evaluation of the numerical reflectance of the proposed digital impedance filter boundary formulation.

This paper won the AES student best paper award at the AES 124th Convention, and and extended version has been published in the Journal of the Audio Engineering Society

BibTeX:
@inproceedings{aes08,
  author = {Konrad Kowalczyk and Maarten van Walstijn},
  title = {Modelling Frequency-Dependent Boundaries as Digital Impedance Filters in FDTD and K-DWM Room Acoustics Simulations},
  booktitle = {124th Audio Engineering (AES) Convention, Amsterdam},
  year = {2008},
  url = {http:\sarc.qub.ac.ukvanwalstijnpubspapers8.pdf}
}
van Walstijn, M. & Kowalczyk, K. (2008), "On the Numerical Solution of the 2D Wave equation with Compact FDTD Schemes", In 11th Int. Conference on Digital Audio Effects (DAFx-08), Espoo, Finland., pp. 205-212.
Abstract: his paper discusses compact-stencil finite difference time domain (FDTD) schemes for approximating the 2D wave equation in the context of digital audio. Stability, accuracy, and efficiency are investigated and new ways of viewing and interpreting the results are discussed. It is shown that if a tight accuracy constraint is applied, implicit schemes outperform explicit schemes. The paper also discusses the relevance to digital waveguide mesh modelling, and highlights the optimally efficient explicit scheme.
BibTeX:
@inproceedings{dafx08,
  author = {Maarten van Walstijn and Konrad Kowalczyk},
  title = {On the Numerical Solution of the 2D Wave equation with Compact FDTD Schemes},
  booktitle = {11th Int. Conference on Digital Audio Effects (DAFx-08), Espoo, Finland},
  year = {2008},
  pages = {205-212},
  url = {http:\sarc.qub.ac.ukvanwalstijnpubspapers8.pdf}
}
Kowalczyk, K. & van Walstijn, M. (2008), "Formulation of a locally reacting wall in finite difference modelling of acoustic spaces", Acta Acustica united with Acustica. Vol. 94, pp. 891-906.
Abstract: In this paper, we present new methods for constructing and analysing formulations of locally reacting surfaces that can be used in finite difference time domain (FDTD) simulations of acoustic spaces. Novel FDTD formulations of frequency-independent and simple frequency-dependent impedance boundaries are proposed for 2D and 3D acoustic systems, including a full treatment of corners and boundary edges. The proposed boundary formulations are designed for virtual acoustics applications using the standard leapfrog scheme based on a rectilinear grid, and apply to FDTD as well as Kirchhoff variable digital waveguide mesh (K-DWM) methods. In addition, new analytic evaluation methods that accurately predict the reflectance of numerical boundary formulations are proposed. numerical experiments and numerical boundary analysis (NBA) are analysed in time and frequency domains in terms of the pressure wave reflectance for different angles of incidence and various impedances. The results show that the proposed boundary formulations structurally adhere well to the theoretical reflectance. In particular, both reflectance magnitude and phase are closely approximated even at high angles of incidence and low impedances. Furthermore, excellent agreement was found between the numerical boundary analysis and the experimental results, validating both as tools for researching FDTD boundary formulations.
BibTeX:
@article{aca08,
  author = {Konrad Kowalczyk and Maarten van Walstijn},
  title = {Formulation of a locally reacting wall in finite difference modelling of acoustic spaces},
  journal = {Acta Acustica united with Acustica},
  year = {2008},
  volume = {94},
  pages = {891-906},
  url = {http://www.sarc.qub.ac.uk/~mvanwalstijn/pubs/papers/aca08.pdf}
}
Kowalczyk, K. & van Walstijn, M. (2007), "Formulation of a Locally Reacting Wall in Finite Difference Modelling of Acoustic Spaces", In International Symposium of Room Acoustics (ISRA 2007), Sevilla.
Abstract: This paper presents a new model for modelling locally reacting walls, that can used in finite difference modelling of acoustic spaces. The new 2D/3D finite difference boundary formulation is compared to the more
conventional 1D formulation in terms of pressure wave reflection for different wall impedances and angles of incidence. The results show that the 2D formulation adheres significantly better to the continuous-time formulation for all angles of incidence than the 1D formulations; in particular it is shown that only the 2D formulation properly preserves the phase.
BibTeX:
@inproceedings{isra07,
  author = {Kowalczyk, K. and van Walstijn, M.},
  title = {Formulation of a Locally Reacting Wall in Finite Difference Modelling of Acoustic Spaces},
  booktitle = {International Symposium of Room Acoustics (ISRA 2007), Sevilla},
  year = {2007}
}
Kuster, M. & van Walstijn, M. (2007), "Spatial Coherence Between Microphones with Arbitrary First-Order Directivity in Reverberent Acoustic Fields", In International Congress on Acoustics (ICA 2007), Madrid, Spain.
Abstract: The theoretical expressions for the spatial correlation and spatial coherence between signals representing the pressure and the components of the particle velocity vector in a reverberant acoustic field are established in the literature and have also been corroborated with measurements [F. Jacobsen, J. Acoust. Soc. Am., 108(1), 2000]. In the present paper, expressions are derived from theory for the spatial coherence between microphone signals whose directivities can be written as a combination of pressure and particle velocity components. The resulting expressions are a combination of the already established expressions for the coherence functions between pressure and the components of the particle velocity vector. The theory has been verified on the reverberant tails of measured room impulse responses in rooms of various size and acoustic characteristics.
BibTeX:
@inproceedings{ica07,
  author = {Martin Kuster and Maarten van Walstijn},
  title = {Spatial Coherence Between Microphones with Arbitrary First-Order Directivity in Reverberent Acoustic Fields},
  booktitle = {International Congress on Acoustics (ICA 2007), Madrid, Spain},
  year = {2007},
  url = {http:\sarc.qub.ac.ukvanwalstijnpubspapers7b.pdf}
}
Kowalczyk, K. & van Walstijn, M. (2007), "On-Line Simulation of 2D Resonators with Reduced Dispersion Error using Compact Implicit Finite Difference Methods", In IEEE International Conference on Acoustics, Speech and Signal Processing (ICASSP 2007). 15-20 2007. Volume 1, pp. I-285 -I-288.
Abstract: This paper presents a method for on-line simulation of 2D resonators with reduced direction-dependent frequency error. The use of a compact implicit finite difference (FD) technique is proposed to reduce the dispersion error remarkably. In particular, a computationally efficient method that allows solving 2D implicit problems with a set of three-diagonal equations, namely the alternating direction implicit is discussed. Efficient equation factorisation together with optimally matched free parameters allows more accurate simulation for wider frequency ranges. With the use of this technique, the dispersion error is limited to 1.1% within the bandwidth up to half of the Nyquist frequency. The compact implicit scheme is compared to compact explicit FD schemes in terms of numerical dispersion error, membrane impulse response, and computational cost.
BibTeX:
@inproceedings{icassp07,
  author = {Kowalczyk, K. and van Walstijn, M.},
  title = {On-Line Simulation of 2D Resonators with Reduced Dispersion Error using Compact Implicit Finite Difference Methods},
  booktitle = {IEEE International Conference on Acoustics, Speech and Signal Processing (ICASSP 2007)},
  year = {2007},
  volume = {1},
  pages = {I-285 -I-288},
  doi = {http://dx.doi.org/10.1109/ICASSP.2007.366672}
}

Created on 04/04/2011.