Fast auralization using radial basis functions type of artificial neural network techniques amirsh.nll@gmail.com

1. Amir Shokri
Amirsh.nll@gmail.com
Fast auralization using
radial basis functions
type of artificial neural
network techniques

2. This work presents a new technique to produce fast and reliable auralizations with a computer code for
room acoustics simulation. It discusses the binaural room impulse responses generation classic method
and presents a new technique using radial basis functions type of artificial neural networks. The radial basis
functions type of artificial neural networks is briefly presented and its training and testing proce-dures are
discussed. The artificial neural network models the filtered head-related impulse responses for 64,442
directions uniformly distributed around the head with a significant reduction in computa-tional cost of
around 90% in the generation of binaural impulse responses. It is shown that the filtered head-related
impulse responses calculated with the classical convolution method and with the artificial neural network
technique are almost indistinguishable. It is concluded that the new technique produces fastest and
reliable binaural room impulse responses for auralization purposes.
a b s t r a c t

3. This work deals with room acoustics computer simulation and its techniques to generate auralization at
selected seats in the room. In general, the room acoustics simulation follows the requirements of
geometrical acoustics. This means that the sound waves can be treated as acoustic rays that leave the
sound source and propagate in the room, reflecting and refracting on their internal surfaces. There are two
main ways of modeling acous-tic rays: the ray-tracing method and the image source method. There are
also hybrid algorithms that use the image source method for the calculation of first specular reflections
and the ray-tracing method for the calculus of the remaining ones. However, as already pointed out by
several authors, diffuse reflection plays an important role in room acoustics, providing a greater uniformity
in the sound field. Having in mind the room’s auralization, the diffuse reflections are also fundamental,
leading to greater authenticity. In this case, it seems essential to have a good model to deal with diffuse
reflections, since the ray-tracing technique cannot handle properly. One of the ways to approxi-mately
model diffuse reflections is the radiosity technique.
Introduction

4. ○ Radial basis functions type of artificial neural network
○ Training and testing the artificial neural network set
○ Fast auralization with ann technique
○ Computational cost
○ Comparative results for filtered HRIRs
○ Conclusion remarks
Index

5. An artificial neural network (ANN) is an information processing system based on simplified mathematical
models of biological neurons whose learning process results from experience. The knowledge gained by
the network through the examples are stored in the form of connection synaptic weights that are adjusted
in order to make the correct decisions when presented to new entries. In other words, the network has the
ability to generalize the learned information. The process of adjusting synaptic weights is performed by the
learning algorithm. Artificial neural networks are useful tools for solving many types of problems as, for
instance, classification, grouping, optimization, approximation and forecast-ing. One of the main
applications of ANNs is on pattern recognition, and this is the application under consideration here: the
ANNs are trained to learn the HRIRs patterns.
Radial basis functions type of artificial neural network

6. Fig 1

7. Fig 2

8. The RBF parameters were calculated as follows: first the centers are obtained using the non-supervised K-
means algorithm. Once the centers have been calculated, the widths are deter-mined. Finally, after
defining the parameters of the radial func-tions, the free parameters of the output layer are computed
using the same procedures that are used for the output layer of other types of neural networks.
Training and testing the artificial neural network set

9. Fig 3

10. Fig 4

11. Fig 5

12. Once the acoustic field in the room simulation is completed, the goal in sequel consists in the
determination of the room impulse mono (RIRs) and binaural (BRIRs) responses at selected points. As
regards the calculation of RIRs, it is about converting the energy arrival, via Hilbert’s transform [48] and
filtering in octave bands, obtaining filtered impulse responses, whose computational cost is relatively
small. In order to compute the BRIRs, however, it is necessary to take into account the head-related
impulse responses (HRIRs) – or their corresponding in frequency domain, the so-called head-related
transfer functions (HRTFs). In the computa-tional codes that generate auralization, this is usually done via
the convolution procedure.
Fast auralization with ann technique

13. Fig 6

14. In order to examine the convolution method (CM) numerical efficiency and that of the artificial neural
network method (ANNM), a comparison is made as to the number of arithmetic operations that each
technique requires.
The number of operations in the convolution method to com-pute the filtered HRIRs equals the sum of two
parts. The first one corresponds to the number of multiplications between the ray spectrum (in octave
bands) and the HRTF of the considered direc-tion. Note, however, that due to the HRTF symmetry, only l/2
prod-ucts, with l being the number of samples, are necessary. The second one corresponds to the number
of operations for calculating the inverse Fourier transform.
Computational cost

15. Fig 7

16. Fig8

17. Table 1

18. As mentioned, the convolution technique is the classic BRIR generation method and it is present in almost
all acoustic field sim-ulation software with auralization, to our knowledge. Therefore, in order to verify the
reliability of the method of generating BRIRs with artificial neural networks of the radial basis function type,
a comparison between the two methods is presented in the sequel. Since, once the filtered HRIRs are
generated, the procedure is iden-tical, involving the delays and sum to generate the BRIRs, the com-
parison between the two methods will be done among the filtered HRIRs. In other words, since the
procedures of delay and sum of the filtered HRIRs are exactly the same in the two techniques, if the
filtered HRIRs computed by both techniques are almost identical, the resulting BRIR will be also the same.
Comparative results for filtered HRIRs

19. Fig 9 & 10

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