type of artificial neural network techniques Amir Shokri - - PowerPoint PPT Presentation

Amir Shokri Amirsh.nll@gmail.com

Fast auralization using radial basis functions type of artificial neural network techniques

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

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

○ 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

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

Fig 1

Fig 2

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

Fig 3

Fig 4

Fig 5

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

Fig 6

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

• f operations for calculating the inverse Fourier transform.

Computational cost

Fig 7

Fig8

Table 1

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

Fig 9 & 10

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