In spatial hearing, complex valued head-related transfer function (HRTF) can be represented as a real valued head-related impulse response (HRIR). Using Karhunen-Loeve expansion, the spatial features of the normalized HRIRs on measurement space can be extracted as spatial character functions. A neural network model based on Von-Mises function is used to approximate the discrete spatial character function of HRIR. As a result, a time-domain binaural model is established and it fits the measured HRIRs well.published_or_final_versio

Chan, FHY

Lam, FK

Lo, TF

Wang, WB

Weng, T

Wu, ZY

HKU Scholars Hub

Title Neural network model of binaural hearing based on spatialfeature extraction of the head related transfer functionAuthor(s) Wu, ZY; Weng, T; Wang, WB; Lo, TF; Chan, FHY; Lam, FKCitationThe 20th IEEE Engineering in Medicine and Biology SocietyConference Proceedings, Hong Kong, China, 29 October - 1November 1998, v. 3, p. 1109-1112Issued Date 1998URL http://hdl.handle.net/10722/46119Rights Creative Commons: Attribution 3.0 Hong Kong LicenseProceedings of the 20th Annual International Conference of the IEEE Engineering in Medicine and Biology Society, Vol. 20, No 3, 1998 NEURAL NETWORK MODEL OF BINAURAL HEARING BASED ON SPATIAL FEATURE EXTRACTION OF THE HEAD RELATED TRANSFER FUNCTION Zhenyang Wu, Tao Weng, and Weibin Wang Department of Radio Engineering Southeast University, Si Pai Lou #2, Nanjing 210018, P. R. C. Email: zhenyang@seu.edu.cn T.F. Lo, Francis H. Y. Chan, and F. K. Lam Department of Electrical and Electronic Engineering, University of Hong Kong, Pokfulam Road, Hong Kong Email: fhychan@hkueee.hku.hk Abstract - In spatia1 hearing, complex valued head-related transfer function (HRTF) can be represented as a real valued head-related impulse response (HRIR). Using Karhunen-Loeve expansion, the spatial features of the normalized HRIRs on measurement space can be extracted as spatial character functions. A neural network model based on Von-Mises function is used to approximate the discrete spatial character function of HRIR. As a result, a time-domain binaural model is established and it fits the measured HRIRs well. Keywords: Spatial Hearing, Feature Extraction, Neural Networks 1. Introduction Extensive physical and behavioral studies have revealed that the external ear plays an important role in spatial hearing. The external ear provides directional amplification of the incident sound pressure level and also modifies the spectrum of the incoming sound according to the incidence angle of that sound. Direction-dependent transformation of the external ear is referred as head-related transfer function (HRTF) or head-related impulse response (HRIR) to acknowledge its primary acoustical importance. In virtual auditory space (VAS) applications and physiological study, HRTFs in continuous spatial locations are often desired. Kistler and Wightman [l] established a model based on principal component analysis and minimum-phase reconstruction. Principal component analysis (PCA) is applied to the logarithms of the HRTF magnitudes after the removal of direction- independent and subject-dependent spectral features. Chen [2 ]  hrther proposed a spatial feature extraction and regularization (SFER) model for the HRTFs. In this model the HRTFs are expressed as weighted combinations of a set of complex valued eigentransfer functions. Both the PCA model and the SFER model have focused on the frequency components and involve complex-valued or logarithmic computation, therefore their applicability in real time case is limited. In a previous work, Wu and Chan et a1 [3] presented binaural model based on the spatial features extracted from the measured HRIRs of a cat. In this model HRIRs are approximated as weighted combinations of a set of real valued basis fimctions. A simple linear interpolation algorithm is employed to obtain the modeled binaural HRIRs. The real valued operations and linear interpolation are very effective for speeding up the model computation in real time implementation. In this paper, we extend this model to the measured HRIRs of a KEMAR and develop a neural network model to establish the continuous human hearing space. 2. Spatial feature extraction of the HRIR[3] The measured HRIRs come from the Media Laboratory of MIT[4]. The measurement was conducted on a mannequin KEMAR in an anechoic chamber. The spherical space around the KEMAR was sampled at elevations from -40" (40" below the horizontal plane) to 90" (directly overhead) in 10" increments. The azimuth increment sizes were chosen to maintain approximately 5" great-circle increments. In total, 710 locations were sampled. The impulse responses were obtained using a maximum length(ML) sequence measurement technique with a sampling rate of 44.1 kHz. Because these data were contaminated by various types of disturbances such as random noise and acoustic reflections, they must be preprocessed before computation. A denoising algorithm based on singularity detection with wavelet is adopted. The speaker response is also equalized by using the inverse filter of the speaker response. After that, the HRIRs are shortened to 128-point long and shifted along the time axis to remove the ITDs of different locations. Let hi denote the HRIR of location (e,,cp,), j=1,2;**P, P=710. The HRIRs are the function of both space and time and through spatial feature extraction 0-7803-5164-9/98/$10.00 0 1998 IEEE 1109 we can separate tlhe spatial features from the temporal features. Using Karhunen-Loeve expansion we derive orthonormal basis functions ofhi,  that is h j  = Qwj i- ha, M =Cwi(Qj,<pj)qj +ha, + ~ j  (1) i=l where the ha, is the space sample average and Q = [q, , q2 ,e * -q,v ] is an orthonormal transformation matrix whose columns are chosen as the eigenvectors of the time auto-covariance matrix R h . We call g 6=1,2,. . .M) the eigentranfer hnctions (EF). EFs only contain the temporal information of the HRIRs while the weight vector Wj = [w, (0 j ,CP ,i ), wz (0 j ,CP j 1,. * *, wM (0 j ,CP j )I only contain the spatial information of the HRIRs. We call w,. the spatial character functions (SCF) and w is calculated by w = Q T  (h, - ha,,) (2) In our model, the first 10 components can represent more than 95% of the variation in the normalized HRIRs. 3. The neural network model of HRIR in continuous hearing space Because the SCF we obtained from the spatial feature extraction exists only in several discrete space locations, we hope: to find the SCF in an arbitrary space location. In practice, we can use several basis functions to approach the SCF in the desired position, that is ;Y ( ~ , < p ) = ( ~ , f , ( 8 , c p ) + C z f , ( ~ , c p )  + .*. +%f” ((0 9 0 )  (3) In this case, a two-layer BP (Back-Propagation) network is developed to approach the SCF. The inputs to the network are the location in the space. The hidden layer unit gives thle corresponding output according to its input 8 and cp.  Here the Von Mises Function is used as the basis fimction[5]: VM(8 ,cp) =: exp{k[sincp sin p cos(8 -a) +coscp cos p -13) (4) where k,a,p are the parameters and a,OE[0,2n], p , q ~ [ O , a ] .  The output of the network is SCF. The connectivity of the network is indicated schematically in figure 1. The learning algorithm used here is as follows: Q ( n  + 1) = Q ( n )  +q(n)AQ + P [ W )  - Q ( n  - 111 (5) where R = [wt T ,  aT , BT , kT 3, A n  =[AwtT ,A aT , A  BT ,AkT]. awti, = [ti - yi (e ,q )IVM (e ,cp ,a j ,  P j ,  k j  (6) A a j  = kj[sincp sin p j  sin@ -aj)] N x C {[ti - Yi (0 $9 )Iwti,j 1 1 (7) where tj is teacher and y j  is the output. Among the total 710 (e ,cp j )  data sets, 600 are chosen for training the net and the rest are used to test the generalization performance of the model. 4. Results Figure 2 gives the 3D plot of the first component of SCF . Above is the SCF in discrete space locations and below is the network output of the SCF in different space locations. Table 1 gives the final error of the SCF and the reconstruction error according to these SCFs. Acknowlegement The present work was supported in part by University of Hong Kong Research Grants and National Natural Science Foundation of China. The authors would like to thank Mr. Bill Gardener and Kieth Martin of MIT lab for providing the KEMAR data. REFERENCES [I]  D. J. Kistler, and E L. Wightman “A Model of Head-related Transfer Functions Based on Principal Components Analysis and Minimum- phase Reconsttuction,” J. Acoust. SOC. Am. 91, 1637-1647. 1110 [2] J. Chen, B. D.Van Veen, and K. E. Hecox “A [4] w. G. Gardner and K. D. Martin “ HRTF measurements of a KEMAR,” J. Acoust. SOC. Am. [5] R. L. Jenison, et al. “A spherical basis function Spatial Feature Extraction and Regularization Acoust. SOC. Am. 97,439-452. [3] Z. Wu, F. H. Y. Chan, F. K. Lam and J. Chan “A time domain binaural model based on spatial feature extraction for the head-related transfer function” J. Acoust. SOC. Am. 102,2211-2218. Model for the Head-related Transfer Function,” J. 97,3907-3908. neural network for modeling auditory space, ” Neural Computation, 8, 115-128. Rms error of the SCF Training sed Test set Table 1 Rms error of the HRIR using the output SCF Rms error of the HRIR using original SCF Training set I Test set Total space positions Components of SCF 0.0829 0.1148 1 2  0.0856 0.2483 0.2484 0.24 18 0.1064 0.1792 0.1870 0.1640 1 3  0.1118 0.0822 0.0661 0.0402 0.0393 0.0337 1 4  0.1269 0.1352 0.1379 0.1127 0.0821 0.099 1 0.1009 0.0728 0.0722 0.0816 0.0848 0.0533 0.0521 0.0758 0.0789 0.0464 0.043 1 0.0673 0.0675 0.0368 0.0408 0.0503 0.0539 0.0292 1 9  0.0521 I 0.0519 I 0.3001 I 0.3041 I 0.2978 I 0.1024 I 0.1269 I 0.1352 I 0.1379 I 0.1127 I Output layer Hidden layer Input layer 4 4 4 4 ‘ 1  Figure 1 The neural network model 1111 I. 

Neural network model of binaural hearing based on spatial feature extraction of the head related transfer function

http://hub.hku.hk/bitstream/10722/46119/1/45231.pdf

Neural network model of binaural hearing based on spatial feature extraction of the head related transfer function

Abstract

Similar works

Full text

Available Versions

HKU Scholars Hub