binaural weighting of monaural spectral cues for sound localization for human listeners cues for vertical plane localization are provided by direction dependent pinna filtering this study quantified listeners weighting of the spectral cues from each ear as a function of stimulus lateral angle interaural time difference itd and interaural level difference ild subjects indicated the apparent position of headphone presented noise bursts synthesized in virtual auditory space the synthesis filters for the two ears either corresponded to the same location or to two different locations separated vertically by 20deg weighting of each ear s spectral information was determined by a multiple regression between the elevations to which each ear s spectrum corresponded and the vertical component of listeners responses the apparent horizontal source location was controlled either by choosing synthesis filters corresponding to locations on or 30deg left or right of the median plane or by attenuating or delaying the signal at one ear for broadband stimuli spectral weightin

spatiospectral concentration on a sphere we pose and solve the analogue of slepian s time frequency concentration problem on the surface of the unit sphere to determine an orthogonal family of strictly bandlimited functions that are optimally concentrated within a closed region of the sphere or alternatively of strictly spacelimited functions that are optimally concentrated in the spherical harmonic domain such a basis of simultaneously spatially and spectrally concentrated functions should be a useful data analysis and representation tool in a variety of geophysical and planetary applications as well as in medical imaging computer science cosmology and numerical analysis the spherical slepian functions can be found by solving either an algebraic eigenvalue problem in the spectral domain or a fredholm integral equation in the spatial domain the associated eigenvalues are a measure of the spatiospectral concentration when the concentration region is an axisymmetric polar cap the spatiospectral projection operator commutes with a sturm liouville operator this enables the eigenfunctions to be computed extremely accurately and efficiently even when their area bandwidth product or shannon number is large in the asymptotic limit of a small spatial region and a large spherical harmonic bandwidth the spherical concentration problem reduces to its planar equivalent which exhibits self similarity when the shannon number is kept invariant

sound localization in noise in hearing impaired listeners the present study assesses the ability of four listeners with high frequency bilateral symmetrical sensorineural hearing loss to perform horizontal localization of a click train in the presence of a white noise masker the speaker array and stimuli are identical to those described in the preceding abstract the localization performance of hearing impaired listeners is inferior to that of normal hearing listeners in all conditions both groups of listeners show the same pattern of performance when noise is presented straight ahead performance is not affected by noise when the signal to noise ratio s n is greater than 0 db below this value performance degrades when s n decreases when noise is presented at the side the performance of impaired listeners starts to worsen at higher s n s 6 to 12 db s n than normal hearing listeners and reaches a lower level the normal hearing listeners in the low pass conditions reproduce the general form of the effects of noise on hearing impaired listeners but not

analyzing head related transfer function measurements using surface spherical harmonics a continuous functional representation of a large set of head related transfer function measurements hrtfs is developed the hrtfs are represented as a weighted sum of surface spherical harmonics sshs up to degree 17 a gaussian quadrature method is used to pick out a set of experimentally efficient measurement directions anechoic impulse responses are measured for these directions between a source loudspeaker and the entrance to the ear canal of a head and torso simulator hats three separate ssh analyses are carried out the first forms a ssh representation from the time responses with the variable onset delay caused by interaural differences intact by applying the analysis to each time sample in turn the second ssh model is formed in exactly the same way except using impulse responses in which the variable onset delays have been equalized the final ssh analysis is carried out in the frequency domain by applying the technique on a frequency bin by frequency bin basis to the magnitude and unwrapped phase responses of the hrtfs the accuracy and interpolation performance of each of the computed ssh models is investigated and the usefulness of the ssh technique in analyzing directional hearing and particularly in spatializing sounds is discussed

virtual localization improved by scaling nonindividualized external ear transfer functions in frequency this study examined virtual sound localization in three conditions that differed according to the directional transfer functions dtfs that were used to synthesize the virtual targets the own ear and other ear conditions used dtfs measured from listeners own ears and those measured from other subjects respectively the scaled ear condition employed other ear dtfs that were scaled in frequency to minimize the mismatch between spectral features in the listener s and the other subject s dtfs all measures of localization error typically were lowest in the own ear condition in other ear conditions all error measures tended to increase in proportion to the inter subject differences in dtfs when spectral features in an other ear set of dtfs fell systematically lower in frequency than in a listener s own dtfs low frontal targets typically were reported as low in the rear and high rear targets were reported as high in front when spectral features in a set of dtfs fell systematically higher in frequency than in a listener s own dtfs elevation judgements showed an upward bias in the scaled ear condition all measures of performance tended to improve relative to the other ear condition in the majority of cases frequency scaling more than halved the penalty for use of another subject s dtfs

signals on graphs uncertainty principle and sampling in many applications the observations can be represented as a signal defined over the vertices of a graph the analysis of such signals requires the extension of standard signal processing tools in this paper first we provide a class of graph signals that are maximally concentrated on the graph domain and on its dual then building on this framework we derive an uncertainty principle for graph signals and illustrate the conditions for the recovery of band limited signals from a subset of samples we show an interesting link between uncertainty principle and sampling and propose alternative signal recovery algorithms including a generalization to frame based reconstruction methods after showing that the performance of signal recovery algorithms is significantly affected by the location of samples we suggest and compare a few alternative sampling strategies finally we provide the conditions for perfect recovery of a useful signal corrupted by sparse noise showing that this problem is also intrinsically related to vertex frequency localization properties

improving jacobi and gauss seidel iterations abstract when convergent jacobi or gauss seidel iterations can be applied to solve systems of linear equations a natural question is how convergence rates are affected if the original system is modified by performing some gaussian elimination we prove that if the initial iteration matrix is nonnegative then such elimination improves convergence our results extend those contained in 4

slepian spatial spectral concentration problem on the sphere analytical formulation for limited colatitude longitude spatial region in this paper we develop an analytical formulation for the slepian spatial spectral concentration problem on the sphere for a limited colatitude longitude spatial region on the sphere defined as the cartesian product of a range of positive colatitudes and longitudes the solution of the slepian problem is a set of functions that are optimally concentrated and orthogonal within a spatial or spectral region these properties make them useful for applications where measurements are taken within a spatially limited region of the sphere and or a signal is only to be analyzed within a region of the sphere to support localized spectral spatial analysis and estimation and sparse representation of localized data in these applications we exploit the expansion of spherical harmonics in the complex exponential basis to develop an analytical formulation for the slepian concentration problem for a limited colatitude longitude spatial region we also extend the analytical formulation for spatial regions that are comprised of a union of rotated limited colatitude longitude subregions by exploiting various symmetries of the proposed formulation we design a computationally efficient algorithm for the implementation of the proposed analytical formulation such a reduction in computation time is demonstrated through numerical experiments we present illustrations of our results with the help of numerical examples and show that the representation of a spatially concentrated signal is indeed sparse in the slepian basis

a comparative study of interaural time delay estimation methods the interaural time delay itd is an important binaural cue for sound source localization calculations of itd values are obtained either from measured time domain head related impulse responses hrirs or from their frequency transform head related transfer functions hrtfs numerous methods exist in current literature based on a variety of definitions and assumptions of the nature of the itd as an acoustic cue this work presents a thorough comparative study of the degree of variability between some of the most common methods for calculating the itd from measured data thirty two different calculations or variations are compared for positions on the horizontal plane for the hrtf measured on both a kemar mannequin and a rigid sphere specifically the spatial variations of the methods are investigated included is a discussion of the primary potential causes of these differences such as the existence of multiple peaks in the hrir of the contra lateral ear for azimuths near the inter aural axis due to multipath propagation and head pinnae shadowing

individual differences in external ear transfer functions reduced by scaling in frequency this study examined inter subject differences in the transfer functions from the free field to the human ear canal which are commonly know as head related transfer functions the directional components of such transfer functions are referred here to as directional transfer functions dtfs the dtfs of 45 subjects varied systematically among subjects in regard to the frequencies of spectral features such as peaks and notches inter subject spectral differences in dtfs were quantified between 3 7 and 12 9 khz for sound source directions throughout the coordinate sphere for each pair of subjects an optimal frequency scale factor aligned spectral features between subjects and thus minimized inter subject spectral differences frequency scaling of dtfs reduced spectral differences by a median value of 15 5 across all pairs of subjects and by more than half in 9 5 of subject pairs optimal scale factors showed a median value of 1 061 and a maximum of 1 38 the optimal scale factor between any pair of subjects correlated highly with the ratios of subjects maximum interaural delays sizes of their external ears and widths of their heads

preconditioned gaor methods for solving weighted linear least squares problems in this paper we present the preconditioned generalized accelerated overrelaxation gaor method for solving linear systems based on a class of weighted linear least square problems two kinds of preconditioning are proposed and each one contains three preconditioners we compare the spectral radii of the iteration matrices of the preconditioned and the original methods the comparison results show that the convergence rate of the preconditioned gaor methods is indeed better than the rate of the original method whenever the original method is convergent finally a numerical example is presented in order to confirm these theoretical results

estimation of interaural level difference based on anthropometry and its effect on sound localization individualization of head related transfer functions hrtfs is important for highly accurate sound localization systems such as virtual auditory displays a method to estimate interaural level differences ilds from a listener s anthropometry is presented in this paper to avoid the burden of direct measurement of hrtfs the main result presented in this paper is that localization is improved with nonindividualized hrtf if ild is fitted to the listener first the relationship between ilds and the anthropometric parameters was analyzed using multiple regression analysis the azimuthal variation of the ilds in each 1 3 octave band was then estimated from the listener s anthropometric parameters a psychoacoustical experiment was carried out to evaluate its effectiveness the experimental results show that the adjustment of the frequency characteristics of ilds for a listener with the proposed method is effective for localization accuracy

sensitivity of human subjects to head related transfer function phase spectra head related transfer functions hrtfs for human subjects in anechoic space were modeled with modified phase spectra including minimum phase plus delay linear phase and reversed phase plus delay functions the overall wide band interaural time delay itd for the modeled hrtfs was made consistent with that of the empirical hrtfs by setting the position dependent frequency independent delay in the hrtf for the lagging ear signal analysis of the minimum phase plus delay reconstructions indicated that model hrtfs deviate from empirical hrtf measurements maximally for contralateral azimuths and low elevations subjects assessed the perceptual validity of the model hrtfs in a four interval two alternative forced choice discrimination paradigm results indicate that monaural discrimination performance of subjects was at chance for all three types of hrtf models binaural discrimination performance was at chance for the linear phase hrtfs was above chance for some locations for the minimum phase plus delay hrtfs and was above chance for all tested locations for the reversed phase plus delay hrtfs an analysis of low frequency timing information showed that all of these results are consistent with efficient use of interaural time differences in the low frequency components of the stimulus waveforms it is concluded that listeners are insensitive to hrtf phase spectra as long as the overall itd of the low frequency components does not provide a reliable cue in particular the minimum phase plus delay approximation to the hrtf phase spectrum is an adequate approximation as long as the low frequency itd is appropriate these results and conclusions are all limited to the anechoic case when the hrtfs correspond to brief impulse responses limited to a few milliseconds

a spatial feature extraction and regularization model for the head related transfer function a functional representation is proposed for complex valued amplitude and phase head related transfer functions hrtfs including both frequency and spatial dependence the frequency variation is spanned by a set of eigentransfer functions efs that are generated using the karhunen loeve expansion any hrtf is represented as a weighted combination of the efs where the weights are functions of the hrtfs spatial location and are termed spatial characteristic functions scfs samples of the scfs are obtained by projecting the measured hrtfs onto the efs a regularization framework is employed to obtain a functional representation for the scfs by fitting each set of scf samples with a two dimensional spline acoustic validation of the model s fidelity and predictive capability is provided using 2188 measured hrtfs from a kemar manikin and 1816 measured hrtfs from an anesthetized live cat errors between measured and modeled hrtfs are generally less than one percent larger errors occur in the contralateral regions for kemar and lower back regions for the cat as a consequence of the relatively small hrtf amplitudes resulting from head shadowing methods for reducing these errors are discussed

generating 3d audio using a regularized hrtf hrir filter 3d sound is generated using an improved hrtf modeling technique for synthesizing hrtfs with varying degrees of smoothness and generalization a plurality n of spatial characteristic function sets are regularized or smoothed before combination with corresponding eigen filter functions and summed to provide an hrtf or hrir filter having improved smoothness in a continuous auditory space a trade off is allowed between accuracy in localization and smoothness by controlling the smoothness level of the regularizing models with a lambda factor improved smoothness in the hrtf filter allows the perception by the listener of a smoothly moving sound rendering free of annoying discontinuities creating clicks in the 3d sound

insights into head related transfer function spatial dimensionality and continuous representation this paper studies head related transfer function hrtf sampling and synthesis in a three dimensional auditory scene based on a general modal decomposition of the hrtf in all frequency range angle domains the main finding is that the hrtf decomposition with the derived spatial basis function modes can be well approximated by a finite number which is defined as the spatial dimensionality of the hrtf the dimensionality determines the minimum number of parameters to represent the hrtf corresponding to all directions and also the required spatial resolution in hrtf measurement the general model is further developed to a continuous hrtf representation in which the normalized spatial modes can achieve hrtf near field and far field representations in one formulation the remaining hrtf spectral components are compactly represented using a fourier spherical bessel series where the aim is to generate the hrtf with much higher spectral resolution in fewer parameters from typical measurements which usually have limited spectral resolution constrained by sampling conditions a low computation algorithm is developed to obtain the model coefficients from the existing measurements the hrtf synthesis using the proposed model is validated by three sets of data i synthetic hrtfs from the spherical head model ii the mit kemar knowles electronics mannequin for acoustics research data and iii 45 subject cipic hrtf measurements

a spatial compression technique for head related transfer function interpolation and complexity estimation a head related transfer function hrtf model employing legendre polynomials lps is evaluated as an hrtf spatial complexity indicator and interpolation technique in the azimuth plane lps are a set of orthogonal functions derived on the sphere which can be used to compress an hrtf dataset by transforming it into a lower dimensional space the lp compression technique was applied to various hrtf datasets both real and synthetic to determine how much different hrtfs can be compressed with respect to their structural complexity and their spatial resolution the spatial complexity of different datasets was evaluated quantitatively by defining an hrtf spatial complexity index which considers the rate of change in hrtf power spectrum with respect to spatial position the results indicate that the compression realized by the lp technique is largely independent of the number of spatial samples in the hrtf dataset while compressibility tracks the hrtf spatial complexity index so that more lp coefficients are needed to represent an hrtf dataset with a larger complexity index the slope of the complexity index with respect to sub sampling density can be used as a predictor for high interpolation error

the aor iterative method for new preconditioned linear systems 461 abstract in this paper we apply the aor method to preconditioned linear systems different from those considered in evans and martins internat j comput math 5 1995 69 76 gunawardena et al linear algebra appl 154 156 1991 123 143 and li and evans technical report no 901 department of computer studies university of loughborough 1994 our results show that some improvements in the convergence rate of this iterative method can be obtained

effect of perceptually irrelevant variance in head related transfer functions on principal component analysis the significant amount of variance in head related transfer functions hrtfs resulting from source location and subject dependencies have led researchers to use principal components analysis pca to approximate hrtfs with a small set of basis functions pca minimizes a mean square error and consequently may spend modeling effort on perceptually irrelevant properties to investigate the extent of this effect pca performance was studied before and after removal of perceptually irrelevant variance the results indicate that from the sixth pca component onward a substantial amount of perceptually irrelevant variance is being accounted for

improvements of preconditioned aor iterative method for l matrices in this paper we improve the preconditioned aor method of linear systems considered by evans et al the aor iterative method for new preconditioned linear systems comput appl math 132 2001 461 466 in evans paper the coefficient matrix of linear system have to be an l matrix with a i i 1a i 1 i 0 i 1 n 1 and 0

on the variation of interaural time differences with frequency interaural time difference itd is a major cue to sound localization in humans and animals for a given subject and position in space itd depends on frequency this variation is analyzed here using a head related transfer functions hrtfs database collected from the literature and comprising human hrtfs from 130 subjects and animal hrtfs from six specimens of different species for humans the itd is found to vary with frequency in a way that shows consistent differences with respect to a spherical head model maximal itd values were found to be about 800 s in low frequencies and 600 s in high frequencies the itd variation with frequency up to 200 s for some positions occurs within the frequency range where itd is used to judge the lateral position of a sound source in addition itd varies substantially within the bandwidth of a single auditory filter leading to systematic differences between envelope and fine structure itds because the frequency dependent pattern of itd does not display spherical symmetries it potentially provides cues to elevation and resolves front back confusion the fact that the relation between position and itds strongly depends on the sound s spectrum in turn suggests that humans and animals make use of this relationship for the localization of sounds

spectro temporal factors in two dimensional human sound localization this paper describes the effect of spectro temporal factors on human sound localization performance in two dimensions 2d subjects responded with saccadic eye movements to acoustic stimuli presented in the frontal hemisphere both the horizontal azimuth and vertical elevation stimulus location were varied randomly three types of stimuli were used having different spectro temporal patterns but identically shaped broadband averaged power spectra noise bursts frequency modulated tones and trains of short noise bursts in all subjects the elevation components of the saccadic responses varied systematically with the different temporal parameters whereas the azimuth response components remained equally accurate for all stimulus conditions the data show that the auditory system does not calculate a final elevation estimate from a long term order 100 ms integration of sensory input instead the results suggest that the auditory system may apply a multiple look strategy in which the final estim

a new maximum margin algorithm for one class problems and its boosting implementation in this paper each one class problem is regarded as trying to estimate a function that is positive on a desired slab and negative on the complement the main advantage of this viewpoint is that the loss function and the expected risk can be defined to ensure that the slab can contain as many samples as possible inspired by the nature of svms the intuitive margin is also defined as a result a new linear optimization problem to maximize the margin and some theoretically motivated learning algorithms are obtained moreover the proposed algorithms can be implemented by boosting techniques to solve nonlinear one class classifications

individualized head related transfer functions based on population grouping a method is proposed to divide a population into different groups for partial individualization of head related transfer functions hrtfs borrowing the basic idea in sizing system design factor analysis is used to identify the most representative measurements which are then in a case study used to group the population the comparison between the group mean hrtfs and the population mean hrtfs shows that the group mean hrtfs could greatly reduce spectral distortion at most sampled positions

compression of head related transfer function using autoregressive moving average models and legendre polynomials head related transfer functions hrtfs are generally large datasets which can be an important constraint for embedded real time applications a method is proposed here to reduce redundancy and compress the datasets in this method hrtfs are first compressed by conversion into autoregressive moving average arma filters whose coefficients are calculated using prony s method such filters are specified by a few coefficients which can generate the full head related impulse responses hrirs next legendre polynomials lps are used to compress the arma filter coefficients lps are derived on the sphere and form an orthonormal basis set for spherical functions higher order lps capture increasingly fine spatial details the number of lps needed to represent an hrtf therefore is indicative of its spatial complexity the results indicate that compression ratios can exceed 98 while maintaining a spectral error of less than 4 db in the recovered hrtfs

range dependence of the response of a spherical head model the head related transfer function hrtf varies with range as well as with azimuth and elevation to better understand its close range behavior a theoretical and experimental investigation of the hrtf for an ideal rigid sphere was performed an algorithm was developed for computing the variation in sound pressure at the surface of the sphere as a function of direction and range to the sound source the impulse response was also measured experimentally the results may be summarized as follows first the experimental measurements were in close agreement with the theoretical solution second the variation of low frequency interaural level difference with range is significant for ranges smaller than about five times the sphere radius third the impulse response reveals the source of the ripples observed in the magnitude response and provides direct evidence that the interaural time difference is not a strong function of range fourth the time delay is well approximated by well known ray tracing formula due to woodworth and schlosberg finally except for this time delay the hrtf for the ideal sphere appears to be minimum phase permitting exact recovery of the impulse response from the magnitude response in the frequency domain

sampling theory approach to prolate spheroidal wavefunctions we use the whittaker shannon sampling theorem to show that the eigenvalue problem for the sinc kernel is equivalent to a discrete eigenvalue problem the well known eigenfunctions namely the prolate spheroidal wavefunctions their corresponding eigenvalues and the orthogonality and completeness properties are determined without invoking the prolate spheroidal differential equation this analysis based on the sampling theorem may be used for calculating the eigenvalues and eigenfunctions of bandlimited kernels in general as we illustrate with an additional example of the sinc2 kernel

on the extrapolation of band limited functions with energy constraints a modification of the algorithm proposed by papoulis and gerchberg for extrapolating band limited functions is suggested to extend its applicability over data corrupted by noise we assume that energy constraints are known either for the band limited signal or for the noise in addition the discrete formulation of the iterative algorithm is derived and the transition from the continuous algorithm to its digital implementation is presented

some new preconditioned generalized aor methods for generalized least squares problems in this paper we present some new preconditioned gaor methods for solving generalized least squares problems and their comparison results comparison results show that the convergence rates of the new preconditioned gaor methods are better than those of the preconditioned gaor methods presented by zhou et al 2009 19 and wang et al 2013 18 whenever these methods are convergent lastly numerical experiments are provided to confirm the theoretical results

median plane sound localization as a function of the number of spectral channels using a channel vocoder using a vocoder median plane sound localization performance was measured in eight normal hearing listeners as a function of the number of spectral channels the channels were contiguous and logarithmically spaced in the range from 0 3 to 16 khz acutely testing vocoded stimuli showed significantly worse localization compared to noises and 100 pulses click trains both of which were tested after feedback training however localization for the vocoded stimuli was better than chance a second experiment was performed using two different 12 channel spacings for the vocoded stimuli now including feedback training one spacing was from experiment 1 the second spacing called the speech localization spacing assigned more channels to the frequency range associated with speech there was no significant difference in localization between the two spacings however even with training localizing 12 channel vocoded stimuli remained worse than localizing virtual wideband noises by 4 8 degrees in local root mean square error and 5 2 in quadrant error rate speech understanding for the speech localization spacing was not significantly different from that for a typical spacing used by cochlear implant users these experiments suggest that current cochlear implants have a sufficient number of spectral channels for some vertical plane sound localization capabilities albeit worse than normal hearing listeners without loss of speech understanding

observations on a principal components analysis of head related transfer functions a recent principal components analysis kistler and wightman 1992 has shown that the transfer functions of the human external ear for a wide range of source locations can be expressed as weighted sums of a small number of basis vectors directional transfer functions obtained in this laboratory using substantially different measurement techniques yielded principal component basis vectors that are remarkably similar to those reported by kistler and wightman when this subject population was divided in half according to the overall physical sizes of subjects basis vectors computed for the subpopulation of smaller subjects were shifted systematically to higher frequencies relative to those computed for the subpopulation of larger subjects

infinite impulse response models of the head related transfer function head related transfer functions hrtfs measured from human subjects were approximated using infinite impulse response iir filter models models were restricted to rational transfer functions plus simple delays so that specific models are characterized by the locations of poles and zeros in the complex plane the all pole case with no nontrivial zeros is treated first using the theory of linear prediction then the general pole zero model is derived using a weighted least squares wls formulation of the modified least squares problem proposed by kalman 1958 both estimation algorithms are based on solutions of sets of linear equations and result in efficient computational schemes to find low order model hrtfs the validity of each of these two low order models was assessed in psychophysical experiments specifically a four interval two alternative forced choice paradigm was used to test the discriminability of virtual stimuli constructed from empirical and model hrtfs for corresponding locations for these experiments the stimuli were 80 ms noise tokens generated from a wideband noise generator results show that sounds synthesized through model hrtfs were indistinguishable from sounds synthesized from original hrtf measurements for the majority of positions tested the advantages of the techniques described here are the computational efficiencies achieved for low order iir models properties of the all pole and pole zero estimators are discussed in the context of low order hrtf representations and implications for basic and applied contexts are considered

new support vector algorithms we propose a new class of support vector algorithms for regression and classification in these algorithms a parameter lets one effectively control the number of support vectors while this can be useful in its own right the parameterization has the additional benefit of enabling us to eliminate one of the other free parameters of the algorithm the accuracy parameter epsilon in the regression case and the regularization constant c in the classification case we describe the algorithms give some theoretical results concerning the meaning and the choice of and report experimental results

a spherical basis function neural network for modeling auditory space this paper describes a neural network for approximation problems on the sphere the von mises basis function is introduced whose activation depends on polar rather than cartesian input coordinates the architecture of the von mises basis function vmbf neural network is presented along with the corresponding gradient descent learning rules the vmbf neural network is used to solve a particular spherical problem of approximating acoustic parameters used to model perceptual auditory space this model ultimately serves as a signal processing engine to synthesize a virtual auditory environment under headphone listening conditions advantages of the vmbf over standard planar radial basis functions rbfs are discussed

interpretations on principal components analysis of head related impulse responses in the median plane a principal components analysis of the median plane head related impulse responses hrirs in the cipic hrtf database reveals that the individual hrirs can be reconstructed by a linear combination of 12 principal components pcs within 5 of error in the least squares sense the pcs include the intersubject and interelevation variations in the median plane hrirs each pc provides sound cues for the front back discrimination and or the vertical perception there exist common systematic elevation dependencies in the weights of lower numbered pcs which contribute to the pinna head diffractions whereas the elevation dependencies in the weights of higher numbered pcs are different from subject to subject

voice activity detection method and apparatus using the same free field to eardrum transfer functions fetf s are developed by comparing auditory data for points in three dimensional space for a model ear and auditory data collected for the same listening location with a microphone each fetf is represented as a weighted sum of frequency dependent functions obtained from an expansion of the measured fetf s covariance matrix spatial transformation characteristic functions stcf s are applied to transform the weighted frequency dependent factors to functions of spatial variables for azimuth and elevation a generalized spline model is fit to each stcf to filter out noise and permit interpolation of the stcf between measured points sound is reproduced for a selected direction by synthesizing the weighted frequency dependent factors with the smoothed and interpolated stcf s

maximal azimuthal resolution needed in measurements of head related transfer functions the head related transfer function hrtf is a continuous function of sound source position measurement of the hrtf can only be undertaken at discrete positions in space however determination of angular resolutions so as to reconstruct hrtfs at unmeasured positions has been an open problem azimuthal fourier analysis was proposed to analyze the variation in the hrtf in each elevation plane as a result an azimuthal sampling theorem and a corresponding interpolation formula were derived it was proved that the maximal azimuthal resolution of measurements is 360 2q 1 where q represents the highest order in the truncation of the azimuthal fourier expansion of the hrtf the maximal azimuthal resolutions for the hrtf with and without arrival time correction were investigated results show that the arrival time correction can reduce the burden of measurements since a larger azimuthal resolution is possible without introducing obvious interpolation error a psychoacoustic experiment was also conducted t

a hybrid algorithm for selecting head related transfer function based on similarity of anthropometric structures abstract as the basic data for virtual auditory technology head related transfer function hrtf has many applications in the areas of room acoustic modeling spatial hearing and multimedia how to individualize hrtf fast and effectively has become an opening problem at present based on the similarity and relativity of anthropometric structures a hybrid hrtf customization algorithm which has combined the method of principal component analysis pca multiple linear regression mlr and database matching dm has been presented in this paper the hrtfs selected by both the best match and the worst match have been applied into obtaining binaurally auralized sounds which are then used for subjective listening experiments and the results are compared for the area in the horizontal plane the localization results have shown that the selection of hrtfs can enhance the localization accuracy and can also abate the problem of front back confusion

a comparison theorem for the iterative method with the preconditioner i s max in 1991 gunawardena et al linear algebra appl 154 156 1991 123 have reported the modified gauss seidel method with a preconditioner i s in this article we propose to use a preconditioner i smax instead of i s here smax is constructed by only the largest element at each row of the upper triangular part of a by using the lemma established neumann and plemmons linear algebra appl 88 89 1987 559 we get the comparison theorem for the proposed method simple numerical examples are also given

method and apparatus for regularizing measured hrtf for smooth 3d digital audio the present invention provides an improved hrtf modeling technique for synthesizing hrtfs with varying degrees of smoothness and generalization a plurality n of spatial characteristic function sets are regularized or smoothed before combination with corresponding eigen filter functions and summed to provide an hrtf or hrir filter having improved smoothness in a continuous auditory space a trade off is allowed between accuracy in localization and smoothness by controlling the smoothness level of the regularizing models with a lambda factor improved smoothness in the hrtf filter allows the perception by the listener of a smoothly moving sound rendering free of annoying discontinuities creating clicks in the 3d sound

learning linear pca with convex semi definite programming the aim of this paper is to learn a linear principal component using the nature of support vector machines svms to this end a complete svm like framework of linear pca svpca for deciding the projection direction is constructed where new expected risk and margin are introduced within this framework a new semi definite programming problem for maximizing the margin is formulated and a new definition of support vectors is established as a weighted case of regular pca our svpca coincides with the regular pca if all the samples play the same part in data compression theoretical explanation indicates that svpca is based on a margin based generalization bound and thus good prediction ability is ensured furthermore the robust form of svpca with a interpretable parameter is achieved using the soft idea in svms the great advantage lies in the fact that svpca is a learning algorithm without local minima because of the convexity of the semi definite optimization problems to validate the performance of svpca several experiments are conducted and numerical results have demonstrated that their generalization ability is better than that of regular pca finally some existing problems are also discussed

on the detection of dispersion in the head related transfer function because of dispersion in head related transfer functions hrtfs the interaural time difference itd varies with frequency this physical effect ought to have consequences for the size or shape of the auditory image of broadband noise because different frequency regions of the noise have different itds however virtual reality experiments suggest that human listeners are insensitive to head related dispersion the experiments of this article test that suggestion by experiments that isolate dispersion from amplitude effects in the hrtf and attempt to optimize the opportunity for detecting it nevertheless the experiments find that the only effect of dispersion is to shift the lateralization of the auditory image this negative result is explained in terms of the cross correlation function for head dispersed noise although the broad band cross correlation function differs considerably from 1 0 the cross correlation functions within bands characteristic of auditory filters do not a detailed study of the lateralization shifts show that the experimental shifts can be successfully calculated as an average of stimulus itds as weighted by raatgever s frequency weighting function thesis delft the netherlands 1980

an optimal dimensionality sampling scheme on the sphere with fast spherical harmonic transforms we develop a sampling scheme on the sphere that permits accurate computation of the spherical harmonic transform and its inverse for signals band limited at l using only l 2 samples we obtain the optimal number of samples given by the degrees of freedom of the signal in harmonic space the number of samples required in our scheme is a factor of two or four fewer than existing techniques which require either 2l 2 or 4l 2 samples we note however that we do not recover a sampling theorem on the sphere where spherical harmonic transforms are theoretically exact nevertheless we achieve high accuracy even for very large band limits for our optimal dimensionality sampling scheme we develop a fast and accurate algorithm to compute the spherical harmonic transform and inverse with computational complexity comparable with existing schemes in practice we conduct numerical experiments to study in detail the stability accuracy and computational complexity of the proposed transforms we also highlight the advantages of the proposed sampling scheme and associated transforms in the context of potential applications

approximate polytope ensemble for one class classification in this work a new one class classification ensemble strategy called approximate polytope ensemble is presented the main contribution of the paper is threefold first the geometrical concept of convex hull is used to define the boundary of the target class defining the problem expansions and contractions of this geometrical structure are introduced in order to avoid over fitting second the decision whether a point belongs to the convex hull model in high dimensional spaces is approximated by means of random projections and an ensemble decision process finally a tiling strategy is proposed in order to model non convex structures experimental results show that the proposed strategy is significantly better than state of the art one class classification methods on over 200 datasets highlightsthe methodology uses a convex hull for modeling one class classification problems random projections are used to approximate the convex hull in high dimensional spaces expansions of the approximate hulls are considered to set the optimal operating point exhaustive validation is performed on three different typologies of problems

a new preconditioned aor iterative method for l matrices li et al y t li c li s wu improvements of preconditioned aor iterative methods for l matrices j comput appl math 206 2007 656 665 have considered the modified aor method with a preconditioner i s a in this paper we present a new preconditioner i s a b instead of i s a the comparison theorems and numerical experiments show that the proposed new method can achieve faster convergence than the preconditioner introduced by li et al

computation of the head related transfer function via the fast multipole accelerated boundary element method and its spherical harmonic representation the head related transfer function hrtf is computed using the fast multipole accelerated boundary element method for efficiency the hrtf is computed using the reciprocity principle by placing a source at the ear and computing its field analysis is presented to modify the boundary value problem accordingly to compute the hrtf corresponding to different ranges via a single computation a compact and accurate representation of the hrtf termed the spherical spectrum is developed computations are reduced to a two stage process the computation of the spherical spectrum and a subsequent evaluation of the hrtf this representation allows easy interpolation and range extrapolation of hrtfs hrtf computations are performed for the range of audible frequencies up to 20khz for several models including a sphere human head models the neumann ku 100 fritz and the knowles kemar kemar manikins and head and torso model the kemar manikin comparisons between the different cases are provided comparis

letter to the editor a note on preconditioned aor method for l matrices in this note some errors in a recent article by li et al improvements of preconditioned aor iterative methods for l matrices j comput appl math 206 2007 656 665 are pointed out and some correct results are presented

boundary element method calculation of individual head related transfer function ii impedance effects and comparisons to real measurements following previous work by the author involving the calculation of an individual head related transfer function hrtf using a boundary element method bem approach impedance conditions are now included to take account of the acoustic properties of human hair in addition comparisons are made here between calculations and measured values for the hrtf of a specific individual numerous works have been published regarding the measurement of hrtfs but rarely are several methods compared for the same individual the results presented in the work compare two different measurement techniques and a computational bem for acquiring an individual hrtf impedance effects have been incorporated in the bem model for hair based on measured data providing a final set for comparison measurement results show significant variations for the same individual computational results show good agreement within the range of experimental variations definite trends are observed for many directions while the limitations of the methods are also highlighted for others the effects of incorporating hair impedance are shown to provide an improvement in the correlation of computational results indicating an affect of hair impedance on the hrtf

estimating the support of a high dimensional distribution suppose you are given some data set drawn from an underlying probability distribution p and you want to estimate a simple subset s of input space such that the probability that a test point drawn from p lies outside of s equals some a priori specified value between 0 and 1 we propose a method to approach this problem by trying to estimate a function f that is positive on s and negative on the complement the functional form of f is given by a kernel expansion in terms of a potentially small subset of the training data it is regularized by controlling the length of the weight vector in an associated feature space the expansion coefficients are found by solving a quadratic programming problem which we do by carrying out sequential optimization over pairs of input patterns we also provide a theoretical analysis of the statistical performance of our algorithm the algorithm is a natural extension of the support vector algorithm to the case of unlabeled data

a new method based on generalized taylor expansion for computing a series solution of the linear systems in this paper based on the generalized taylor expansion and using the iteration matrix g of the iterative methods we introduce a new method for computing a series solution of the linear systems this method can be used to accelerate the convergence of the basic iterative methods in addition we show that by applying the new method to a divergent iterative scheme it is possible to construct a convergent series solution and to find the convergence intervals of control parameter for special cases numerical experiments are given to show the efficiency of the new method

a model of head related transfer functions based on principal components analysis and minimum phase reconstruction free field to eardrum transfer functions hrtfs were measured from both ears of 10 subjects with sound sources at 265 different positions a principal components analysis of the resulting 5300 hrtf magnitude functions revealed that the hrtfs can be modeled as a linear combination of five basic spectral shapes basis functions and that this representation accounts for approximately 90 of the variance in the original hrtf magnitude functions hrtf phase was modeled by assuming that hrtfs are minimum phase functions and that interaural phase differences can be approximated by a simple time delay subjects judgments of the apparent directions of headphone presented sounds that had been synthesized from the modeled hrtfs were nearly identical to their judgments of sounds synthesized from measured hrtfs with fewer than five basis functions used in the model a less faithful reconstruction of the hrtf was produced and the frequency of large localization errors increased dramatically

comparison results of the preconditioned aor methods for l matrices abstract in this paper we first provide comparison results of several types of the preconditioned aor paor methods for solving a linear system whose coefficient matrix is an l matrix satisfying some weaker conditions than those used in the recent literature next we propose an application of paor method to a preconditioner of krylov subspace method lastly numerical results are provided to show that krylov subspace method with the paor preconditioner performs quite well as compared with the ilu 0 preconditioner

efficient computation of slepian functions for arbitrary regions on the sphere in this paper we develop a new method for the fast and memory efficient computation of slepian functions on the sphere slepian functions which arise as the solution of the slepian concentration problem on the sphere have desirable properties for applications where measurements are only available within a spatially limited region on the sphere and or a function is required to be analyzed over the spatially limited region slepian functions are currently not easily computed for large band limits for an arbitrary spatial region due to high computational and large memory storage requirements for the special case of a polar cap the symmetry of the region enables the decomposition of the slepian concentration problem into smaller subproblems and consequently the efficient computation of slepian functions for large band limits by exploiting the efficient computation of slepian functions for the polar cap region on the sphere we develop a formulation supported by a fast algorithm for the approximate computation of slepian functions for an arbitrary spatial region to enable the analysis of modern datasets that support large band limits for the proposed algorithm we carry out accuracy analysis of the approximation computational complexity analysis and review of memory storage requirements we illustrate through numerical experiments that the proposed method enables faster computation and has smaller storage requirements while allowing for sufficiently accurate computation of the slepian functions

head related transfer function hrtf synthesis based on a three dimensional array model and singular value decomposition an external ear model based on a three dimensional array beamformer is presented to synthesize the head related transfer functions hrtfs the array coefficients are calculated by matching the measured hrtfs with a frequency domain template in light of the characteristics of human hearing a non uniform sampling technique is also devised to reduce the problem to a manageable size the model matching problem is then solved by using singular value decomposition procedure numerical simulations are carried out to investigate various array configurations in relation to approximation performance a subjective experiment of sound localization is undertaken to demonstrate the validity of the proposed technique from the results the proposed beamformer based technique proves to be an effective method for modeling the hrtfs

a local representation of the head related transfer function spatial descriptions of the head related transfer function hrtf using spherical harmonics which is commonly used for the purpose consider all directions simultaneously however in perceptual studies it is necessary to model hrtfs with different angular resolutions at different directions to this end an alternative spatial representation of the hrtf based on local analysis functions is introduced the proposal is shown to have the potential to describe the local features of the hrtf this is verified by comparing the reconstruction error achieved by the proposal to that of the spherical harmonic decomposition when reconstructing the hrtf inside a spherical cap

intrinsic limits of dimensionality and richness in random multipath fields we study the dimensions or degrees of freedom of farfield multipath that is observed in a limited source free region of space the multipath fields are studied as solutions to the wave equation in an infinite dimensional vector space we prove two universal upper bounds on the truncation error of fixed and random multipath fields a direct consequence of the derived bounds is that both fixed and random multipath fields have an effective finite dimension for circular and spherical spatial regions we show that this finite dimension is proportional to the radius and area of the region respectively we use the karhunen loegraveve kl expansion of random multipath fields to quantify the notion of multipath richness the multipath richness is defined as the number of significant eigenvalues in the kl expansion that achieve 99 of the total multipath energy we establish a lower bound on the largest eigenvalue this lower bound quantifies to some extent the well known reduction of multipath richness with reducing the angular power spread of multipath angular power spectrum

differential and weighted slepian concentration problems on the sphere in this work we present a generalized formulation of the slepian concentration problem on the sphere for finding band limited functions with an optimal concentration in the spatial domain by introducing weighting functions in the formulation of classical slepian concentration problem and assigning different values to these weighting functions we present two variants of the concentration problem namely the differential and the weighted slepian concentration problem in the differential slepian concentration problem we consider two regions on the sphere and find band limited functions such that the energy is maximized in one region at the expense of the energy in the other region we propose non negative weighting using a spatial window function to formulate and solve the weighted slepian concentration problem each problem can be solved by formulating it in the harmonic domain as an eigenvalue problem the solution of which yields eigenfunctions that serve as alternative basis functions for the representation of band limited signals and are referred to as slepian functions we also present and analyse the properties of the slepian functions to support the applications in acoustics and cosmology we also provide a demonstration for the use of the proposed slepian functions for the robust signal modeling and the estimation of the energy spectrum of red and white stochastic processes on the sphere

recovery of individual head related transfer functions from a small set of measurementsa head related transfer functions hrtfs vary with individuals and in practice measuring hrtfs with high directional resolution for each individual is tiresome based on a basis functions representation of hrtfs the present work proposes a method for recovering individual hrtfs from a small set of measurements the hrtfs are represented by a combination of a small set of spatial basis functions sbfs with frequency and individual dependent weights the sbfs are derived by applying spatial principal component analysis to a baseline hrtf dataset with high directional resolution the individual weights for any subject outside the dataset are estimated from measurements at a few source directions and then the hrtfs with high directional resolution are recovered by combining the sbfs and the individual weights in an illustrative case the sbfs derived from a baseline dataset that includes 20 subjects are used to recover the hrtf magnitudes for six subjects outside the baseline dataset results show that individual hrtf magnitudes can be recovered from measurements at 73 directions with a mean signal to distortion ratio of 19 db the proposed method is also applicable to recovering head related impulse responses the results of psychoacoustic experiments indicate that in most cases the recovered and measured hrtfs are indistinguishable

localized analysis of signals on the sphere over polygon regions to support localized signal analysis on the sphere for applications in geophysics cosmology acoustics and beyond we develop a framework for the analytic evaluation of the integral of spherical signals and for the analytic solution of the slepian spatial spectral concentration problem over simple spherical polygons we propose a polygon right angle triangulation method for the division of a simple spherical polygon into spherical right angle triangles which allows us to decompose the problem of integrating signals or solving the spatial spectral concentration problem over the polygon region into sub problems that require the evaluation of the integral of complex exponential functions over spherical right angle triangles of arbitrary orientation and position we derive closed form expressions for the evaluation of such integrals by appropriately choosing the rotations and using wigner d functions the proposed framework enables us to solve the slepian spatial spectral concentration problem for simple spherical polygons resulting in bandlimited spatially optimally concentrated basis functions for signal representation and reconstruction localized analysis and signal modeling on the sphere we also present convergence criterion for the infinite series expansions involved in the evaluation of the integral of complex exponential functions and establish the validity of the proposed developments by evaluating the integral and computing the slepian basis functions over the geographical region of australia and the volcanic plateau of tharsis using the earth and mars topography maps respectively

regularized principal manifolds many settings of unsupervised learning can be viewed as quantization problems the minimization of the expected quantization error subject to some restrictions this allows the use of tools such as regularization from the theory of supervised risk minimization for unsupervised learning this setting turns out to be closely related to principal curves the generative topographic map and robust coding we explore this connection in two ways 1 we propose an algorithm for finding principal manifolds that can be regularized in a variety of ways and 2 we derive uniform convergence bounds and hence bounds on the learning rates of the algorithm in particular we give bounds on the covering numbers which allows us to obtain nearly optimal learning rates for certain types of regularization operators experimental results demonstrate the feasibility of the approach