on the relationship between robust minimum variance beamformers with probabilistic and worst case distortionless response constraints an interesting relationship between the probability constrained and worst case optimization based robust minimum variance mv beamformers has been discovered it is shown that both in the cases of circularly symmetric gaussian and worst case distributions of the steering vector mismatch the probability constrained robust mv beamforming problem can be tightly approximated as a convex second order cone programming socp problem the latter problem is mathematically equivalent to that resulting from the deterministic worst case approach and therefore probability constrained beamformers can be interpreted and implemented using their deterministic worst case counterparts however an important advantage of the developed probability constrained mv beamformers with respect to their standard worst case counterparts is that the former approaches enable to explicitly quantify the parameters of the uncertainty region in terms of the beamformer outage probability

pure tone threshold estimation from extrapolated distortion product otoacoustic emission i o functions in normal and cochlear hearing loss ears a new method for direct pure tone threshold estimation from input output functions of distortion product otoacoustic emissions dpoaes in humans is presented previous methods use statistical models relating dpoae level to hearing threshold including additional parameters e g age or slope of dpoae i o function here we derive a dpoae threshold from extrapolated dpoae i o functions directly cubic 2 f1 f2 distortion products and pure tone threshold at f2 were measured at 51 frequencies between f2 500 hz and 8 khz at up to ten primary tone levels between l2 65 and 20 db spl in 30 normally hearing and 119 sensorineural hearing loss ears using an optimized primary tone level setting l1 0 4l2 39 db that accounts for the nonlinear interaction of the two primaries at the dpoae generation site at f2 the pressure of the 2 f1 f2 distortion product pdp is a linear function of the primary tone level l2 linear regression yields correlation coefficients higher than 0 8 in the majority of the dpoae i o functions

adaptive filtering in subbands with critical sampling analysis experiments and application to acoustic echo cancellation an exact analysis of the critically subsampled two band modelization scheme is given and it is demonstrated that adaptive cross filters between the subbands are necessary for modelization with small output errors it is shown that perfect reconstruction filter banks can yield exact modelization these results are extended to the critically subsampled multiband schemes and important computational savings are seen to be achieved by using good quality filter banks the problem of adaptive identification in critically subsampled subbands is considered and an appropriate adaptation algorithm is derived the authors give a detailed analysis of the computational complexity of all the discussed schemes and experimentally verify the theoretical results that are obtained the adaptive behavior of the subband schemes that were tested is discussed

the bandwidth performance of a two element adaptive array with tapped delay line processing the bandwidth performance of a two element adaptive array with a tapped delay line behind each element is examined it is shown how the number of taps and the delay between taps affect the bandwidth performance of the array an array with two weights and one delay behind each element is found to yield optimal performance equal to that obtained with continuous wave interference for any value of intertap delay between zero and t sub 90 b where t sub 90 is a quarter wavelength delay time and b is the fractional signal bandwidth delays less that t sub 90 yield optimal performance but result in large array weights delays larger than t sub 90 b yield suboptimal signal to interference plus noise ratio when each element has only two weights for delays between t sub 90 b and 4t sub 90 b the performance is suboptimal with only two taps but approaches the optimal if more taps are added to each element delays larger than t sub 90 b result in suboptimal performance regardless of the number of taps used

otoacoustic emissions from normal hearing and hearing impaired subjects distortion product responses distortion product otoacoustic emissions dpoae were measured in normal hearing and hearing impaired human subjects analyses based on decision theory were used to evaluate dpoae test performance specifically relative operating characteristic roc curves were constructed and the areas under these curves were used to estimate the extent to which normal and impaired ears could be correctly identified by these measures dpoae amplitude and dpoae noise measurements were able to distinguish between normal and impaired subjects at 4000 8000 and to a lesser extent at 2000 hz the ability of these measures to distinguish between groups decreased however as frequency and audiometric criterion used to separate normal and hearing impaired ears decreased at 500 hz performance was no better than chance regardless of the audiometric criterion for normal hearing cumulative distributions of misses hearing impaired ears incorrectly identified as normal hearing and false alarms normal hearing ears identified as hearing impaired were constructed and used to evaluate test performance for a range of hit rates i e the percentage of correctly identified hearing impaired ears depending on the desired hit rate criterion values of 5 to 12 db spl for dpoae amplitudes and 8 to 15 db for dpoae noise accurately distinguished normal hearing ears from those with thresholds greater than 20 db hl for the two frequencies at which performance was best 4000 and 8000 hz it would appear that dpoae measurements can be used to accurately identify the presence of high frequency hearing loss but are not accurate predictors of hearing status at lower frequencies at least for the conditions of the present measurements

reducing reflected contributions to ear canal distortion product otoacoustic emissions in humans distortion product otoacoustic emission dpoae fine structure has been attributed to the interaction of two cochlear source mechanisms distortion and reflection sources a suppressor presented near the 2f1 f2 frequency reduces the reflection source contribution and therefore dpoae fine structure optimal relationships between stimulus and suppressor conditions however have not been described in this study the relationship between suppressor level l3 and stimulus level l2 was evaluated to determine the l3 that was most effective at reducing fine structure subjects were initially screened to find individuals who produced dpoae fine structure a difference in the prevalence of fine structure in two frequency intervals was observed at 2 khz 11 of 12 subjects exhibited fine structure as compared to 5 of 22 subjects at 4 khz only subjects demonstrating fine structure participated in subsequent measurements dpoae responses were evaluated in 1 3 octave intervals centered at 2 or 4 khz with 4 subjects contributing data at each interval multiple l3 s were evaluated for each l2 which ranged from 20 to 80 db spl the results indicated that one or more l3 s at each l2 were roughly equally effective at reducing dpoae fine structure however no single l3 was effective at all l2 s in every subject

shrinkage of covariance matrices for linear signal estimation using cross validation linear estimation of signals is often based on covariance matrices estimated from training which can perform poorly if the training data are limited and the estimated covariance matrices are ill conditioned shrinking the covariance matrix toward a scaled identity matrix can improve the robustness against the model uncertainty provided the shrinkage factor is appropriately chosen this paper introduces several cross validation schemes for choosing the shrinkage factors in applications where the covariance matrices are replaced with sample covariance matrices or constructed from least squares estimates of the linear model parameters for cases where the training and out of training data are identically distributed we derive leave one out cross validation loocv schemes that repeatedly split the training data with respect to time to determine the optimal shrinkage factors for either model fitting or signal estimation for cases where they are distributed differently we develop alternative loocv schemes that repeatedly split the out of training observations with respect to space we derive computationally efficient implementations of those schemes and provide examples to demonstrate their performance

fine structure of the 2f1 f2 acoustic distortion product changes with primary level the fine frequency structure of the 2f1 f2 acoustic distortion product adp fine structure was examined in ten human subjects with normal hearing primary frequencies f1 and f2 were incremented in steps of 1 32 octave with an f2 f1 ratio of 1 2 the primary levels were kept equal to each other and varied from 45 to 65 db spl in 2 5 db steps the results show that the adp fine structure is characterized by a series of peaks and valleys across frequency with a peak to peak frequency spacing of about 3 32 octave and a peak to valley amplitude ratio of up to 20 db at frequencies below 4000 hz as primary level increases the sharpness of the adp fine structure is not significantly reduced and the pattern gradually shifts to lower frequencies at frequencies above 4000 hz a flattening of the pattern is sometimes observed at high levels a consequence of the underlying process responsible for the fine structure is that adp input output i o functions can be highly variable in shape dramatic shape change

measuring distortion product otoacoustic emissions using continuously sweeping primaries distortion product otoacoustic emission dpoae level from normal hearing individuals can vary by as much as 30db with small frequency changes a phenomenon known as dpoae fine structure this fine structure is hypothesized to stem from the interaction of components from two different regions of the cochlea the nonlinear generator region and the reflection component from the dp region an efficient procedure to separate these two components would improve the clinical and research utility of dpoae by permitting separate evaluation of different cochlea regions in this paper two procedures for evaluating dpoae fine structure are compared dpoae generated by fixed frequency primaries versus continuously sweeping primaries the sweep dpoae data are analyzed with a least squares fit filter sweep rates of greater than 8s per octave permit rapid evaluation of the cochlear fine structure a higher sweep rate of 2s per octave provided dpoae without fine structure under these conditions the longer latency reflection component falls outside the range of the filter consequently dpoae obtained with sweeping tones can be used either to get more rapid estimates of dpoae fine structure or to obtain estimates of dpoae from the generator region uncontaminated by energy from the reflection region

a bayesian approach to robust adaptive beamforming an adaptive beamformer that is robust to uncertainty in source direction of arrival doa is derived using a bayesian approach the doa is assumed to be a discrete random variable with a known a priori probability density function pdf that reflects the level of uncertainty in the source doa the resulting beamformer is a weighted sum of minimum variance distortionless response mvdr beamformers pointed at a set of candidate doas where the relative contribution of each mvdr beamformer is determined from the a posteriori pdf of the doa conditioned on previously observed data a simple approximation to the a posteriori pdf results in a straightforward implementation performance of the approximate bayesian beamformer is compared with linearly constrained minimum variance lcmv beamformers and data driven approaches that attempt to estimate signal characteristics or the steering vector from the data

distortion product otoacoustic emission input output characteristics in normal hearing and hearing impaired human ears dpoae input output i o functions were measured at 7f2 frequencies 1 to 8 khz f2 f1 1 22 over a range of levels 5 to 95 db spl in normal hearing and hearing impaired human ears l1 l2 was level dependent in order to produce the largest 2f1 f2 responses in normal ears system distortion was determined by collecting dp data in six different acoustic cavities these data were used to derive a multiple linear regression model to predict system distortion levels the model was tested on cochlear implant users and used to estimate system distortion in all other ears at most but not all f2 s measurements in cochlear implant ears were consistent with model predictions at all f2 frequencies the ears with normal auditory thresholds produced i o functions characterized by compressive nonlinear regions at moderate levels with more rapid growth at low and high stimulus levels as auditory threshold increased dpoae threshold increased accompanied by dpoae amplitude reductions notably over the range of levels where normal ears showed compression the slope of the i o function was steeper in impaired ears the data from normal hearing ears resembled direct measurements of basilar membrane displacement in lower animals data from ears with hearing loss showed that the compressive region was affected by cochlear damage however responses at high levels of stimulation resembled those observed in normal ears

relation of distortion product otoacoustic emission input output functions to loudness the aim of this study is to further explore the relationship between distortion product otoacoustic emission dpoae measurements and categorical loudness scaling cls measurements using multiple linear regression mlr analysis recently thorson et al j acoust soc am 131 1282 1295 2012 obtained predictions of cls loudness ratings from dpoae input output i o functions using mlr analysis the present study extends that work by 1 considering two different and potentially improved mlr models one for predicting loudness rating at specified input level and the other for predicting the input level for each loudness category and 2 validating the new models predictions using an independent set of data strong correlations were obtained between predicted and measured data during the validation process with overall root mean square errors in the range 10 43 16 78 db for the prediction of cls input level supporting the view that dpoae i o measurements can predict cls loudness ratings and input levels and thus may be useful for fitting hearing aids

technical efficiency estimation with multiple inputs and multiple outputs using regression analysis regression and linear programming provide the basis for popular techniques for estimating technical efficiency regression based approaches are typically parametric and can be both deterministic or stochastic where the later allows for measurement error in contrast linear programming models are nonparametric and allow multiple inputs and outputs the purported disadvantage of the regression based models is the inability to allow multiple outputs without additional data on input prices in this paper deterministic cross sectional and stochastic panel data regression models that allow multiple inputs and outputs are developed notably technical efficiency can be estimated using regression models characterized by multiple input multiple output environments without input price data we provide multiple examples including a monte carlo analysis

correspondence between behavioral and individually optimized otoacoustic emission estimates of human cochlear input output curves previous studies have shown a high within subject correspondence between distortion product otoacoustic emission dpoae input output i o curves and behaviorally inferred basilar membrane bm i o curves for frequencies above 2 khz for lower frequencies dpoae i o curves contained notches and plateaus that did not have a counterpart in corresponding behavioral curves it was hypothesized that this might improve by using individualized optimal dpoae primary levels here data from previous studies are re analyzed to test this hypothesis by comparing behaviorally inferred bm i o curves and dpoae i o curves measured with well established group average primary levels and two individualized primary level rules one optimized to maximize dpoae levels and one intended for primaries to evoke comparable bm responses at the f2 cochlear region test frequencies were 0 5 1 and 4 khz behavioral i o curves were obtained from temporal forward masking curves results showed high within subject correspondence between behavioral and dpoae i o curves at 4 khz only regardless of the primary level rule plateaus and notches were equally common in low frequency dpoae i o curves for individualized and group average dpoae primary levels at 0 5 and 1 khz results are discussed in terms of the adequacy of dpoae i o curves for inferring individual cochlear nonlinearity characteristics

reliability of distortion product otoacoustic emissions and their relation to loudness the reliability of distortion product otoacoustic emission dpoae measurements and their relation to loudness measurements was examined in 16 normal hearing subjects and 58 subjects with hearing loss the level of the distortion product l d was compared across two sessions and resulted in correlations that exceeded 0 90 the reliability of dpoaes was less when parameters from nonlinear fits to the input output i o functions were compared across visits next the relationship between dpoae i o parameters and the slope of the low level portion of the categorical loudness scaling cls function soft slope was assessed correlations of 0 65 0 74 and 0 81 at 1 2 and 4 khz were observed between cls soft slope and combined dpoae parameters behavioral threshold had correlations of 0 82 0 83 and 0 88 at 1 2 and 4 khz with cls soft slope combining dpoaes and behavioral threshold provided little additional information lastly a multivariate approach utilizing the entire dpoae i o function was used to predict the cls rating for each input level db spl standard error of the estimate when using this method ranged from 2 4 to 3 0 categorical units cu suggesting that dpoae i o functions can predict cls measures within the cu step size used in this study 5

linear minimax regret estimation of deterministic parameters with bounded data uncertainties we develop a new linear estimator for estimating an unknown parameter vector x in a linear model in the presence of bounded data uncertainties the estimator is designed to minimize the worst case regret over all bounded data vectors namely the worst case difference between the mean squared error mse attainable using a linear estimator that does not know the true parameters x and the optimal mse attained using a linear estimator that knows x we demonstrate through several examples that the minimax regret estimator can significantly increase the performance over the conventional least squares estimator as well as several other least squares alternatives

notes on technical efficiency estimation with multiple inputs and outputs collier johnson and ruggiero 2011 deal with the problem of estimating technical efficiency using regression analysis that allows multiple inputs and outputs this revives an old problem in the analysis of production in this note we provide an alternative maximum likelihood estimator that addresses the concerns a monte carlo experiment shows that the technique works well in practice a test for homotheticity a critical assumption in collier johnson and ruggiero 2011 is constructed and its behavior is examined using monte carlo simulation and an empirical application to european banking

a competitive mean squared error approach to beamforming we treat the problem of beamforming for signal estimation where the goal is to estimate a signal amplitude from a set of array observations conventional beamforming methods typically aim at maximizing the signal to interference plus noise ratio sinr however this does not guarantee a small mean squared error mse so that on average the resulting signal estimate can be far from the true signal here we consider strategies that attempt to minimize the mse between the estimated and unknown signal waveforms the methods we suggest all maximize the sinr but at the same time are designed to have good mse performance since the mse depends on the signal power which is unknown we develop competitive beamforming approaches that minimize a robust mse measure two design strategies are proposed minimax mse and minimax regret we demonstrate through numerical examples that the suggested minimax beamformers can outperform several existing standard and robust methods over a wide range of signal to noise ratio snr values finally we apply our techniques to subband beamforming and illustrate their advantage in estimating a wideband signal

minimax estimation of deterministic parameters in linear models with a random model matrix we consider the problem of estimating an unknown deterministic parameter vector in a linear model with a random model matrix with known second order statistics we first seek the linear estimator that minimizes the worst case mean squared error mse across all parameter vectors whose possibly weighted norm is bounded above we show that the minimax mse estimator can be found by solving a semidefinite programming problem and develop necessary and sufficient optimality conditions on the minimax mse estimator using these conditions we derive closed form expressions for the minimax mse estimator in some special cases we then demonstrate through examples that the minimax mse estimator can improve the performance over both a baysian approach and a least squares method we then consider the case in which the norm of the parameter vector is also bounded below since the minimax mse approach cannot account for a nonzero lower bound we consider in this case a minimax regret method in which we seek the estimator that minimizes the worst case difference between the mse attainable using a linear estimator that does not know the parameter vector and the optimal mse attained using a linear estimator that knows the parameter vector for analytical tractability we restrict our attention to the scalar case and develop a closed form expression for the minimax regret estimator

distortion product otoacoustic emissions cochlear source contributions and clinical test performance it has been proposed that the clinical accuracy of distortion product otoacoustic emissions dpoaes is affected by the interaction of distortion and reflection sources contributing to the response this study evaluated changes in dichotomous decision test performance and threshold prediction accuracy when dpoae source contribution was controlled data were obtained from 205 normal and impaired ears with l2 ranging from 0 to 80db spl and f2 2 and 4khz data were collected for control conditions no suppressor f3 and with f3 presented at three levels that previously had been shown to reduce the reflection source contribution the results indicated that controlling source contribution with a suppressor did not improve diagnostic accuracy as reflected by relative operating characteristic curve area and frequently resulted in poorer test performance compared to control conditions likewise correlations between dpoae and behavioral thresholds were not strengthened when using the suppressors to control sou

a competitive minimax approach to robust estimation of random parameters we consider the problem of estimating in the presence of model uncertainties a random vector x that is observed through a linear transformation h and corrupted by additive noise we first assume that both the covariance matrix of x and the transformation h are not completely specified and develop the linear estimator that minimizes the worst case mean squared error mse across all possible covariance matrices and transformations h in the region of uncertainty although the minimax approach has enjoyed widespread use in the design of robust methods we show that its performance is often unsatisfactory to improve the performance over the minimax mse estimator we develop a competitive minimax approach for the case where h is known but the covariance of x is subject to uncertainties and seek the linear estimator that minimizes the worst case regret namely the worst case difference between the mse attainable using a linear estimator ignorant of the signal covariance and the optimal mse attained using a linear estimator that knows the signal covariance the linear minimax regret estimator is shown to be equal to a minimum mse mmse estimator corresponding to a certain choice of signal covariance that depends explicitly on the uncertainty region we demonstrate through examples that the minimax regret approach can improve the performance over both the minimax mse approach and a plug in approach in which the estimator is chosen to be equal to the mmse estimator with an estimated covariance matrix replacing the true unknown covariance we then show that although the optimal minimax regret estimator in the case in which the signal and noise are jointly gaussian is nonlinear we often do not lose much by restricting attention to linear estimators

robust competitive estimation with signal and noise covariance uncertainties robust estimation of a random vector in a linear model in the presence of model uncertainties has been studied in several recent works while previous methods considered the case in which the uncertainty is in the signal covariance and possibly the model matrix but the noise covariance is assumed to be completely specified here we extend the results to the case where the noise statistics may also be subjected to uncertainties we propose several different approaches to robust estimation which differ in their assumptions on the given statistics in the first method we assume that the model matrix and both the signal and the noise covariance matrices are uncertain and develop a minimax mean squared error mse estimator that minimizes the worst case mse in the region of uncertainty the second strategy assumes that the model matrix is given and tries to uniformly approach the performance of the linear minimum mse estimator that knows the signal and noise covariances by minimizing a worst case regret measure the regret is defined as the difference or ratio between the mse attainable using a linear estimator ignorant of the signal and noise covariances and the minimum mse possible when the statistics are known as we show earlier solutions follow directly from our more general results however the approach taken here in developing the robust estimators is considerably simpler than previous methods

robustness of adaptive narrowband beamforming with respect to bandwidth this paper addresses the robustness of adaptive narrowband beamforming with respect to bandwidth based on the loss of performance in terms of signal to interference plus noise ratio sinr the criterion used by zatman to define a narrowband environment i e the ratio between the jammer plus noise covariance matrix and the noise eigenvalue is studied from the point of view of a loss of sinr after narrowband beamforming under non narrowband conditions using theoretical results about the eigenvalues and eigenvectors of covariance matrices for signals closely spaced in frequency by lee it is shown that zatman s criterion can be interpreted as an upper bound on the sinr loss which is nearly reached under certain conditions that are specified

cochlear generation of intermodulation distortion revealed by dpoae frequency functions in normal and impaired ears distortion product otoacoustic emission dpoae frequency functions were measured in normal hearing and hearing impaired ears a fixed f2 swept f1 paradigm was used with f2 fixed at half octave intervals from 1 to 8 khz l1 was always 10 db greater than l2 and l2 was varied from 65 to 10 db spl in 5 db steps the responses were quantified by the frequency and amplitude of the peak response peak responses were closer to f2 in higher frequency regions and for lower intensity stimulation results from hearing impaired subjects suggest that audiometric thresholds at the distortion product frequency fdp in addition to hearing status at f2 can affect dpoae results results are discussed in terms of several manifestations of a second resonance model as well as a dual source model for the generation of dpoaes as measured in the ear canal of humans it appears that a dual source model accounts for the data better than second filter models

analysis of parameters for the estimation of loudness from tone burst otoacoustic emissions there is evidence that tone burst otoacoustic emissions tboaes might be useful for estimating loudness however within listener comparisons between loudness and tboae measurements are an essential prerequisite to determine appropriate analysis parameters for loudness estimation from tboae measurements the purpose of the present work was to collect tboae measurements and loudness estimates across a wide range of levels in the same listeners therefore tboaes were recorded for 1 and 4 khz stimuli and then analyzed using a wide range of parameters to determine which parameter set yielded the lowest mean square error estimation of loudness with respect to a psychoacoustical cross modality matching procedure and the inflected exponential inex loudness model the present results show strong agreement between 1 khz loudness estimates derived from tboaes and loudness estimated using cross modality matching cmm with tboae estimation accounting for almost 90 of the cmm variance additionally the results indicate that analysis parameters may vary within a reasonable range without compromising the results i e the estimates exhibit some parametric robustness the lack of adequate parametric optimization for tboaes at 4 khz suggests that measurements at this frequency are strongly contaminated by ear canal resonances meaning that deriving loudness estimates from tboaes at this frequency is significantly more challenging than at 1 khz

loudness growth in 1 2 octave bands lgob a procedure for the assessment of loudness in this paper a method that has been developed for the assessment and quantification of loudness perception in normal hearing and hearing impaired persons is described the method has been named lgob which stands for loudness growth in 1 2 octave bands the method uses 1 2 octave bands of noise centered at 0 25 0 5 1 0 2 0 and 4 0 khz with subjective levels between a subject s threshold of hearing and the too loud level the noise bands are presented to the subject randomized over frequency and level and the subject is asked to respond with a loudness rating one of very soft soft ok loud very loud too loud subject responses normal and hearing impaired are then compared to the average responses of a group of normal hearing subjects this procedure allows one to estimate the subject s loudness growth relative to normals as a function of frequency and level the results may be displayed either as isoloudness contours or as recruitment curves in its present form the measurements take less than 30 min the signal presentation and analysis is done using a pc and a pc plug in board having a digital to analog converter

the use of distortion product otoacoustic emission suppression as an estimate of response growth distortion product otoacoustic emission dpoae levels in response to primary pairs f2 2 or 4 khz l2 ranging from 20 to 60 db spl l1 0 4l2 39 db were measured with and without suppressor tones f3 which varied from 1 octave below to 12 octave above f2 in normal hearing subjects suppressor level l3 varied from 5 to 85 db spl dpoae levels were converted into decrements by subtracting the level in the presence of the suppressor from the level in the absence of a suppressor dpoae decrement vs l3 functions showed steeper slopes when f3 f2 this pattern is similar to other measurements of response growth such as direct measures of basilar membrane motion single unit rate level functions suppression of basilar membrane motion and discharge rate suppression from lower animals as l2 increased the l3 necessary to maintain 3 db of suppression increased at a rate of about 1 db db when f3 was approximately equal to f2 but increased more slowly when f3 f2 functions r

asymptotically optimal linear shrinkage of sample lmmse and mvdr filters conventional implementations of the linear minimum mean square lmmse and minimum variance distortionless response mvdr estimators rely on the sample matrix inversion smi technique i e on the sample covariance matrix scm this approach is optimal in the large sample size regime nonetheless in small sample size situations those sample estimators suffer a large performance degradation thus the aim of this paper is to propose corrections of these sample methods that counteract their performance degradation in the small sample size regime and keep their optimality in large sample size situations to this aim a twofold approach is proposed first shrinkage estimators are considered as they are known to be robust to the small sample size regime namely the proposed methods are based on shrinking the sample lmmse or sample mvdr filters towards a variously called matched filter or conventional bartlett beamformer in array processing second random matrix theory is used to obtain the optimal shrinkage factors for large filters the simulation results highlight that the proposed methods outperform the sample lmmse and mvdr also provided that the sample size is higher than the observation dimension they improve classical diagonal loading dl and ledoit wolf lw techniques which counteract the small sample size degradation by regularizing the scm finally compared to state of the art dl the proposed methods reduce the computational cost and the proposed shrinkage of the lmmse obtains performance gains

rate of loudness growth for pure tones in normal and impaired hearing the present article provides an analysis of loudness growth rates in normal and cochlear impaired hearing for diverse groups with respect to age and backgrounds slopes are obtained from absolute magnitude estimation and magnitude production of loudness measured values and from cross modality matching and absolute magnitude estimation of apparent length predicted values consistent with an earlier study r p hellman and c h meiselman j acoust soc am 88 2596 2606 1990 slopes calculated within the 15 30 db stimulus range above the elevated threshold increase in size with the degree of hearing loss the corresponding range of loudness values in normal hearing yields a slope near 0 60 independent of the threshold levels this pattern of loudness growth holds for individuals and groups but the intersubject variability of the slope is more labile being larger across than within groups and larger for the measured slopes than for the predicted values determined from the predicted slopes the coefficient of variation sigma m is approximately constant in normal and impaired hearing ranging from 20 27 in contrast sigma m obtained from the measured slopes increases with the degree of hearing loss to a value of almost 50 for a 75 db loss the overall stability and systematics of the observed effects further demonstrate that the loudness intensity relation can be specified with reasonable precision and accuracy from cross modality matching

broadband beamforming using tdl form iir filters conventional broadband beamforming structures make use of finite impulse response fir filters in each channel large numbers of coefficients are required to retain the desired signal to interference plus noise ratio sinr performance as the operating bandwidth increases it has been proven that the optimal frequency dependent array weighting of broadband beamformers could be better approximated by infinite impulse response iir filters however some potential problems such as stability monitoring and sensitivity to quantization errors of the iir filters make the implementation of the iir beamformers difficult in this paper new broadband iir beamformers are proposed to solve these problems the main contributions of this paper include 1 the frost based and generalized sidelobe canceller gsc based broadband beamformers utilizing a kind of tapped delay line form tdl form iir filters are proposed 2 the combined recursive gauss newton rgn algorithm is designed to compute the feedforward and feedback weights in the frost based implementation and 3 in the gsc based structure the unconstrained rgn algorithm is customized for the tdl form iir filters in the adaptive beamforming part compared with the beamformer using direct form iir filters the new iir beamformers offer much easier stability monitoring and less sensitivity to the coefficient quantization while comparable sinr improvement over the conventional fir beamformer is achieved

similarity in loudness and distortion product otoacoustic emission input output functions implications for an objective hearing aid adjustment the aim of the present study was to compare distortion product otoacoustic emissions dpoaes to loudness with regard to the potentiality of dpoaes to determine characteristic quantities of the cochlear impaired ear and to derive objective hearing aid parameters recently neely et al j acoust soc am 114 1499 1507 2003 compared dpoae input output functions to the fletcher and munson j acoust soc am 5 82 108 1933 loudness function finding a close resemblance in the slope characteristics of both measures the present study extended their work by performing both loudness and dpoae measurements in the same subject sample and by developing a method for the estimation of gain needed to compensate for loss of cochlear sensitivity and compression dpoaes and loudness exhibited similar behavior when plotted on a logarithmic scale and slope increased with increasing hearing loss confirming the findings of neely et al to compensate for undesired nonpathological impacts on the magnitude of dpoae level normalization of dpoae data was implemented a close resemblance between gain functions based on loudness and normalized dpoae data was achieved these findings suggest that dpoaes are able to quantify the loss of cochlear sensitivity and compression and thus might provide parameters for a noncooperative hearing aid adjustment

consistent reduced rank lmmse estimation with a limited number of samples per observation dimension an improved construction of the optimal reduced rank linear minimum mean square error mmse estimator of a signal waveform of interest is derived that is consistent under a limited number of samples per filtering degree of freedom the new filter design generalizes traditional filter realizations based on directly replacing the theoretical covariance matrix by its sample estimate and being consistent when all dimensions in the model but the number of samples remain bounded our solution not only generalizes the conventional estimator but also turns out to appropriately characterize model mismatch constraints due to finite sample size limitations of fundamental importance in practical situations the proposed implementation results from a generalized consistent estimation of the set of mmse filter subspace coefficients on the reduced dimensional subspace results are based on the theory of the spectral analysis of large dimensional random matrices in particular we build on the analytical description of the asymptotic spectrum of sample covariance type matrices in the limiting regime defined as both the number of samples and the observation dimension grow without bound at the same rate as a result the proposed mmse signal waveform estimator is shown to present a superior mean square error performance under a finite sample size by avoiding the breakdown experienced as the selected rank increases

modeling distortion product otoacoustic emission input output functions using segmented regression distortion product otoacoustic emissions dpoaes are low level acoustic signals the detection of which involves extraction from a background of noise boege and janssen j acoust soc am 111 1810 1818 2002 described a method for modeling the presence and growth of these responses while improving growth function parameter estimation this technique excludes a significant fraction of the data especially low level responses and relies on ad hoc model fit acceptance criteria the statistical difficulties associated with these limitations are described and a weighted segmented linear regression model that avoids them is proposed a simple test is presented for the presence of dpoae growth this technique is compared to that of boege and janssen in a dataset of 9 556 input output i o functions collected over 4years on 866 ears from 379 construction apprentices and 63 age matched controls comparisons are made on the entire dataset and within audiometric hearing loss categories segmented regress

distortion product otoacoustic emission measured with continuously varying stimulus level distortion product otoacoustic emissions dpoae are measured by stimulating the ear with two simultaneous tones a novel method for measuring dpoaes has been developed in which the tone levels vary continuously instead of in discrete steps varying the tone levels continuously may offer advantages for characterizing dpoae level as a function of stimulus level for equivalent primary levels dpoae levels measured with the continuous level method were the same as levels obtained with the discrete level method thus validating the new method continuous level measurements were used to determine the optimal l1 for each l2 in individual subjects n 20 at f2 1 2 4 and 8 khz by using a lissajous path that covered a wide range of stimulus levels the optimal l1 defined as the l1 that resulted in the largest dpoae for each l2 varied across subjects and across frequency the optimal difference between l1 and l2 decreased with increasing l2 at all frequencies and increased with frequency when l2 was low whe

sources of distortion product otoacoustic emissions revealed by suppression experiments and inverse fast fourier transforms in normal ears primary and secondary sources combine to produce the 2f1 f2 distortion product otoacoustic emission dpoae measured in the ear canals of humans dpoaes were obtained in nine normal hearing subjects using a fixed f2 paradigm in which f1 was varied the f2 was 2 or 4 khz and absolute and relative primary levels were varied data were obtained with and without a third tone f3 placed 15 6 hz below 2f1 f2 the level of f3 was varied in order to suppress the stimulus frequency otoacoustic emission sfoae coming from the 2f1 f2 place these data were converted from the complex frequency domain into an equivalent time representation using an inverse fast fourier transform ifft iffts of unsuppressed dpoae data were characterized by two or more peaks relative amplitudes of these peaks depended on overall primary level and on primary level differences the suppressor eliminated later peaks but early peaks remained relatively unaltered results are interpreted to mean that the dpoae measured in humans includes components from the f2 place intermodulation distortion and dp place in the form of a sfoae these findings build on previous work by providing evidence that multiple peaks in the ifft are due to a secondary source at the dp place

directional distance functions optimal endogenous directions a substantial literature has dealt with the problem of estimating multiple input and multiple output production functions where inputs and outputs can be good and bad numerous studies can be found in the areas of productivity analysis industrial organization labor economics and health economics while many papers have estimated the more restrictive output and input oriented distance functions here we estimate a more general directional distance function a seminal paper on directional distance functions by chambers 1998 as well as papers by fare et al 1997 chambers et al 1998 fare and grosskopf 2000 grosskopf 2003 fare et al 2005 and hudgins and primont 2007 do not address the issue of how to choose an optimal direction set typically the direction is arbitrarily selected to be 1 for good outputs and 1 for inputs and bad outputs by estimating the directional distance function together with the first order conditions for cost minimization and profit maximization using bayesian methods we are able to estimate optimal firm specific directions for each input and output which are consistent with allocative and technical efficiency we apply these methods to an electric utility panel data set which contains firm specific prices and quantities of good inputs and outputs as well as the quantities of bad inputs and outputs estimated firm specific directions for each input and output are quite different from those normally assumed in the literature the computed firm specific technical efficiency technical change and productivity change based on estimated optimal directions are substantially higher than those calculated using fixed directions

cochlear compression estimates from measurements of distortion product otoacoustic emissions evidence of the compressive growth of basilar membrane displacement can be seen in distortion product otoacoustic emission dpoae levels measured as a function of stimulus level when the levels of the two stimulus tones f1 and f2 are related by the formula l1 39 db 0 4 l2 kummer et al j acoust soc am 103 3431 3444 1998 the shape of the function relating dpoae level to l2 is similar up to an l2 of 70 db spl to the classic fletcher and munson j acoust soc am 9 1 10 1933 loudness function when plotted on a logarithmic scale explicit estimates of compression have been derived based on recent dpoae measurements from the laboratory if dpoae growth rate is defined as the slope of the dpoae i o function in db db then a cogent definition of compression is the reciprocal of the growth rate in humans with normal hearing compression varies from about 1 at threshold to about 4 at 70 db spl with hearing loss compression is still about 1 at threshold but grows more slowly above thresh

eigenvalues and eigenvectors of covariance matrices for signals closely spaced in frequency the eigenstructures of common covariance matrices are identified for the general case of m closely spaced signals it is shown that the largest signal space eigenvalue is relatively insensitive to signal separation by contrast the ith largest eigenvalue is proportional to delta omega sup 2 i 1 or delta omega sup 4 i 1 where delta omega is a measure of signal separation therefore matrix conditioning degrades rapidly as signal separation is reduced it is also shown that the limiting eigenvectors have remarkably simple structures the results are very general and apply to planar far field direction finding problems involving almost arbitrary scenarios and also to time series analysis of sinusoids exponentials and other signals

distribution of standing wave errors in real ear sound level measurements standing waves can cause measurement errors when sound pressure level spl measurements are performed in a closed ear canal e g during probe microphone system calibration for distortion product otoacoustic emission dpoae testing alternative calibration methods such as forward pressure level fpl minimize the influence of standing waves by calculating the forward going sound waves separate from the reflections that cause errors previous research compared test performance burke et al 2010 and threshold prediction rogers et al 2010 using spl and multiple fpl calibration conditions and surprisingly found no significant improvements when using fpl relative to spl except at 8 khz the present study examined the calibration data collected by burke et al and rogers et al from 155 human subjects in order to describe the frequency location and magnitude of standing wave pressure minima to see if these errors might explain trends in test performance results indicate that while individual resu

robust adaptive beamforming for general rank signal models the performance of adaptive beamforming methods is known to degrade severely in the presence of even small mismatches between the actual and presumed array responses to the desired signal such mismatches may frequently occur in practical situations because of violation of underlying assumptions on the environment sources or sensor array this is especially true when the desired signal components are present in the beamformer training data snapshots because in this case the adaptive array performance is very sensitive to array and model imperfections the similar phenomenon of performance degradation can occur even when the array response to the desired signal is known exactly but the training sample size is small we propose a new powerful approach to robust adaptive beamforming in the presence of unknown arbitrary type mismatches of the desired signal array response our approach is developed for the most general case of an arbitrary dimension of the desired signal subspace and is applicable to both the rank one point source and higher rank scattered source fluctuating wavefront desired signal models the proposed robust adaptive beamformers are based on explicit modeling of uncertainties in the desired signal array response and data covariance matrix as well as worst case performance optimization simple closed form solutions to the considered robust adaptive beamforming problems are derived our new beamformers have a computational complexity comparable with that of the traditional adaptive beamforming algorithms while at the same time offer a significantly improved robustness and faster convergence rates

a class of constrained adaptive beamforming algorithms based on uniform linear arrays a new class of adaptive beamforming algorithms is proposed based on a uniformly spaced linear array by constraining its weight vector to a specific conjugate symmetric form the method is applied to the well known reference signal based rsb beamformer and the linearly constrained minimum variance lcmv beamformer as two implementation examples the effect of the additional constraint is equivalent to adding a second step in the derived adaptive algorithm however a difference arises for the rsb case since no direction of arrival doa information of the desired signal is available which leads to a two stage structure for incorporating the imposed constraint compared to the traditional algorithms the proposed ones can achieve a faster convergence speed and a higher steady state output signal to interference plus noise ratio given the same stepsize

categorical loudness scaling and equal loudness contours in listeners with normal hearing and hearing loss this study describes procedures for constructing equal loudness contours elcs in units of phons from categorical loudness scaling cls data and characterizes the impact of hearing loss on these estimates of loudness additionally this study developed a metric level dependent loudness loss which uses cls data to specify the deviation from normal loudness perception at various loudness levels and as function of frequency for an individual listener with hearing loss cls measurements were made in 87 participants with hearing loss and 61 participants with normal hearing an assessment of the reliability of cls measurements was conducted on a subset of the data cls measurements were reliable there was a systematic increase in the slope of the low level segment of the cls functions with increase in the degree of hearing loss elcs derived from cls measurements were similar to standardized elcs international organization for standardization iso 226 2003 the presence of hearing loss decreased the vertical spacing of the elcs reflecting loudness recruitment and reduced cochlear compression representing cls data in phons may lead to wider acceptance of cls measurements like the audiogram that specifies hearing loss at threshold level dependent loudness loss describes deficit for suprathreshold sounds such information may have implications for the fitting of hearing aids

influence of primary level and primary frequency ratios on human distortion product otoacoustic emissions the combined influence of primary level differences l1 l2 and primary frequency ratio f2 f1 on distortion product otoacoustic emission dpoae level was investigated in 20 normal hearing subjects dpoaes were recorded with continuously varying stimulus levels neely et al j acoust soc am 117 1248 1259 2005 for the following stimulus conditions f2 1 2 4 and 8 khz and f2 f1 1 05 to 1 4 various l1 l2 including one individually optimized to produce the largest dpoae for broadly spaced primary frequencies at low l2 levels the largest dpoaes were recorded when l1 was much higher than l2 with l1 remaining relatively constant as l2 increased as f2 fl decreased the largest dpoaes were observed when l1 was closer to l2 and increased as l2 increased optimal values for l1 l2 and f2 f1 were derived from these data in general average dpoae levels for the new l1 l2 and f2 f1 were equivalent to or larger than those observed for other stimulus combinations including the l1 l2 described by kummer et al j acoust soc am 103 3431 3444 1998 and those defined by neely et al in which l1 l2 was evaluated but f2 f1 was fixed at 1 2

further efforts to predict pure tone thresholds from distortion product otoacoustic emission input output functions recently boege and janssen j acoust soc am 111 1810 1818 2002 fit linear equations to distortion product otoacoustic emission dpoae input output i o functions after the dpoae level in db spl was converted into pressure in pa significant correlations were observed between these dpoae thresholds and audiometric thresholds the present study extends their work by 1 evaluating the effect of frequency 2 determining the behavioral thresholds in those conditions that did not meet inclusion criteria and 3 including a wider range of stimulus levels dpoae i o functions were measured in as many as 278 ears of subjects with normal and impaired hearing nine f2 frequencies 500 to 8000 hz in 12 octave steps were used l2 ranged from 10 to 85 db spl 5 db steps and l1 was set according to the equation l1 0 4l2 39 db kummer et al j acoust soc am 103 3431 3444 1998 for l2 levels up to 65 db spl beyond which l1 l2 for the same conditions as those used by boege and janssen we o

blind minimax estimation we consider the linear regression problem of estimating an unknown deterministic parameter vector based on measurements corrupted by colored gaussian noise we present and analyze blind minimax estimators bmes which consist of a bounded parameter set minimax estimator whose parameter set is itself estimated from measurements thus our approach does not require any prior assumption or knowledge and the proposed estimator can be applied to any linear regression problem we demonstrate analytically that the bmes strictly dominate the least squares ls estimator i e they achieve lower mean squared error mse for any value of the parameter vector both stein s estimator and its positive part correction can be derived within the blind minimax framework furthermore our approach can be readily extended to a wider class of estimation problems than stein s estimator which is defined only for white noise and nontransformed measurements we show through simulations that the bmes generally outperform previous extensions of stein s technique

robust mean squared error estimation in the presence of model uncertainties we consider the problem of estimating an unknown parameter vector x in a linear model that may be subject to uncertainties where the vector x is known to satisfy a weighted norm constraint we first assume that the model is known exactly and seek the linear estimator that minimizes the worst case mean squared error mse across all possible values of x we show that for an arbitrary choice of weighting the optimal minimax mse estimator can be formulated as a solution to a semidefinite programming problem sdp which can be solved very efficiently we then develop a closed form expression for the minimax mse estimator for a broad class of weighting matrices and show that it coincides with the shrunken estimator of mayer and willke with a specific choice of shrinkage factor that explicitly takes the prior information into account next we consider the case in which the model matrix is subject to uncertainties and seek the robust linear estimator that minimizes the worst case mse across all possible values of x and all possible values of the model matrix as we show the robust minimax mse estimator can also be formulated as a solution to an sdp finally we demonstrate through several examples that the minimax mse estimator can significantly increase the performance over the conventional least squares estimator and when the model matrix is subject to uncertainties the robust minimax mse estimator can lead to a considerable improvement in performance over the minimax mse estimator

sources of dpoaes revealed by suppression experiments inverse fast fourier transforms and sfoaes in impaired ears dpoae sources are modeled by intermodulation distortion generated near the f2 place and a reflection of this distortion near the dp place in a previous paper inverse fast fourier transforms iffts of dpoae filter functions in normal ears were consistent with this model konrad martin et al j acoust soc am 109 2862 2879 2001 in the present article similar measurements were made in ears with specific hearing loss configurations it was hypothesized that hearing loss at f2 or dp frequencies would influence the relative contributions to the dpoae from the corresponding basilar membrane places and would affect the relative magnitudes of sfoaes at frequencies equal to f2 and fdp dpoaes were measured with f2 4 khz f1 varied and a suppressor near fdp l2 was 25 55 db spl l1 l2 10 db sfoaes were measured at f2 and at 2 7 khz the average fdp produced by the f1 sweep for stimulus levels of 20 60 db spl sfoae results supported predictions of the pattern of amplitude differences between sfoaes

a projection approach for robust adaptive beamforming it is well known that calibration errors can seriously degrade performance in adaptive arrays particularly when the input signal to noise ratio is large the effect is caused by the perturbation of the presumed steering vector from its optimal value although it is not as widely known similar degradation occurs in sampled matrix inversion processing when the covariance matrix is estimated while the desired signal is present in the snapshot data under these conditions performance loss is due to errors in the estimated covariance matrix and occurs even when the steering vector is known exactly in the paper a new method based of modification of the steering vector is proposed to overcome both the problems of perturbation and of sample covariance errors the method involves projection of the presumed steering vector onto the observed signal plus interference subspace an analysis is also presented illustrating that the sample covariance errors can be viewed as a particular type of perturbation error and a simple approximation is derived for the expected beamformer performance as a function of the number of data snapshots both analytical and experimental results are presented that illustrate the advantages of the proposed method

response vector constrained robust lcmv beamforming based on semidefinite programming although linearly constrained minimum variance lcmv beamforming is robust against imprecise target information it usually leads to relatively high sidelobe and distorted mainlobe which would induce a high false alarm probability to circumvent this problem this work devises a novel robust lcmv beamforming approach by utilizing response vector optimization it intends to find the optimal response vector in lieu of the all one response vector in traditional lcmv beamformer the proposed robust beamformer is first formulated as a nonconvex quadratically constrained quadratic programming problem and then transformed into a semidefinite programming problem which can be efficiently and exactly solved the proposed beamformer not only improves the performance in terms of signal to interference plus noise ratio substantially but also possesses low sidelobe and well maintained mainlobe moreover since the response vector is quite small in size the complexity of calculating the optimal response vector is negligible additionally the proposed beamformer is also extended to two dimensional space time adaptive processing simulation results are presented to demonstrate the superiority of the proposed approach

on loudness at threshold absolute thresholds for and loudness matches between pure tones and four and ten tone complexes were used to assess the form of the function relating loudness to sensation level sl at low and moderate levels the components of the tone complexes had equal sls and were separated by one two four or six critical bands six listeners with normal hearing were tested the thresholds for the multitone complexes indicate that they generally can be detected even when the level of a single component is a few db below the threshold the average detection advantage is consistent with predictions for multiple observations in independent frequency selective auditory channels but differences among listeners are apparent the loudness matches also vary somewhat among listeners five of the six listeners matched tone complexes composed of subthreshold components to a pure tone a few db above threshold this indicates that the loudness of tones at or even below threshold is greater than zero for these five listeners a simple model of loudness summation was used to obtain loudness functions from the individual listeners loudness matches the slopes of the loudness functions log loudness plotted as a function of log intensity generally exceed unity at low levels and are near 0 2 at 40 db sl this shallow slope at moderate levels agrees with loudness functions derived from data on temporal integration of loudness the average loudness function derived from the present data also is in good agreement with a variety of previous data obtained by magnitude estimation magnitude production ratio production and measurements of binaural loudness summation