design of two dimensional digital filters using singular value decomposition and balanced approximation method it is shown that the singular value decomposition svd of the sampled amplitude response of a two dimensional 2 d digital filter possesses a special structure every singular vector is either mirror image symmetric or antisymmetric with respect to its midpoint consequently the svd can be applied along with 1 d finite impulse response fir techniques for the design of linear phase 2 d filters with arbitrary prescribed amplitude responses which are symmetrical with respect to the origin of the omega psi omega sub 2 plane the balanced approximation method is applied to linear phase 2 d fir filters of the type that may be obtained by using the svd method the method leads to economical and computationally efficient filters usually infinite impulse response filters which have prescribed amplitude responses and whose phase responses are approximately linear

effect of component relative entropy on the discrimination of simultaneous tone complexes results are reported from a number of experiments investigating the effects of stimulus uncertainty on the discrimination of simultaneous multitone complexes with few exceptions the data were well described by a model in which average threshold for the detection of a change in one or more components varies with the components relative entropy core in the complex r a lutfi j acoust soc am 94 748 758 1993 in different experiments thresholds for the detection of a change in target level were found to be linearly related to core for manipulations in the number of targets the number of context tones and the relative degree of level perturbation on tones from trial to trial the slopes of the functions did not change with measures taken at different points on the psychometric function and in most cases were close to the theoretical value of b 1 0 as predicted by strict application of the model also as predicted but for the exception of one listener increasing the level of the target beyond that of the context had little or no effect on threshold a correlational analysis of the trial by trial data revealed a tendency of listeners to give negative weight to frequencies immediately above the target and to adjust weights in response to changes in the relative degree of level perturbation though inconsistent with the basic premise of the model the variation in weights was not so great as to materially affect the predictions for mean thresholds

optimization algorithms on subspaces revisiting missing data problem in low rank matrix low rank matrix approximation has applications in many fields such as 3d reconstruction from an image sequence and 2d filter design in this paper one issue with low rank matrix approximation is re investigated the missing data problem much effort was devoted to this problem and the wiberg algorithm or the damped newton algorithm were recommended in previous studies however the wiberg or damped newton algorithms do not suit for large especially long matrices because one needs to solve a large linear system in every iteration in this paper we revitalize the usage of the levenberg marquardt algorithm for solving the missing data problem by utilizing the property that low rank approximation is a minimization problem on subspaces in two proposed implementations of the levenberg marquardt algorithm one only needs to solve a much smaller linear system in every iteration especially for long matrices simulations and experiments on real data show the superiority of the proposed algorithms though the proposed algorithms achieve a high success rate in estimating the optimal solution by random initialization as illustrated by real examples it still remains an open issue how to properly do the initialization in a severe situation that is a large amount of data is missing and with high level noise

heteroscedastic low rank matrix approximation by the wiberg algorithm low rank matrix approximation has applications in many fields such as 2 d filter design and 3 d reconstruction from an image sequence in this paper one issue with low rank matrix approximation is investigated heteroscedastic noise in most of previous research the covariance matrix of the heteroscedastic noise is assumed to be positive definite this requirement restricts the usefulness of results derived from such research in this paper we extend the wiberg algorithm which originally deals with the missing data problem with low rank approximation to the cases where the heteroscedastic noise has a singular covariance matrix experiments show that the proposed wiberg algorithm converges much faster than the bilinear approach and consequently avoids many nonconvergent cases in the bilinear approach experiments also show that to some extent the wiberg algorithm can tolerate outliers and is not sensitive to parameter variation

a recency effect in sound localization in a free field pointing task listeners localized trains of 4 32 spatially distributed gabor clicks narrowband impulses centered at 4 khz carrier frequency and repeating at an interval of 5ms multiple regression coefficients estimated the perceptual weight applied to each click in a train during location judgments temporal weighting functions obtained in this way exhibited two key features onset dominance as evidenced by high weight on the initial click and upweighting of late arriving sound as evidenced by weights that gradually increased over the duration of each click train across all tested click train durations and despite randomly varying the durations from trial to trial the greatest post onset weights were consistently found for clicks at or near the offset the results imply a special importance of late arriving sound rather than feedforward recovery from onset dominance and are broadly consistent with recency effects resulting from temporal integration

left vs right representations for solving weighted low rank approximation problems the weighted low rank approximation problem in general has no analytical solution in terms of the singular value decomposition and is solved numerically using optimization methods four representations of the rank constraint that turn the abstract problem formulation into parameter optimization problems are presented the parameter optimization problem is partially solved analytically which results in an equivalent quadratically constrained problem a commonly used re parameterization avoids the quadratic constraint and makes the equivalent problem a nonlinear least squares problem however it might be necessary to change this re parameterization during the iteration process it is shown how the cost function can be computed efficiently in two special cases row wise and column wise weighting

effect of variability in level on forward masking and on increment detection in the first of four experiments all with the same four subjects varying the level of a forward masker from interval to interval in a two interval forced choice 2ifc adaptive procedure had little effect on threshold in the second experiment the signal level was fixed and performance was measured in units of d varying the level of the forward masker again had little effect analyses of trial by trial data indicated that subjects did not vote for the interval with the higher level masker as would an energy detector performance was better on trials where the masker level in the interval with the signal was lower and was relatively independent of masker level in the nonsignal interval in the third experiment these results were replicated for a wider range of masker variability and with maskers lower in frequency than the signal in the fourth experiment the same range of variability from interval to interval was imposed on the level of the pedestal in an increment detection task results were sim

a multistage representation of the wiener filter based on orthogonal projections the wiener filter is analyzed for stationary complex gaussian signals from an information theoretic point of view a dual port analysis of the wiener filter leads to a decomposition based on orthogonal projections and results in a new multistage method for implementing the wiener filter using a nested chain of scalar wiener filters this new representation of the wiener filter provides the capability to perform an information theoretic analysis of previous basis dependent reduced rank wiener filters this analysis demonstrates that the cross spectral metric is optimal in the sense that it maximizes mutual information between the observed and desired processes a new reduced rank wiener filter is developed based on this new structure which evolves a basis using successive projections of the desired signal onto orthogonal lower dimensional subspaces the performance is evaluated using a comparative computer analysis model and it is demonstrated that the low complexity multistage reduced rank wiener filter is capable of outperforming the more complex eigendecomposition based methods

spectral shape discrimination by hearing impaired and normal hearing listeners the ability to discriminate between sounds with different spectral shapes was evaluated for normal hearing and hearing impaired listeners listeners discriminated between a standard stimulus and a signal stimulus in which half of the standard components were decreased in level and half were increased in level in one condition the standard stimulus was the sum of six equal amplitude tones equal spl and in another the standard stimulus was the sum of six tones at equal sensation levels re audiometric thresholds for individual subjects equal sl spectral weights were estimated in conditions where the amplitudes of the individual tones were perturbed slightly on every presentation sensitivity was similar in all conditions for normal hearing and hearing impaired listeners the presence of perturbation and equal sl components increased thresholds for both groups but only small differences in weighting strategy were measured between the groups depending on whether the equal spl or equal sl condition was tested the average data suggest that normal hearing listeners may rely more on the central components of the spectrum whereas hearing impaired listeners may have been more likely to use the edges however individual weighting functions were quite variable especially for the hi listeners perhaps reflecting difficulty in processing changes in spectral shape due to hearing loss differences in weighting strategy without changes in sensitivity suggest that factors other than spectral weights such as internal noise or difficulty encoding a reference stimulus also may dominate performance

multilayer neural networks for reduced rank approximation this paper is developed in two parts first the authors formulate the solution to the general reduced rank linear approximation problem relaxing the invertibility assumption of the input autocorrelation matrix used by previous authors the authors treatment unifies linear regression wiener filtering full rank approximation auto association networks svd and principal component analysis pca as special cases the authors analysis also shows that two layer linear neural networks with reduced number of hidden units trained with the least squares error criterion produce weights that correspond to the generalized singular value decomposition of the input teacher cross correlation matrix and the input data matrix as a corollary the linear two layer backpropagation model with reduced hidden layer extracts an arbitrary linear combination of the generalized singular vector components second the authors investigate artificial neural network models for the solution of the related generalized eigenvalue problem by introducing and utilizing the extended concept of deflation originally proposed for the standard eigenvalue problem the authors are able to find that a sequential version of linear bp can extract the exact generalized eigenvector components the advantage of this approach is that it s easier to update the model structure by adding one more unit or pruning one or more units when the application requires it an alternative approach for extracting the exact components is to use a set of lateral connections among the hidden units trained in such a way as to enforce orthogonality among the upper and lower layer weights the authors call this the lateral orthogonalization network lon and show via theoretical analysis and verify via simulation that the network extracts the desired components the advantage of the lon based model is that it can be applied in a parallel fashion so that the components are extracted concurrently finally the authors show the application of their results to the solution of the identification problem of systems whose excitation has a non invertible autocorrelation matrix previous identification methods usually rely on the invertibility assumption of the input autocorrelation therefore they can not be applied to this case

variation in spectral shape discrimination weighting functions at different stimulus levels and signal strengths this study evaluated whether weights for spectral shape discrimination depend on overall stimulus level and signal strength the degree of spectral shape change between two stimuli five listeners discriminated between standard stimuli that were the sum of six equal amplitude tones and signal stimuli created by decreasing the amplitudes of three low frequency components and increasing the amplitudes of three high frequency components weighting functions were influenced by stimulus level in that the relative contribution of the low frequency decremented components to the high frequency incremented components decreased with increasing stimulus level although individual variability was present a follow up experiment suggested that the level dependence was due to greater reliance on high frequency components rather than incremented components excitation pattern analyses indicated that the level dependence is primarily but not solely driven by cochlear factors in general different signal strengths had no effect on the weighting functions when normalized but two of the five listeners showed variability in the shape of the weighting function across signal strengths results suggest that the effects of stimulus level on weighting functions and individual variability in the shapes of the weighting functions should be considered when comparing weighting functions across conditions and groups that might require different stimulus levels and signal strengths

perceptual weights in auditory level discrimination perceptual weights in level discrimination also called intensity discrimination were determined for 3 7 15 and 24 component tone complexes with flat spectral envelopes using a correlational paradigm each frequency component was randomly and independently perturbed in level on each presentation for the target interval frequency component levels were additionally increased by the level increment to be detected l 20 log10 p p p where p is pressure weights were calculated from the across trial correlation between the level perturbations for each frequency component and the interval chosen by the listener two conditions were investigated 1 l was equal across frequency components and 2 l increased progressively across frequency components for both conditions data for four listeners usually showed the greatest weight for the highest frequency component the two to four highest frequency components generally were most important for level discrimination the effect of increasing l

variable projection for affinely structured low rank approximation in weighted 2 norms the structured low rank approximation problem for general affine structures weighted 2 norms and fixed elements is considered the variable projection principle is used to reduce the dimensionality of the optimization problem algorithms for evaluation of the cost function the gradient and an approximation of the hessian are developed for mxn mosaic hankel matrices the algorithms have complexity o m 2n

interpolation based unitary precoding for spatial multiplexing mimo ofdm with limited feedback spatial multiplexing with linear precoding is a simple technique for achieving high spectral efficiency in multiple input multiple output orthogonal frequency division multiplexing mimo ofdm systems linear precoding requires channel state information for each ofdm subcarrier which can be achieved using feedback to reduce the amount of feedback this paper proposes a limited feedback architecture that combines precoder quantization with a special matrix interpolator in the proposed system the receiver sends information about a fraction of the precoding matrices to the transmitter and the transmitter reconstructs the precoding matrices for all the subcarriers a new interpolator is proposed inspired by spherical interpolation that respects the orthogonal columns of the precoding matrices and the performance invariance to right multiplication by a unitary matrix the interpolator is parameterized by a set of unitary matrices a construction of a suitable set is briefly described simulations illustrate the performance of limited feedback precoding with coding estimation or prediction error and time variation for bit error rate ber mutual information and mean squared error mse

perception of temporal patterns defined by tonal sequences this experiment tested how listeners discriminate between the temporal patterns defined by two sequences of tones two arrhythmic sequences of n tones were played successively n 8 12 or 16 tone duration 35 ms frequency 1000 hz and the listener reported whether the sequences had the same or different temporal patterns in the first sequence the durations of the intertone gaps were chosen at random in the second sequence the gaps were either a the same as the first sequence or b chosen at random discrimination performance increased with the variability of the gap sequences and decreased with the size of the correlation between the sequences a discrimination model based on computation of the sample correlation between the sequences of gaps but limited by an internal variability of approximately 15 ms described observer performance in a variety of conditions

masker fluctuation and the masking level difference previous work suggests that for some listeners masker fluctuation may be advantageous for nos detection this study tested the hypothesis that the benefit of masker fluctuation to binaural analysis is based on the ability to take advantage of epochs of low masker energy in the fluctuating masker where the cues underlying binaural signal detection are more salient the hypothesis was evaluated using the time domain version of coss analysis derived by buus et al j acoust soc am 99 2288 2297 1996 which measures the perceptual weight applied by a listener within a relatively brief time window as a function of the masker level during the window the results indicated a dependency of signal detection on short term masker level in the nos condition but not in the noso condition this finding supports a new perspective indicating that binaural signal detection depends upon the envelope of a masker in a way that is fundamentally different from that typically associated with monaural detection

different auditory filter bandwidth estimates based on profile analysis notched noise and hybrid tasks auditory filter bandwidths were estimated in three experiments the first experiment was a profile analysis experiment the stimuli were composed of sinusoidal components ranging in frequency from 200 to 5000 hz the standard stimulus was the sum of equal amplitude tones and the signal stimulus had a power spectrum that varied up down up down the number of components ranged from four to 60 interval by interval level randomization prevented the change in level of a single component from reliably indicating the change from standard to signal the second experiment was a notched noise experiment in which the 1000 hz tone to be detected was added to a noise with a notch arithmetically centered at 1000 hz detection thresholds were estimated both in the presence of and in the absence of level randomization in the third hybrid experiment a 1000 hz tone was to be detected and the masker was composed of equal amplitude sinusoidal components ranging in frequency from 200 to 5000 hz for this experiment thr

the geometry of weighted low rank approximations the low rank approximation problem is to approximate optimally with respect to some norm a matrix by one of the same dimension but smaller rank it is known that under the frobenius norm the best low rank approximation can be found by using the singular value decomposition svd although this is no longer true under weighted norms in general it is demonstrated here that the weighted low rank approximation problem can be solved by finding the subspace that minimizes a particular cost function a number of advantages of this parameterization over the traditional parameterization are elucidated finding the minimizing subspace is equivalent to minimizing a cost function on the grassmann manifold a general framework for constructing optimization algorithms on manifolds is presented and it is shown that existing algorithms in the literature are special cases of this framework within this framework two novel algorithms a steepest descent algorithm and a newton like algorithm are derived for solving the weighted low rank approximation problem they are compared with other algorithms for low rank approximation as well as with other algorithms for minimizing a cost function on a grassmann manifold

further comments on proportional duration and proportional variance as factors in auditory pattern discrimination this brief comment in response to the letter by gary kidd j acoust soc am 97 xxx 1995 asserts that two recent accounts of the discrimination of variable tone patterns are more similar than they are different the real difference being that only one the core model develops a shared premise into an explicit prediction for d advantages of the core model are more accurate predictions for the effects of proportional duration and the ability to make explicit predictions for the effects of other important variables and their interaction

software for weighted structured low rank approximation a software package is presented that computes locally optimal solutions to low rank approximation problems with the following features mosaic hankel structure constraint on the approximating matrix weighted 2 norm approximation criterion fixed elements in the approximating matrix missing elements in the data matrix and linear constraints on an approximating matrix s left kernel basis it implements a variable projection type algorithm and allows the user to choose standard local optimization methods for the solution of the parameter optimization problem for an mxn data matrix with n m the computational complexity of the cost function and derivative evaluation is o m 2n the package is suitable for applications with n m in statistical estimation and data modeling the main application areas of the package n m corresponds to modeling of large amount of data by a low complexity model performance results on benchmark system identification problems from the database daisy and approximate common divisor problems are presented

pilot assisted channel estimation based on second order statistics a survey about linear channel estimation exploiting slowly varying channel properties is given for receivers with multiple antenna elements the slowly varying channel properties are described by the channel s second order statistics first a detailed comparison of classical linear pilot based channel estimators a novel matched filter and reduced rank rr approaches is made in a common framework with respect to the model they assume for the channel their performance mse and complexity the matched filter channel estimator is introduced which exploits second order statistics with quadratic order of complexity for flat correlated rayleigh fading channels an analytical performance comparison of all estimators in terms of the uncoded bit error probability is provided it is a generalization of previous results and shows that the matched filter is a low complexity alternative with good performance at an interesting signal to noise ratio snr range the effects of these approaches on linear equalization are briefly discussed in the context of direct sequence code division multiple access ds cdma where the focus is on a generalization of the rake receiver in space and time which reduces the channel rank based on its second order statistics resulting in a complexity reduction of the equalizer for this discussion a new notation for the generalized rake is presented which allows for its interpretation in the context of channel estimation and reveals alternatives for implementation we conclude that exploiting second order channel statistics results in significant performance gains and rr channel estimation should only be used together with equalization in the reduced signal subspace

evaluation of simple models of auditory profile analysis using random reference spectra this article describes further study of the finding reported by green et al j acoust soc am 73 639 643 1983 and others that in certain conditions the threshold of detectability for an intensity increment to the center tone of a multitone reference spectrum decreased as the number of nonsignal tones increased that result was considered remarkable since critical band theory would predict that these nonsignal tones spaced outside the critical band containing the signal would have no effect on or at most slightly decrease within band detectability and certainly could not account for the result of improved detectability found in the study cited above recently henn and turner j acoust soc am 88 126 131 1990 were unable to replicate the result described above concluding that the phenomenon exists only in limited conditions and that it is highly individual in nature further they speculated that the most likely reason for the discrepancy between their study and previous s

spectral peak selection in spectral shape discrimination by normal hearing and hearing impaired listeners spectral shape discrimination thresholds were measured in the presence and absence of noise to determine whether normal hearing and hearing impaired listeners rely primarily on spectral peaks in the excitation pattern when discriminating between stimuli with different spectral shapes standard stimuli were the sum of 2 4 6 8 10 20 or 30 equal amplitude tones with frequencies fixed between 200 and 4000hz signal stimuli were generated by increasing and decreasing the levels of every other standard component the function relating the spectral shape discrimination threshold to the number of components n showed an initial decrease in threshold with increasing n and then an increase in threshold when the number of components reached 10 and 6 for normal hearing and hearing impaired listeners respectively the presence of a 50 db spl hz noise led to a 1 7db increase in threshold for normal hearing listeners and a 3 5db increase for hearing impaired listeners multichannel modeling and the relatively s

optimal reduced rank estimation and filtering this paper provides a unified view of and a further insight into a class of optimal reduced rank estimators and filters an alternating power ap method for computing the optimal reduced rank estimators and filters is derived and analyzed the ap method is a generalization of the conventional power method for subspace computation which is shown to be globally and exponentially convergent under weak conditions when the rank reduction is relatively large the ap method is computationally more efficient than the conventional methods the ap method is useful for adaptive computation of the canonical components of a desired reduced rank estimate which in turn facilitates the detection of a time varying rank the study shown in this paper is particularly useful for applications that involve a large number of sources and a large number of receivers where rank reduction is either inherent in the multivariate system or required to reduce the model complexity and or the computational load

optimization algorithms exploiting unitary constraints this paper presents novel algorithms that iteratively converge to a local minimum of a real valued function f x subject to the constraint that the columns of the complex valued matrix x are mutually orthogonal and have unit norm the algorithms are derived by reformulating the constrained optimization problem as an unconstrained one on a suitable manifold this significantly reduces the dimensionality of the optimization problem pertinent features of the proposed framework are illustrated by using the framework to derive an algorithm for computing the eigenvector associated with either the largest or the smallest eigenvalue of a hermitian matrix

unitary evolutions and horizontal lifts in quantum stochastic calculus unitarity is proved for a class of solutions of quantum stochastic differential equations with unbounded coefficients the resulting processes are then used to construct algebraic quantum diffusions applications include an existence proof for a class of diffusions on the non commutative two torus and a geometric interpretation for diffusions driven by the classical poisson process

rank reduction for modeling stationary signals rank reduction is developed as a general principle for trading off model bias and model variance in the analysis and synthesis of signals the principle is applied to three basic problems stationary time series modeling stationary time series whitening and vector quantization each problem brings its own surprises and insights

informational masking with small set sizes informational masking refers to interference in the detectability of a sound or discrimination of some property of a sound beyond that which can be attributed to interactions at the auditory periphery in the current experiments the signal to be detected was a tone added to a 6 tone masker and informational masking was introduced by randomly choosing the frequencies of the tones that comprise the masker the primary question was whether small numbers of maskers could replace randomly drawn maskers without sacrificing the underlying detection schemes adopted by observers similar to the method used by wright and saberi j acoust soc am 105 1765 1775 1999 detection thresholds were measured for different masker set sizes where set size refers to the number of 6 tone maskers from which any one masker was drawn set sizes of 3 6 12 and 24 were tested as well as conditions in which the maskers were chosen at random in addition observers memory for maskers was coarsely evaluated large differences in thresholds were found across observers and across different masker sets even for set sizes of 24 the memory test suggests some recognition of maskers for some observers post hoc analysis of the data included an evaluation of the relative contribution of different frequencies using a single linear model as a base for comparison a linear model fitted to each condition was also evaluated although the data were fitted better using many rather than one linear model the reduction in quality of fit was modest this result suggests substantial consistency in decision strategies regardless of masker set size

temporal weights in the level discrimination of time varying sounds to determine how listeners weight different portions of the signal when integrating level information they were presented with 1 s noise samples the levels of which randomly changed every 100 ms by repeatedly and independently drawing from a normal distribution a given stimulus could be derived from one of two such distributions a decibel apart and listeners had to classify each sound as belonging to the soft or loud group subsequently logistic regression analyses were used to determine to what extent each of the ten temporal segments contributed to the overall judgment in experiment 1 a nonoptimal weighting strategy was found that emphasized the beginning and to a lesser extent the ending of the sounds when listeners received trial by trial feedback however they approached equal weighting of all stimulus components in experiment 2 a spectral change was introduced in the middle of the stimulus sequence changing from low pass to high pass noise and vice versa the temporal location of the stimulus change was strongly weighted much as a new onset these findings are not accounted for by current models of loudness or intensity discrimination but are consistent with the idea that temporal weighting in loudness judgments is driven by salient events

a molecular description of profile analysis decision weights and internal noise systematic inefficiencies and internal noise in a spectral profile discrimination task were investigated listeners detected a 1000 hz sinusoid added in phase to the central component of a complex consisting of 11 equal intensity sinusoids parameters for a channel model that employs decision weights and internal noise were estimated with molecular psychophysical techniques maximum likelihood predictions of the model were generally within a few decibels of observed thresholds the degree to which an assumption of ideal weights leads to overestimation of internal noise was also assessed

effect of temporal position proportional variance and proportional duration on decision weights in temporal pattern discrimination two experiments investigated how listeners allocate their attention to different segments of a temporal pattern the experiments allowed a direct test of the predictions of the proportion of total duration ptd rule and the component relative entropy core model listeners had to decide whether two sequences of nine tones had the same or different temporal patterns tone duration 25 ms tone frequency 1000 hz a sequence s temporal pattern was determined by the time intervals between each tone s offset and the next tone s onset on same trials the time intervals at corresponding temporal positions in the two sequences were identical on different trials the corresponding time intervals were randomly varied listener attention to different temporal positions within a sequence was assessed by calculating the decision weights at each position the results supported the core model and were inconsistent with the ptd rule manipulating the mean of the time intervals within the sequence had no consistent ef

a model of auditory pattern analysis based on component relative entropy recently results from detection and information theory have been used to predict performance of human observers in experiments involving the discriminability of changes in individual components of unfamiliar or uncertain tone patterns r a lutfi j acoust soc am 91 3391 3401 1992 in this paper the theoretical analysis is expanded to yield a general rule of pattern analysis that accounts for nearly all of the major results of such experiments conducted over the last 18 years the rule can be stated as follows component discriminability in an unfamiliar tone pattern profile or sequence is a linearly increasing function of the component s relative entropy core in the pattern ancillary the threshold for detection of a change decreases by one order of magnitude factor of 10 for each one bit increase in core this precise relation of threshold to core is demonstrated repeatedly in a review of past studies and is shown to account for the relative effects of a variety of important variables and their interactions such variables include the total duration of the pattern the number of tones in the pattern the number of tones subject to change the relative level and duration of individual tones in the pattern the relative variability and the physical dimension of the tones parameters that are subject to change the number and position of targets in the pattern the psychophysical procedure used method of adjustment versus same different the type of discrimination task frequency versus intensity discrimination and the manner of presentation of the tones simultaneous or sequential the core rule seems to reflect a general property of auditory analysis wherein the perception of patterns in an ensemble is dominated by those features that dominate the variance of the ensemble

reduced rank adaptive filtering a novel rank reduction scheme is introduced for adaptive filtering problems this rank reduction method uses a cross spectral metric to select the optimal lower dimensional subspace for reduced rank adaptive filtering as a function of the basis vectors of the full rank space

a grassmann rayleigh quotient iteration for computing invariant subspaces the classical rayleigh quotient iteration rqi allows one to compute a one dimensional invariant subspace of a symmetric matrix a here we propose a generalization of the rqi which computes a p dimensional invariant subspace of a cubic convergence is preserved and the cost per iteration is low compared to other methods proposed in the literature

wiener filters in canonical coordinates for transform coding filtering and quantizing canonical correlations are used to decompose the wiener filter into a whitening transform coder a canonical filter and a coloring transform decoder the outputs of the whitening transform coder are called canonical coordinates these are the coordinates that are reduced in rank and quantized in our finite precision version of the gauss markov theorem canonical correlations are in fact cosines of the canonical angles between a source vector and a measurement vector they produce new formulas for error covariance spectral flatness and entropy

reduced rank linear regression and weighted low rank approximations this paper addresses parameter estimation in reduced rank linear regressions this estimation problem has applications in several subject areas including system identification sensor array processing econometrics and statistics a new estimation procedure based on instrumental variable principles is derived and analyzed the proposed method is designed to handle noise that is both spatially and temporally autocorrelated an asymptotical analysis shows that the proposed method outperforms previous methods when the noise is temporally correlated and that it is asymptotically efficient otherwise a numerical study indicates that the performance is significantly improved also for finite sample set sizes in addition the cramer rao lower bound crb on unbiased estimator covariance for the data model is derived a statistical test for rank determination is also developed an important step in the new algorithm is the weighted low rank approximation wlra as the wlra lacks a closed form solution in its general form two new noniterative and approximate solutions are derived both of them asymptotically optimal when part of the estimation procedure proposed here these methods are also interesting in their own right since the wlra has several applications

level discrimination of single tones in a multitone complex by normal hearing and hearing impaired listeners a conditional on a single stimulus coss analysis procedure j acoust soc am 86 1743 1746 1989 was used to estimate how well normal hearing and hearing impaired listeners selectively attend to individual spectral components of a broadband signal in a level discrimination task on each trial two multitone complexes consisting of six octave frequencies from 250 to 8000 hz were presented to listeners the levels of the individual tones were chosen independently and at random on each presentation the target tone was selected within a block of trials as the 250 1000 or 4000 hz component on each trial listeners were asked to indicate which of the two complex sounds contained the higher level target as a group normal hearing listeners exhibited greater selectivity than hearing impaired listeners to the 250 hz target while hearing impaired listeners showed greater selectivity than normal hearing listeners to the 4000 hz target which is in the region of their hearing loss both groups of listeners displayed large variability in their ability to selectively weight the 1000 hz target trial by trial analysis showed a decrease in weighting efficiency with increasing frequency for normal hearing listeners but a relatively constant weighting efficiency across frequency for hearing impaired listeners interestingly hearing impaired listeners selectively weighted the 4000 hz target which was in the region of their hearing loss more efficiently than did the normal hearing listeners

spectral weights in profile listening the coss analysis suggested by berg b g berg j acoust soc am 86 1743 1746 1989 is applied to a profile listening task the listener s task is to detect an increment in the level of the middle component of an n component spectrum the overall level of the components is randomly selected from a 20 db range on each presentation thus the detection task is essentially one of detecting a change in spectral shape to implement the coss analysis a small perturbation in level is added to each component of the complex coss functions are generated from these perturbations and the spectral weight that the listener assigns to each component is estimated data are reported for n 3 5 and 11 components and for perturbations with standard deviations of 0 5 1 and 2 db the estimated weights are similar to those derived for an optimum detector namely the level at the signal component is compared with the average level of the nonsignal components this result supports the view that profile analysis invol

data adaptive rank shaping methods for solving least squares problems there are two types of problems in the theory of least squares signal processing parameter estimation and signal extraction parameter estimation is called inversion and signal extraction is called filtering in this paper we present a unified theory of rank shaping for solving overdetermined and underdetermined versions of these problems we develop several data dependent rank shaping methods and evaluate their performance our key result is a data adaptive wiener filter that automatically adjusts its gains to accommodate realizations that are a priori unlikely the adaptive filter dramatically outperforms the wiener filter on a typical realizations and just slightly under performs it on typical realizations this is the most one can hope for in a data adaptive filter

brief paper maximum likelihood identification of noisy input output models this work deals with the identification of errors in variables models corrupted by white and uncorrelated gaussian noises by introducing an auxiliary process it is possible to obtain a maximum likelihood solution of this identification problem by means of a two step iterative algorithm this approach allows also to estimate as a byproduct the noise free input and output sequences moreover an analytic expression of the finite cramer rao lower bound is derived the method does not require any particular assumption on the input process however the ratio of the noise variances is assumed as known the effectiveness of the proposed algorithm has been verified by means of monte carlo simulations

correlation coefficients and correlation ratios as estimates of observer weights in multiple observation tasks advantages of correlational methods are described for estimating the relative reliance or weight observers give to different elements of a complex display when performing auditory or visual discriminations correlational methods differ from other such methods by providing a least squares estimate of weights rather than a maximum likelihood estimate based on a presumed model the main benefit is that these methods can be generally applied in cases where the statistical properties of elements are unknown where correlations exist between elements or where it is necessary to evaluate decision models that are inherently nonlinear

discrimination of frequency variance for tonal sequences real world auditory stimuli are highly variable across occurrences and sources the present study examined the sensitivity of human listeners to differences in global stimulus variability in a two interval forced choice task variance discrimination was measured using sequences of five 100 ms tone pulses the frequency of each pulse was sampled randomly from a distribution that was gaussian in logarithmic frequency in the non signal interval the sampled distribution had a variance of stan2 while in the signal interval the variance of the sequence was sig2 with sig2 stan2 the listener s task was to choose the interval with the larger variance to constrain possible decision strategies the mean frequency of the sampling distribution of each interval was randomly chosen for each presentation psychometric functions were measured for various values of stan2 although the performance was remarkably similar across listeners overall performance was poorer than that of an ideal observer io which perfectly compares interval variances however like the io weber s law behavior was observed with a constant ratio of sig2 stan2 to stan2 yielding similar performance a model which degraded the io with a frequency resolution noise and a computational noise provided a reasonable fit to the real data

auditory profile analysis is there perceptual constancy for spectral shape for stimuli roved in frequency the ability to discriminate between two spectral shapes was investigated using a one interval two alternative forced choice procedure each stimulus consisted of seven components equally spaced on a logarithmic frequency scale frequency ratio of 1 2 between adjacent components the two spectral shapes were produced by first generating a complex each of whose components was equally loud when heard in isolation and then increasing the level of either the third or the fifth component by a certain amount to render pitch an unusable cue the center frequencies of the stimuli were randomly varied between presentations maintaining the ratio between adjacent components over a range of about three octaves 279 2074 hz the data indicate that listeners were not able to distinguish between the two types of profiles even for very large increments in level of the third and the fifth components the results suggest that there is no perceptual constancy for this type of spectral shape for stimuli roved over a sufficiently large frequency range the spectral shape cannot be perceived independently of stimulus frequency the results are related to the multi channel model applied in profile analysis tasks

molecular analysis of the effect of relative tone level on multitone pattern discrimination molecular psychophysics attempts to model the observer s response to stimuli as they vary from trial to trial the approach has gained popularity in multitone pattern discrimination studies as a means of estimating the relative reliance or decision weight listeners give to different tones in the pattern various factors affecting decision weights have been examined but one largely ignored is the relative level of tones in the pattern in the present study listeners detected a level increment in a sequence of 5 100 ms 2 0 khz tone bursts alternating in level between 40 and 80db spl the level increment was made largest on the 40 db tones yet despite this all four highly practiced listeners gave near exclusive weight to the 80 db tones the effect was the same when the tones were replaced by bursts of broadband gaussian noise alternating in level it was reduced only when the level differences were made 10db and it was entirely reversed only when the low level tones alternated with louder bursts of ga

sources of variation in profile analysis i individual differences and extended training this study investigated two sources of variance in the ability to discriminate auditory profiles individual differences and extended training the goals of the study were 1 to determine the range and origins of individual differences in profile analysis and 2 to determine whether those who initially had poor sensitivity to changes in spectral shape could eventually acquire finer sensitivity profile stimuli had 11 components with equal log spacing from 200 2200 hz thresholds ranged from 1 to 25 db signal level relative to the context level across 46 listeners the correlation between spectral shape discrimination thresholds after 2000 trials and pure tone intensity discrimination thresholds was 0 36 the range of individual differences for pure tone intensity discrimination and spectral shape discrimination was about the same two groups of listeners were given extended practice on the profile task one group that showed low thresholds after an initial 2000 trials of practice and another that showed much higher initial thresholds all listeners improved during the course of the first 2000 trials of training most of the poor listeners continued to improve during 9000 trials of training individual differences in the listeners sensitivity to changes in spectral shape still existed after the extended practice

successive versus simultaneous comparison in auditory intensity discrimination the ability to discriminate between two brief sounds having identical frequency components but differing in the intensity of one or more of the components is studied the stimulus manipulations include randomizing the overall intensity of the sounds varying the number and spacing of the components and varying the interval of time between the sounds the results from the experiment in which interstimulus interval is manipulated clearly support a profile analysis mechanism that computes two rough spectral analyses stores a classification of these spectra in memory and compares the two stores this profile mechanism involves a simultaneous comparison of different components of the complex some remote from the signal frequency rather than a successive comparison of the difference in intensity at the signal frequency the simultaneous comparison process is more sensitive when the profile is composed of many components spaced over a wide frequency range

generic weighted filtering of stochastic signals in this paper a new theory of optimal weighted nonlinear filtering is presented two filter models are considered the first model is based on a representation of the filter in the polynomial like form with q terms where each term consists of weighted matrices and the matrix determined from the error minimization problem the second model extends the first one to the case of the filter concatenation the filter models are given in terms of pseudo inverse matrices i e the requirement of invertibility for covariance matrices is omitted thus our filters always exist we develop methods which allow us to exploit advantages associated with the proposed nonlinear filter models the methods consist of the orthogonalization procedure and the reduction of the original problem to q individual minimization problems for smaller matrices this leads to a considerable reduction in the required computational work the error associated with the first filter model decreases when the number q of terms of filter increases its compression ratio can be adjusted by varying a particular value of ranks in each of its q terms this means that the proposed filer structure provides the two degrees of freedom the second filter model provides another degree of freedom a number k of filters in the concatenation variations of the degrees of freedom improve the performance of the proposed filters in particular the error associated with the filter concatenation decreases as the filter number k in the concatenation increases

rank constraints for homographies over two views revisiting the rank four constraint it is well known that one can collect the coefficients of five or more homographies between two views into a large rank deficient matrix in principle this implies that one can refine the accuracy of the estimates of the homography coefficients by exploiting the rank constraint however the standard rank projection approach is impractical for two different reasons it requires many homographies to even score a modest gain and secondly correlations between the errors in the coefficients will lead to poor estimates in this paper we study these problems and provide solutions to each firstly we show that the matrices of the homography coefficients can be recast into two parts each consistent with ranks of only one this immediately establishes the prospect of realistically that is with as few as only three or four homographies exploiting the redundancies of the homographies over two views we also tackle the remaining issue correlated coefficients we compare our approach with the gold standard that is non linear bundle adjustment initialized from the ground truth estimate the ideal initialization the results confirm our theory and show one can implement rank constrained projection and come close to the gold standard in effectiveness indeed our algorithm by itself or our algorithm further refined by a bundle adjustment stage may be a practical algorithm providing generally better results than the standard dlt direct linear transformation algorithm and even better than the bundle adjustment result with the dlt result as the starting point our unoptimized version has roughly the same cost as bundle adjustment and yet can generally produce close to the gold standard estimate as illustrated by comparison with bundle adjustment initialized from the ground truth independent of the merits or otherwise of our algorithm we have illuminated why the naive approach of direct rank projection is relatively doomed to failure moreover in revealing that there are further rank constraints not previously known we have added to the understanding of these issues and this may pave the way for further improvements

effect of time compression and expansion on the discrimination of tonal patterns this experiment tested how well human listeners can discriminate between temporal patterns that are compressed or expanded in time the listener s task was to determine whether two arrhythmic tonal sequences had the same or different temporal patterns according to the pattern correlation model r d sorkin j acoust soc am 87 1695 1701 1990 listeners perform this task by computing the correlation between the pattern of time intervals marked by the tones in each sequence listener performance dropped when one of the sequences was compressed or expanded in time in order for the model to describe the observed performance it was necessary to postulate an internal noise component that was proportional to the magnitude of the difference between the sequence transformations

on possible cues in profile analysis identification of the incremented component the ability to identify the frequency of the incremented component in a multitone complex was assessed in two conditions both using the same 11 tone complexes fixed frequency equilog spaced random phases in the standard plus signal complex all components had equal level except one of the inner nine which was incremented in level by an in phase addition of a sinusoid of the same frequency the signal the overall level and signal position were randomly varied on each presentation in the standard absent condition the standard plus signal complex was presented first and it was followed by a single sinusoid either at the signal frequency or at that of an adjacent component below or above in the standard present condition a complex with equal level components the standard complex was also presented on each trial either before or after the standard plus signal complex in random order these two complexes were followed by the single sinusoid in both conditions the subjects had to indica

survey paper structured low rank approximation and its applications fitting data by a bounded complexity linear model is equivalent to low rank approximation of a matrix constructed from the data the data matrix being hankel structured is equivalent to the existence of a linear time invariant system that fits the data and the rank constraint is related to a bound on the model complexity in the special case of fitting by a static model the data matrix and its low rank approximation are unstructured we outline applications in system theory approximate realization model reduction output error and errors in variables identification signal processing harmonic retrieval sum of damped exponentials and finite impulse response modeling and computer algebra approximate common divisor algorithms based on heuristics and local optimization methods are presented generalizations of the low rank approximation problem result from different approximation criteria e g weighted norm and constraints on the data matrix e g nonnegativity related problems are rank minimization and structured pseudospectra

steepest descent algorithms for optimization under unitary matrix constraint in many engineering applications we deal with constrained optimization problems with respect to complex valued matrices this paper proposes a riemannian geometry approach for optimization of a real valued cost function t of complex valued matrix argument w under the constraint that w is an n times n unitary matrix we derive steepest descent sd algorithms on the lie group of unitary matrices u n the proposed algorithms move towards the optimum along the geodesics but other alternatives are also considered we also address the computational complexity and the numerical stability issues considering both the geodesic and the nongeodesic sd algorithms armijo step size 1 adaptation rule is used similarly to 2 but with reduced complexity the theoretical results are validated by computer simulations the proposed algorithms are applied to blind source separation in mimo systems by using the joint diagonalization approach 3 we show that the proposed algorithms outperform other widely used algorithms

relative weights for frequency glide detection using narrowband noise narrowband noise stimuli were used to derive relative weights for detecting frequency glides in a yes no procedure one stimulus set was restricted to the duration of the glide for the second stimulus set there were fringe noise bands preceding and following the glide for both sets the center frequency of the linear glide was either fixed at 1000hz or randomly chosen on each trial from the range of 800 1200hz relative weights as a function of time were derived using a linear model and the linear classification method a ahumada j vis 2 121 131 2002 sensitivity was better for the fixed than random frequency conditions and weight patterns from the random frequency conditions were less reliable than those obtained from the fixed frequency conditions the magnitudes of the relative weights tended to be larger for the second half of the stimulus suggesting that subjects paid more attention to the later than the earlier parts of stimuli in the random frequency conditions the linear model failed to account for subjects performance unless the stimuli were expressed in terms of relative changes in frequency rather than absolute frequency

maximum likelihood parameter and rank estimation in reduced rank multivariate linear regressions this paper considers the problem of maximum likelihood ml estimation for reduced rank linear regression equations with noise of arbitrary covariance the rank reduced matrix of regression coefficients is parameterized as the product of two full rank factor matrices this parameterization is essentially constraint free but it is not unique which renders the associated ml estimation problem rather nonstandard nevertheless the problem turns out to be tractable and the following results are obtained an explicit expression is derived for the ml estimate of the regression matrix in terms of the data covariances and their eigenelements furthermore a detailed analysis of the statistical properties of the ml parameter estimate is performed additionally a generalized likelihood ratio test glrt is proposed for estimating the rank of the regression matrix the paper also presents the results of some simulation exercises which lend empirical support to the theoretical findings

rational solutions of pairs of diagonal equations one cubic and one quadratic we obtain an essentially optimal estimate for the moment of order 32 3 of the exponential sum having argumentx 3 x 2 subject to modest local solubility hypotheses we thereby establish that pairs of diagonal diophantine equations one cubic and one quadratic possess non trivial integral solutions whenever the number of variables exceeds 10

effect of sequence delay on the discrimination of temporal patterns this experiment tested listeners ability to discriminate between two temporal patterns as a function of the time interval between the pattern onsets the listener s task was to decide whether two arrhythmic sequences of nine tones had the same or different temporal patterns the patterns were defined by the time intervals between the tones according to the temporal pattern correlation model r d sorkin j acoust soc am 87 1695 1701 1990 listeners extract information about the series of time intervals in each sequence and then compute the correlation between the two series in the present experiment the tones in the second sequence were presented at a different frequency than the tones in the first sequence in one condition all time intervals in the second sequence were compressed or expanded by a factor that varied randomly over trials performance was very good when the sequences did not overlap in time but was poor when the sequences overlapped performance was generally consistent with a discrimination mechanism that cannot process more than one pattern at a time

the effect of onset asynchrony on relative weights in profile analysis decision weights were estimated in a profile analysis task to determine whether onset asynchronies between the signal component and the nonsignal components encourage the segregation of the signal relative to the other components the signal component onset was either synchronous or asynchronous with respect to the nonsignal components in the asynchronous conditions thresholds were higher and the decision weights were less efficient than in the synchronous conditions these data are largely consistent with a segregation hypothesis onset asynchrony encourages subjects to shift strategies from one of spectral shape discrimination toward one of intensity discrimination