an iterative method for conformal mapping abstract in this paper we discuss an iterative method for the calculation of the boundary values of the conformal mapping of a simply connected region g onto a region h with smooth boundary the method is based on a certain riemann hilbert problem it turns out that this problem is the linearized version of a singular integral equation of the second kind hence the method is a newton method whenever the boundaries of g and h are sufficiently smooth its convergence is locally quadratic if g is the unit circle the solution of the linearized problem can be represented explicitly in terms of integral transforms from this one derives a quadratically convergent newton like numerical method that avoids the numerical solution of systems of linear equations and therefore in comparison with other methods based on integral equations is quite economical in terms of computer time and storage requirements

a fredholm integral equation of the second kind for conformal mapping abstract we present a fredholm integral equation of the second kind for the derivative of the boundary correspondence function of the conformal mapping of a jordan region with piecewise twice differentiable boundary onto the unit disk one of our derivations of the equation leads to a more general regularisation procedure for some singular integral equations of the first kind the integral equation can be solved numerically by applying the fourier method the convergence to in l 2 of the solution of the discrete equation so obtained follows by simple theorems examples show that the equation often yields better numerical results than both a related method proposed by henrici and warschawski s equation

inverse eigenvalue problems of tridiagonal symmetric matrices and tridiagonal bisymmetric matrices the problem of generating a matrix a with specified eigenpairs where a is a tridiagonal symmetric matrix is presented a general expression of such a matrix is provided and the set of such matrices is denoted by s e moreover the corresponding least squares problem under spectral constraint is considered when the set s e is empty and the corresponding solution set is denoted by s l the best approximation problem associated with s e s l is discussed that is to find the nearest matrix a in s e s l to a given matrix the existence and uniqueness of the best approximation are proved and the expression of this nearest matrix is provided at the same time we also discuss similar problems when a is a tridiagonal bisymmetric matrix

dichotic pitches as illusions of binaural unmasking ii the fourcin pitch and the dichotic repetition pitch the predictions of three models are compared with respect to existing experimental data on the perception of the fourcin pitch fp and the dichotic repetition pitch drp each model generates a central spectrum cs which is examined for peaks at frequencies consistent with the perceived pitches a modified equalization cancellation me c model of binaural unmasking culling and summerfield j acoust soc am 98 785 797 1995 generates a cs which reflects the degree of interaural decorrelation present in each frequency channel this model accounts for the perceived frequencies of fps but produces no output for drp stimuli a restricted equalization cancellation re c model bilsen and goldstein j acoust soc am 55 292 296 1974 sums the time varying excitation in corresponding frequency channels without equalization to form a cs a central activity pattern cap model raatgever and bilsen j acoust soc am 80 429 441 1986 generates a cs by scanning an interaural cross correlation matrix across frequency the re c and cap models yield inaccurate predictions of the perceived frequencies of fps but predict the occurrence of the drp and its correct pitch the complementary predictions of the me c model compared to the re c and cap models together with the evidence that the fp is clearly audible for the majority of listeners while the drp is faintly heard by a minority of listeners suggest that the me c model provides the best available account of the fp and that the drp is produced by a separate mechanism

on the dichotic pitch of simultaneously presented interaurally delayed white noises implications for binaural theory a dichotic pitch known as fourcin pitch fp is perceived when two independent interaurally delayed white noises are presented simultaneously experiments in the past mainly dealt with stimulus situations where one interaural delay was smaller than 4 ms and the other was in the range 0 10 ms here experiments are reported showing a novel pitch percept that occurs when one noise is interaurally delayed at the left ear and the other noise is about equally delayed at the right ear for delays in the range of 4 10 ms it is shown that for both the previously reported fp and the novel pitch the central spectrum cs theory raatgever and bilsen j acoust soc am 80 429 441 1986 provides a correct prediction of both the pitch value and the lateral position of the pitch image where other current theories partly or completely fail further experiments indicate that the lateralized position of the pitch image is essentially not influenced by an interaural intensity difference iid this is also predicted by the cs model and leads to the generalized conclusion that interaural time and intensity differences are processed separately in the auditory system until at least the level where the dichotic pitch is generated

a charge simulation method for the numerical conformal mapping of interior exterior and doubly connected domains abstract a simple numerical method is described for computing the following three conformal maps a from a domain interior to a closed jordan curve onto the interior of the unit disk b from a domain exterior to a closed jordan curve onto the exterior of the unit disk and c from a doubly connected domain bounded by two closed jordan curves onto a circular annulus the numerical method is based on the charge simulation method or the method of fundamental solutions applied to the dirichlet problem of laplace s equation in which a pair of conjugate harmonic functions are approximated by a linear combination of complex logarithmic potentials without integration typical examples show that numerical results of high accuracy can be obtained by the simple method if the domains have no concave corners

temporal pitch perception and the binaural system two experiments examined the relationship between temporal pitch and more generally rate perception and auditory lateralization both used dichotic pulse trains that were filtered into the same high 3900 5400 hz frequency region in order to eliminate place of excitation cues in experiment 1 a 1 s periodic pulse train of rate fr was presented to one ear and a pulse train of rate 2fr was presented to the other in the synchronous condition every other pulse in the 2fr train was simultaneous with a pulse in the opposite ear in each trial subjects concentrated on one of the two binaural images produced by this mixture they matched its perceived location by adjusting the interaural level difference ild of a bandpass noise and its rate pitch was then matched by adjusting the rate of a regular pulse train the results showed that at low fr e g 2 hz subjects heard two pulse trains of rate fr one in the higher rate ear and one in the middle of the head at higher fr 25 hz subjects hea

dominance region for pitch effects of duration and dichotic presentation the dominance region dr for pitch was determined for 16 and 200 ms complex tones containing the first seven harmonics of a fundamental frequency f0 of 250 hz a tone was presented with one of the harmonics mistuned upwards or downwards by 3 followed 500 ms later by a perfectly harmonic tone of the same duration listeners adjusted the f0 of the harmonic tone so that its pitch matched that of the mistuned complex in experiment 1 stimuli were presented monaurally the dr was significantly higher in harmonic number for the short than for the long duration the overall sum of the pitch shifts produced by all harmonics was significantly larger for the short than for the long duration presumably due to stronger perceptual fusion for the former in experiment 2 the mistuned harmonic was presented only contralaterally to the remainder of the complex a similar shift in the dr with duration was observed although the pitch shifts were smaller than for monaural presentation there was no significant effect of duration on the overall pitch shifts the results are discussed in terms of pattern recognition and autocorrelation models of pitch perception and a role of attention in pitch matching is suggested

an autocorrelation model with place dependence to account for the effect of harmonic number on fundamental frequency discrimination fundamental frequency f0 difference limens dls were measured as a function of f0 for sine and random phase harmonic complexes bandpass filtered with 3 db cutoff frequencies of 2 5 and 3 5 khz low region or 5 and 7 khz high region and presented at an average 15 db sensation level approximately 48 db spl per component in a wideband background noise fundamental frequencies ranged from 50 to 300 hz and 100 to 600 hz in the low and high spectral regions respectively in each spectral region f0 dls improved dramatically with increasing f0 as approximately the tenth harmonic appeared in the passband generally f0 dls for complexes with similar harmonic numbers were similar in the two spectral regions the dependence of f0 discrimination on harmonic number presents a significant challenge to autocorrelation ac models of pitch in which predictions generally depend more on spectral region than harmonic number a modification involving a lag window is proposed and tested restricting the ac repr

the construction of band symmetric models for vibratory systems from modal analysis data abstract some natural frequencies and their corresponding mass normalized mode shapes of physical structures may be measured by experiment since the discretization of the continuous model of the structure reflects only a limited degree of coupling between model elements the associated mass and stiffness matrices are typically sparse thus appropriately numbered model elements may lead to banded matrices in this paper a method is presented which determines the bandwidths of the mass and stiffness matrices and then recovers the model by using eigendata this approach falls somewhere between the wider class of system identification problems in which the only structural property assumed is symmetry and hence for which no unique physical model can be constructed and inverse problems in which the model interconnections are known the present approach thus widens the class of models that may be reconstructed

dichotic pitches as illusions of binaural unmasking i huggins pitch and the binaural edge pitch the two most salient dichotic pitches the huggins pitch hp and the binaural edge pitch bep are produced by applying interaural phase transitions of 360 and 180 degrees respectively to a broadband noise this paper examines accounts of these pitches concentrating on a central activity pattern cap model and a modified equalization cancellation me c model the cap model proposes that a dichotic pitch is heard at frequency f when an individual across frequency scan in an interaural cross correlation matrix contains a sharp peak at f the me c model proposes that a dichotic pitch is heard when a plot of interaural decorrelation against frequency contains a peak at f the predictions of the models diverge for the bep at very narrow transition bandwidths the me c model predicts that salience is sustained while the cap model predicts that salience declines and that the dominant percept is of the in phase segment of the noise experiment 1 showed that the salience of the bep was sustained at the narrowest bandwidths that could be generated 0 5 of the transition frequency experiment 2 confirmed that the pitch of a bep produced by a 0 5 transition bandwidth was close to the frequency of the transition band experiment 3 showed that pairs of simultaneous narrow 180 degree transitions whose frequencies corresponded to vowel formants were perceived as the intended vowels moreover the same vowels were perceived whether the in phase portion of the noise lay between the two transition frequencies or on either side of them in contrast different patterns of identification responses were made to diotic band pass and band stop noises whose cutoff frequencies corresponded to the same formants thus the vowel identification responses made to the dichotic stimuli were not based on hearing the in phase portions of the noise as formants these results are not predicted by the cap model but are consistent with the me c model it is argued that the me c model provides a more coherent and parsimonious account of many aspects of the hp and the bep than do alternative models

numerical conformal mapping of multiply connected regions onto the fifth category of koebe s canonical slit regions abstract this paper presents a boundary integral method for approximating the conformal mapping from bounded multiply connected regions onto the fifth category of koebe s classical canonical slit regions the method is based on a uniquely solvable boundary integral equation with generalized neumann kernel the results of some test calculations illustrate the performance of the presented method

inverse eigenvalue problem for a modified vibrating system let lambda i 1 n be the eigenvalues of a simply connected mass spring system suppose that a simple oscillator of mass m and stiffness k is attached to the system and let mu i 1 n

the case of the missing delay lines synthetic delays obtained by cross channel phase interaction temporal models of pitch and harmonic segregation call for delays of up to 30ms to cover the full range of existence of musical pitch to date there is little anatomical or physiological evidence for delays that long we propose a mechanism by which delays may be synthesized from cross channel phase interaction phases of adjacent cochlear filter channels are shifted by an amount proportional to frequency and then combined as a weighted sum to approximate a delay synthetic delays may be used by pitch perception models such as autocorrelation segregation models such as harmonic cancellation and binaural processing models to explain sensitivity to large interaural delays the maximum duration of synthetic delays is limited by the duration of the impulse responses of cochlear filters itself inversely proportional to cochlear filter bandwidth maximum delay is thus frequency dependent this may explain the fact puzzling for temporal pitch models such as autocorrelation that pitch is more salient and eas

detection of static and dynamic changes in interaural correlation this study examines the relation between a static and a dynamic measure of interaural correlation discrimination 1 the just noticeable difference jnd in interaural correlation and 2 the minimum detectable duration of a fixed interaural correlation change embedded within a single noise burst of a given reference correlation for the first task jnds were obtained from reference interaural correlations of 1 1 and from 0 interaural correlation in either the positive or negative direction for the dynamic task duration thresholds were obtained for a brief target noise of 1 1 and 0 interaural correlation embedded in reference marker noise of 1 1 and 0 interaural correlation performance with a reference interaural correlation of 1 was significantly better than with a reference correlation of 1 similarly when the reference noise was interaurally uncorrelated discrimination was significantly better for a target correlation change towards 1 than towards 1 thus for both static and dynamic tasks interaural correlation discrimination in the positive range was significantly better than in the negative range using the two measures the length of a binaural temporal window was estimated its equivalent rectangular duration erd was approximately 86 ms and independent of the interaural correlation configuration

frequency difference limens of pure tones and harmonics within complex stimuli in mongolian gerbils and humans frequency difference limens fdls for pure tones between 200 and 6400hz and for the first the second or the eighth harmonic of an 800hz complex in four mongolian gerbils meriones unguiculatus were determined using a go nogo procedure the 12 harmonics of the complex started either in sine phase or at a random phase gerbils showed very high pure tone fdls ranging from 17 1 weber fraction 200hz to 6 7 6400hz they performed much better in detecting mistuning of a harmonic in the complex in the sine phase condition with fdls decreasing from 0 07 for the first harmonic to 0 02 for the eighth harmonic fdls were about one order of magnitude higher when temporal cues were degraded by randomizing the starting phase of every component in the harmonic complex for every stimulus these results are strikingly different from those obtained in four human subjects who needed about four times higher frequency shifts than gerbils for detecting a mistuned component in a sine phase complex and showed similar

on sufficient and necessary conditions for the jacobi matrix inverse eigenvalue problem in this paper we study the inverse eigenvalue problem of a specially structured jacobi matrix which arises from the discretization of the differential equation governing the axial of a rod with varying cross section ram and elhay 1998 commum numer methods engng 14 597 608 we give a sufficient and some necessary conditions for such inverse eigenvalue problem to have solutions based on these results a simple method for the reconstruction of a jacobi matrix from eigenvalues is developed numerical examples are given to demonstrate our results

effects of spectral smearing and temporal fine structure degradation on speech masking release this study assessed the effects of spectral smearing and temporal fine structure tfs degradation on masking release mr the improvement in speech identification in amplitude modulated compared to steady noise observed for normal hearing listeners syllables and noise stimuli were processed using either a spectral smearing algorithm or a tone excited vocoder the two processing schemes simulated broadening of the auditory filters by factors of 2 and 4 simulations of the early stages of auditory processing showed that the two schemes produced comparable excitation patterns however fundamental frequency f0 information conveyed by tfs was degraded more severely by the vocoder than by the spectral smearing algorithm both schemes reduced mr but for each amount of spectral smearing the vocoder produced a greater reduction in mr than the spectral smearing algorithm consistent with the effects of each scheme on f0 representation moreover the effects of spectral smearing on mr produced by the two schemes were different for manner and voicing finally mr data for listeners with moderate hearing loss were well matched by mr data obtained for normal hearing listeners with vocoded stimuli suggesting that impaired frequency selectivity alone may not be sufficient to account for the reduced mr observed for hearing impaired listeners

psychophysical evidence against the autocorrelation theory of auditory temporal processing nowadays it is widely believed that the temporal structure of the auditory nerve fibers response to sound stimuli plays an important role in auditory perception an influential hypothesis is that information is extracted from this temporal structure by neural operations akin to an autocorrelation algorithm the goal of the present work was to test this hypothesis the stimuli consisted of sequences of unipolar clicks that were high pass filtered and mixed with low pass noise so as to exclude spectral cues in experiment 1 interfering clicks were inserted in an otherwise periodic isochronous click sequence each click belonging to the periodic sequence was followed after a random portion of the period by one interfering click this disrupted the detection of temporal regularity even when the interfering clicks were 5 db less intense than the periodic clicks experiments 2 4 used click sequences that showed a single peak in their autocorrelation functions for some sequences this peak originated from first order temporal regularities that is from the temporal relations between consecutive clicks for other sequences the peak originated instead from second order regularities relative to nonconsecutive clicks the detection of second order regularities appeared to be much more difficult than the detection of comparable first order regularities overall these results do not tally with the current autocorrelation models of temporal processing they suggest that the extraction of temporal information from a group of closely spaced spectral components makes no use of time intervals between nonconsecutive peaks of the amplitude envelope

binaural coherence edge pitch the binaural coherence edge pitch bicep is a dichotic broadband noise pitch effect similar to the binaural edge pitch the noise is made by summing sine waves with equal amplitudes and random phases the interaural phase angle is a constant for sine wave components with frequencies below a chosen frequency and it is a random variable for components with frequencies above that frequency the chosen frequency is a coherence edge because the signals to the two ears are mutually coherent within any band of frequencies below the edge and they are mutually incoherent in any band above the edge sine tone pitch matching experiments show that the bicep exists for coherence edge frequencies between 300 and 1000 hz and that it is always matched by a frequency above the edge frequency by 5 10 the effect can be extended to higher edge frequencies at least 2000 hz if the listener is appropriately cued the results do not depend upon whether the coherent components are presented in phase or completely out of p

an inverse eigenvalue problem for the finite element model of a vibrating rod an inverse eigenvalue problem for the finite element model of a longitudinally vibrating rod whose one end is fixed and the other end is supported on a spring is considered it is known that the mass and stiffness matrices are both tridiagonal for the finite element model of the rod based on linear shape functions it is shown that the cross section areas can be determined from the spectrum of the rod the inverse vibration problem can be recast into an inverse eigenvalue problem of a special jacobi matrix the necessary and sufficient conditions for the construction of a physically realizable rod with positive cross section areas are established a numerical method is presented and an illustrative example is given

fast conformal mapping of multiply connected regions abstract an iterative method is presented which constructs for an unbounded region g with m holes and sufficiently smooth boundary a circular region h and a conformal mapping from h to g with the usual normalization both h and are uniquely determined by g with a few modifications the method can also be applied to a bounded region g with m holes the canonical region h is then the unit disc with m circular holes the proposed method also determines the centers and radii of the boundary circles of h and requires at each iterative step the solution of a riemann hilbert rh problem which has a unique solution numerically the rh problem can be treated efficiently by the method of successive conjugation using the fast fourier transform fft the iteration for the solution of the rh problem converges linearly the conformal mapping method converges quadratically the results of some test calculations exemplify the performance of the method

the lateralization of simple dichotic pitches a simple dichotic pitch arises when a single narrow band possesses a different interaural configuration from a surrounding broadband noise whose interaural configuration is uniform and correlated such pitches were created by interaurally decorrelating a narrow band experiment 1 or by giving a narrow band a different interaural time difference from the noise experiment 2 using an adaptive forced choice procedure listeners adjusted the interaural intensity difference of pointers to match their lateralization to that of the dichotic pitches the primary determinants of lateralization were the interaural configuration of the broadband noise experiment 1 the center frequency of the narrow band experiment 1 and its interaural configuration experiment 2 the ability of two computational models to predict these results was evaluated a version of the central spectrum model j raatgever and f a bilsen j acoust soc am 80 429 441 1986 incorporating realistic frequency selectivity accounted for the main results of experiment 1 but not experiment 2 a new reconstruction comparison model accounted for the main results of both experiments to accommodate the variables shown to influence lateralization this model segregates evidence of the dichotic pitch from the noise reconstructs the cross correlogram of the noise and compares it with the cross correlogram of the original stimulus

relative dominance of individual partials in determining the pitch of complex tones these experiments were conducted to determine the dominance of each partial in determining the residue pitch of a complex tone subjects were required to make pitch matches to a complex tone which had one partial slightly mistuned from its correct harmonic value the shift in residue pitch was measured as a function of the frequency shift of the harmonic for each harmonic in turn for mistunings up to 2 3 the shift in residue pitch was approximately a linear function of the shift in the harmonic but for greater mistunings the shift in residue pitch was reduced the degree to which a given harmonic can influence residue pitch gives a measure of the dominance of that harmonic the dominant harmonics were always contained within the lowest six harmonics for fundamental frequencies of 100 200 and 400 hz but there were marked individual differences in the exact distribution of dominance across harmonics the level of a harmonic relative to adjacent harmonics can have a significant effect on its dominance the implications of the results for theories of pitch perception are discussed

modeling the perception of concurrent vowels vowels with different fundamental frequencies if two vowels with different fundamental frequencies f0 s are presented simultaneously and monaurally listeners often hear two talkers producing different vowels on different pitches this paper describes the evaluation of four computational models of the auditory and perceptual processes which may underlie this ability each model involves four stages i frequency analysis using an auditory filter bank ii determination of the pitches present in the stimulus iii segregation of the competing speech sources by grouping energy associated with each pitch to create two derived spectral patterns and iv classification of the derived spectral patterns to predict the probabilities of listeners vowel identification responses the place models carry out the operations of pitch determination and spectral segregation by analyzing the distribution of rms levels across the channels of the filter bank the place time models carry out these operations by analyzing the periodicities in the wavef

solving constrained quadratic inverse eigenvalue problem via conjugate direction method abstract inverse eigenvalue problems are among the most important problems in numerical linear algebra this paper is concerned with the problem of designing an iterative method for a quadratic inverse eigenvalue problem of the form m x 2 g x k x 0 where m g and k should be partially doubly symmetric under a prescribed submatrix constraint this kind of quadratic inverse eigenvalue problem includes the classical and generalized inverse eigenvalue problems as special cases we propose the conjugate direction cd method for computing the least frobenius norm solutions of this constrained quadratic inverse eigenvalue problem in a finite number of steps in the absence of round off errors the cd method can automatically determine the solvability of this problem finally the overall performance and efficiency of the cd method for computing approximate solutions of the problem are discussed

inverse eigenvalue problems a collection of inverse eigenvalue problems are identified and classified according to their characteristics current developments in both the theoretic and the algorithmic aspects are summarized and reviewed in this paper this exposition also reveals many open questions that deserve further study an extensive bibliography of pertinent literature is attached

perception of the low pitch of frequency shifted complexes when all of the components in a harmonic complex tone are shifted in frequency by f the pitch of the complex shifts roughly in proportion to f for tones with a small number of components the shift is usually somewhat larger than predicted from pitch theories which has been attributed to the influence of combination tones smoorenburg j acoust soc am 48 924 941 1970 experiment 1 assessed whether combination tones influence the pitch of complex tones with more than five harmonics by using noise to mask the combination tones the matching stimulus was a harmonic complex test complexes were bandpass filtered with passbands centered on harmonic numbers 5 resolved 11 intermediate or 16 unresolved and fundamental frequencies f0s were 100 200 or 400 hz for the intermediate and unresolved conditions the matching stimuli were filtered with the same passband to minimize differences in the excitation patterns of the test and matching stimuli for the resolved condition the matching st

multilevel matrix multiplication and fast solution of integral equations abstract a fast multigrid approach is described for the task of calculating k x y u y dy for each x r d discretizing by an equidistant grid with n points and meshsize h and approximating the integrations to o h2s accuracy it is shown that the complexity of this calculation can be reduced from o n2 to o sn provided the kernel k is sufficiently smooth for potential type kernels the complexity is reduced to o sn log n corresponding integral equations can be solved to a similar accuracy in basically the same amount of work using a special kind of distributed relaxation in a multigrid algorithm one and two dimensional numerical tests and theoretical derivations of optimal strategies are reported the method is applicable to the task of multiplying by any matrix with appropriate smoothness properties including most types of many body interactions

the inverse eigenvalue problem of generalized reflexive matrices and its approximation national natural science foundation of china 10961010 natural science foundation of jiangxi china 2007gzs1760 jiangxi education office china gjj08432

a unitary model of pitch perception a model of the mechanism of residue pitch perception is revisited it is evaluated in the context of some new empirical results and it is proposed that the model is able to reconcile a number of differing approaches in the history of theories of pitch perception the model consists of four sequential processing stages peripheral frequency selectivity within channel half wave rectification and low pass filtering within channel periodicity extraction and cross channel aggregation of the output the pitch percept is represented by the aggregated periodicity function using autocorrelation as the periodicity extraction method and the summary autocorrelation function sacf as the method for representing pitch information it is shown that the model can simulate new experimental results that show how the quality of the pitch percept is influenced by the resolvability of the harmonic components of the stimulus complex these include i the pitch of harmonic stimuli whose components alternate in phase ii the increased frequency difference limen of tones consisting of higher harmonics and iii the influence of a mistuned harmonic on the pitch of the complex as a function of its harmonic number to accommodate these paradigms it was necessary to compare stimuli along the length of the sacf rather than relying upon the highest peak alone these new results demonstrate that the model responds differently to complexes consisting of low and high harmonics as a consequence it is not necessary to postulate two separate mechanisms to explain different pitch percepts associated with resolved and unresolved harmonics

spectral pattern harmonic relations and the perceptual grouping of low numbered components mistuning a harmonic increases its salience and produces an exaggerated change in its pitch the effects on component grouping of spectral pattern global pitch and local harmonicity were explored using these phenomena stimuli were either harmonic f0 200 hz or frequency shifted by 25 of f0 component 1 or 2 was replaced by one of a set of sinusoidal probes in the same spectral region listeners either matched the probe pitch by adjusting the frequency of a pure tone experiments 1 and 3 or matched the probe loudness by adjusting the level of a tone of identical frequency experiment 2 probe positions corresponding to greatest perceptual fusion were estimated from the variations in pitch shift and loudness across frequency both measures gave similar estimates for harmonic stimuli fusion was greatest at harmonic values for shifted stimuli fusion was greatest close to the suboctave 225 hz and the frequency 450 hz of component 2 the latter value moved downwards to near 433 hz 2 3 ratio with component 3 when component 1 was removed together these results indicate that the lowest component of a shifted complex is grouped by local harmonicity whereas the higher components are grouped by common spectral spacing global pitch did not influence component grouping

integration of monaural and binaural evidence of vowel formants the intelligibility of speech is sustained at lower signal to noise ratios when the speech has a different interaural configuration from the noise this paper argues that the advantage arises in part because listeners combine evidence of the spectrum of speech in the across frequency profile of interaural decorrelation with evidence in the across frequency profile of intensity to support the argument three experiments examined the ability of listeners to integrate and segregate evidence of vowel formants in these two profiles in experiment 1 listeners achieved accurate identification of the members of a small set of vowels whose first formant was defined by a peak in one profile and whose second formant was defined by a peak in the other profile this result demonstrates that integration is possible experiment 2 demonstrated that integration is not mandatory insofar as listeners could report the identity of a vowel defined entirely in one profile despite the presence of a competing vowel in the other profile the presence of the competing vowel reduced accuracy of identification however showing that segregation was incomplete experiment 3 demonstrated that segregation of the binaural vowel in particular can be increased by the introduction of an onset asynchrony between the competing vowels the results of experiments 2 and 3 show that the intrinsic cues for segregation of the profiles are relatively weak overall the results are compatible with the argument that listeners can integrate evidence of spectral peaks from the two profiles

suggested formulae for calculating auditory filter bandwidths and excitation patterns recent estimates of auditory filter shape are used to derive a simple formula relating the equivalent rectangular bandwidth erb of the auditory filter to center frequency the value of the auditory filter bandwidth continues to decrease as center frequency decreases below 500 hz a formula is also given relating erb rate to frequency finally a method is described for calculating excitation patterns from filter shapes

a fast algorithm for linear complex chebyshev approximations we propose a new algorithm for finding best minimax polynomial approximations in the complex plane the algorithm is the first satisfactory generalization of the well known remez algorithm for real approximations among all available algorithms ours is the only quadratically convergent one numerical examples are presented to illustrate rapid convergence

what makes a melody the perceptual singularity of pitch sequences this study investigated the ability of normal hearing listeners to process random sequences of tones varying in either pitch or loudness same different judgments were collected for pairs of sequences with a variable length up to eight elements and built from only two different elements which were 200 ms harmonic complex tones the two possible elements of all sequences had a fixed level of discriminability corresponding to a d value of about 2 irrespective of the auditory dimension pitch or loudness along which they differed this made it possible to assess sequence processing per se independent of the accuracy of sound encoding pitch sequences were found to be processed more effectively than loudness sequences however that was the case only when the sequence elements included low rank harmonics which could be at least partially resolved in the auditory periphery the effect of roving and transposition was also investigated these manipulations reduced overall performance especially transpo

an inverse eigenvalue problem for pseudo jacobi matrices abstract in this paper the theory on direct and inverse spectral problems for jacobi matrices is revisited in a kind of pseudo jacobi matrices j n r with a mixed path as its graph in the non self adjoint setting in this context a sign change in one of the nondiagonal entries of the matrix yields strong perturbations in its spectral properties the reconstruction of a pseudo jacobi matrix from its spectrum and the spectra of two complementary principal matrices is investigated an algorithm for the reconstruction of matrices from prescribed spectral data is provided and illustrative numerical experiments are performed

left and right inverse eigenvalue problem of r s symmetric matrices and its optimal approximation problem the left and right inverse eigenvalue problem which mainly arises in perturbation analysis of matrix eigenvalue and recursive matters has some practical applications in engineer and scientific computation fields in this paper we give the solvability conditions of and the general expressions to the left and right inverse eigenvalue problem for the r s symmetric and r s skew symmetric solutions the corresponding best approximation problems for the left and right inverse eigenvalue problem are also solved that is given an arbitrary complex n by n matrix a find a r s symmetric or r s skew symmetric matrix a a which is the solution to the left and right inverse eigenvalue problem such that the distance between a and a a is minimized in the frobenius norm we give an explicit solution to the best approximation problem in the r s symmetric and r s skew symmetric solution sets of the left and right inverse eigenvalue problem under the assumption that r r and s s a numerical example is given to illustrate the effectiveness of our method

on capacity computation for symmetric polygonal condensers abstract making use of two different analytical numerical methods for capacity computation we obtain matching to a very high precision numerical values for capacities of a wide family of planar condensers these two methods are based respectively on the use of the lauricella function bezrodnykh and vlasov 2002 bezrodnykh 2016 64 65 and riemann theta functions bogatyrev 2012 grigoriev 2013 bogatyrev and grigor ev 2017 bogatyrev and grigor ev 2018 we apply these results to benchmark the performance of numerical algorithms which are based on adaptive h p finite element method hakula et al 2011 2013 2018 and boundary integral method tsuji 1959 jaswon and symm 1977 albrecht and collatz 1980

representation of conformal maps by rational functions the traditional view in numerical conformal mapping is that once the boundary correspondence function has been found the map and its inverse can be evaluated by contour integrals we propose that it is much simpler and 10 1000 times faster to represent the maps by rational functions computed by the aaa algorithm to justify this claim first we prove a theorem establishing root exponential convergence of rational approximations near corners in a conformal map generalizing a result of d j newman in 1964 this leads to the new algorithm for approximating conformal maps of polygons then we turn to smooth domains and prove a sequence of four theorems establishing that in any conformal map of the unit circle onto a region with a long and slender part there must be a singularity or loss of univalence exponentially close to the boundary and polynomial approximations cannot be accurate unless of exponentially high degree this motivates the application of the new algorithm to smooth domains where it is again found to be highly effective

comparing f0 discrimination in sequential and simultaneous conditions in an influential study carlyon and shackleton j acoust soc am 95 3541 3554 1994 measured listeners performance d in fundamental frequency f0 discrimination between harmonic complex tones hcts presented simultaneously in different spectral regions and compared their performance with that found in a sequential comparison task in this letter it is suggested that carlyon and shackleton s analysis of the simultaneous comparison data did not adequately reflect their assumption that listeners were effectively comparing f0 s across regions a reanalysis consistent with this assumption is described the new results suggest that under the assumption that listeners were effectively comparing f0 across regions their performance in this task was substantially higher than originally estimated by carlyon and shackleton and in some conditions much higher than expected from the performances measured in a traditional f0 discrimination task with sequential hcts possible explanations for this outcome

solving theodorsen s integral equation for conformal maps with the fast fourier transform and various nonlinear iterative methods we investigate several iterative methods for the numerical solution of theodorsen s integral equation the discretization of which is either based on trigonometric polynomials or function families with known attenuation factors all our methods require simultaneous evaluations of a conjugate periodic function at each step and allow us to apply the fast fourier transform for this in particular we discuss the nonlinear jor iteration the nonlinear sor iteration a nonlinear second order euler iteration the nonlinear chebyshev semi iterative method and its cyclic variant under special symmetry conditions for the region to be mapped onto we establish local convergence in the case of discretization by trigonometric interpolation and give simple formulas for the optimal parameters e g the underrelaxation factor and the asymptotic convergence factor weaker related results for the general non symmetric case are presented too practically our methods extend the range of application of theodorsen s method and improve its effectiveness strikingly

fast potential theory ii layer potentials and discrete sums we present three new families of fast algorithms for classical potential theory based on ewald summation and fast transforms of gaussians and fourier series ewald summation separates the green function for a cube into a high frequency localized part and a rapidly converging fourier series each part can then be evaluated efficiently with appropriate fast transform algorithms our algorithms are naturally suited to the use of green functions with boundary conditions imposed on the boundary of a cube rather than free space green functions our first algorithm evaluates classical layer potentials on the boundary of a d dimensional domain with d equal to two or three the quadrature error is o hm e where h is the mesh size on the boundary and m is the order of quadrature used the algorithm evaluates the discretized potential using n elements at o n points in o n log n arithmetic operations the constant in o n log n depends logarithmically on the desired error tolerance our second scheme evaluates a layer potential on the domain itself with the same accuracy it produces md values using n boundary elements in o n md log m arithmetic operations our third method evaluates a discrete sum of values of the green function of the type which occur in particle methods it attains error at a cost o na log n where a 2 1 dd and d is the hausdorff dimension of the set where the sources concentrate in the limit n thus it is o n log n when the sources do not cluster too much and close to o n log n in the important practical case when the points are uniformly distributed over a hypersurface we also sketch an o n log n algorithm based on special functions two dimensional numerical results are presented for all three algorithms layer potentials are evaluated to second order accuracy in times which exhibit considerable speedups even over a reasonably sophisticated direct calculation discrete sum calculations are speeded up astronomically our algorithm reduces the cpu time required for a calculation with 40 000 points from six months to one hour

pitch strength of iterated rippled noise two versions of a cascade add attenuate and delay circuit were used to generate iterated rippled noise irn stimuli irn stimuli produce a repetition pitch whose pitch strength relative to the noise percept can be varied by changing the type of circuit the attenuation or the number of iterations in the circuit listeners were asked to use pitch strength to discriminate between various pairs of irn stimuli which differed in the type of network used to generate the sounds the number of iterations and the attenuation in the network a description based on an exponential function of the first peak of the autocorrelation function of irn stimuli is consistent with the results the discrimination data were well fit by a function based on the difference in the exponential functions of the first peak of the autocorrelation functions a magnitude estimation experiment indicated that pitch strength was an exponential function of the height of the first peak in the autocorrelation function these results suggest that the strength of the pitch of irn stimuli is based on temporal processing as might be revealed by autocorrelation

effect of duration on the frequency discrimination of individual partials in a complex tone and on the discrimination of fundamental frequency thresholds for the discrimination of fundamental frequency fodls and frequency difference limens fdls for individual partials within a complex tone f0 250 hz harmonics 1 7 were measured for stimulus durations of 200 50 and 16 ms the fdls increased with decreasing duration although the results differed across subjects the effect of duration generally decreased as the harmonic number increased from 1 to 4 then increased as the harmonic number increased to 6 and finally decreased for the seventh harmonic for each duration fodls were smaller than the smallest fdl for any individual harmonic indicating that information is combined across harmonics in the discrimination of fo fodls predicted from the fdls corresponded well with observed fodls for the 200 and 16 ms durations but were significantly larger than observed fodls for the 50 ms duration a supplementary pitch matching experiment using two subjects indicated that the contribution of the seventh harmonic to the pitch of the 16 ms complex tone was smaller than would be predicted from the fdl for that harmonic the results are consistent with the idea that the dominant region shifts upward with decreasing duration but that the weight assigned to individual harmonics is not always adjusted in an optimal way

on the construction of a real symmetric five diagonal matrix from its three eigenpairs in this paper an inverse eigenvalue problem of constructing a real symmetric five diagonal matrix from its three eigenpairs is considered the necessary and sufficient conditions for the existence and uniqueness of the solutions are derived three numerical algorithms and three numerical experiments are given

a time domain description for the pitch strength of iterated rippled noise two versions of a cascaded add attenuate and delay circuit were used to generate iterated rippled noise irn stimuli irn stimuli produce a repetition pitch whose strength relative to the noise can be varied by changing the type of circuit the attenuation or the number of iterations in the circuit listeners were asked to discriminate between various pairs of irn stimuli which differed in the type of network used to generate the sounds or the number of iterations n 1 2 3 4 7 and 9 performance was determined for irn stimuli generated with delays of 2 4 and 8 ms and for four bandpass filter conditions 0 2000 250 2000 500 2000 and 750 2000 hz some irn stimuli were extremely difficult to discriminate despite relatively large spectral differences while other irn stimuli produced readily discriminable changes in perception despite small spectral differences these contrasting results are inconsistent with simple spectral explanations for the perception of irn stimuli an explanation based on the first peak of the autocorrelation function of irn stimuli is consistent with the results simulations of the processing performed by the peripheral auditory system i e interval histograms and correlograms produce results which are consistent with the involvement of these temporal processes in the perception of irn stimuli

the normalized correlation accounting for binaural detection across center frequency bernstein and trahiotis l r bernstein and c trahiotis j acoust soc am 100 1754 1763 1996 recently reported the results of experiments designed to determine the form of interaural correlation that accounts for listeners sensitivities to interaural disparities within high frequency stimuli overall those results demonstrated that listeners abilities to discriminate changes in the interaural correlation of the envelope from a base correlation of 1 0 were well accounted for by the use of the normalized correlation the purpose of this study was to determine how well the normalized correlation computed subsequent to half wave rectification and low pass filtering could account for binaural detection data at low intermediate and high frequencies respectively in a four interval two alternative task listeners detected which interval contained a tone between 500 hz and 2 khz added antiphasically to diotic 100 hz wide noise nos nonsignal intervals contained the tone added homophasically noso performance was measured for signal to noise ratios between 30 and 30 db results indicated that a low pass filter function based on physiological measures of synchrony in cochlear nerve fibers in conjunction with the assumption of half wave square law rectification accounted for typically 80 of the variance in the behavioral data

pitch strength of regular interval click trains with different length runs of regular intervals click trains were generated with first and second order statistics following kaernbach and demany j acoust soc am 104 2298 2306 1998 first order intervals are between successive clicks while second order intervals are those between every other click click trains were generated with a repeating alternation of fixed and random intervals which produce a pitch at the reciprocal of the duration of the fixed interval the intervals were then randomly shuffled and compared to the unshuffled alternating click trains in pitch strength comparison experiments in almost all comparisons for the first order interval stimuli the shuffled interval click trains had a stronger pitch strength than the unshuffled interval click trains the shuffled interval click trains only produced stronger pitches for second order interval stimuli when the click trains were unfiltered several experimental conditions and an analysis of runs of regular and random intervals in these click trains suggest that the auditory system is sensitive to runs of regular intervals in a stimulus that contains a mix of regular and random intervals these results indicate that fine structure regularity plays a more important role in pitch perception than randomness and that the long term autocorrelation function or spectra of these click trains are not good predictors of pitch strength

the conjugate function method and conformal mappings in multiply connected domains the conjugate function method is an algorithm for numerical computation of conformal mappings for simply and doubly connected domains in this paper the conjugate function method is generalized for

a nonoverlapping domain decomposition method for symm s equation for conformal mapping symm s equation is a first kind integral equation for computing conformal maps of simply connected regions the package confpack solves symm s equation by an indirect boundary element method using an accurate corner representation this solution technique is extended here to include nonoverlapping domain decomposition degrees of freedom are introduced on one or more interfaces and different unknowns are used leading to a system of second kind equations the corresponding linear system can be expressed in schur complement form the accurate treatment of corners is preserved in the new formulation the results of serial and parallel matlab implementations of the new algorithm show significant speedups as the number of unknowns grows

generalized inverse eigenvalue problem for matrices whose graph is a path abstract in this paper we analyse a special generalized inverse eigenvalue problem a n x b n x for the pair a n b n of matrices each of whose graph is a path on n vertices by investigating the leading principal minors of the matrix a n b n from the given data consisting of b n a matrix a k k n whose graph is a path on k vertices two column vectors x 2 y 2 r n k and distinct real numbers and we construct a n and two column vectors x 1 y 1 r k such that a k is the leading principal sub matrix of a n and x y are the eigenpairs of a n b n where x x 1 t x 2 t t and y y 1 t y 2 t t further numerical examples are also given to demonstrate the applicability of the results developed here

a central spectrum theory of binaural processing evidence from dichotic pitch a theory is presented that describes the binaural processing of interaural time or phase differences it is an elaboration of the central spectrum concept for the explanation of dichotic pitch phenomena f a bilsen pitch of noise signals evidence for a central spectrum j acoust soc am 61 150 161 1977 the generation is postulated for central activity patterns cap due to binaural interaction from these caps the central processor selects specific spectral information that constitutes the information for lateralization dichotic pitch binaural masking etc here a strategy is assumed to be based on central spectra cs rather than on interaural cross correlation for the calculation of the central activity patterns a number of assumptions have been introduced the peripheral filters are supposed to be infinitesimally narrow the analog filter outputs from corresponding filters at both ears are thought to interact by means of a linear delay and add mechanism the squared output power

modeling the identification of concurrent vowels with different fundamental frequencies human listeners are better able to identify two simultaneous vowels if the fundamental frequencies of the vowels are different a computational model is presented which for the first time is able to simulate this phenomenon at least qualitatively the first stage of the model is based upon a bank of bandpass filters and inner hair cell simulators that simulate approximately the most relevant characteristics of the human auditory periphery the output of each filter hair cell channel is then autocorrelated to extract pitch and timbre information the pooled autocorrelation function acf based on all channels is used to derive a pitch estimate for one of the component vowels from a signal composed of two vowels individual channel acfs showing a pitch peak at this value are combined and used to identify the first vowel using a template matching procedure the acfs in the remaining channels are then combined and used to identify the second vowel model recognition performance shows a rapid improvement in

equivalence of nystrom s method and fourier methods for the numerical solution of fredholm integral equations on demontre un resultat d equivalence de la methode de nystrom et de la methode de fourier avec des fonctions orthogonales pour la solution numerique des equations integrales de fredholm on en deduit des estimations d erreur pour la methode de nystrom on decrit exactement la regle de quadrature pour l integration numerique

the effect of cross channel synchrony on the perception of temporal regularity temporal models of pitch are based on the assumption that the auditory system measures the time intervals between neural events and that pitch corresponds to the most common time interval the current experiments were designed to test whether time intervals are analyzed independently in each peripheral channel or whether the time interval analysis in one channel is affected by synchronous activity in other channels regular and irregular click trains were filtered into narrow frequency bands to produce target and flanker stimuli the threshold for discriminating a regular target from an irregular distracter click train was measured in the presence of an irregular masker click train in the target band as a function of the frequency separation between the target band and a flanker band the flanker click train was either regular or irregular the threshold for detecting the regular target was 5 7 db lower when the flanker was regular the data indicate that the detection of temporal regularity and thus pitch involves cross channel processes that can operate over widely separated channels model simulations suggest that these cross channel processes occur after the time interval extraction stage and that they depend on the similarity or consistency of the time interval patterns in the relevant channels

binaural models and the strength of dichotic pitches modern physiologically based models of the binaural system incorporate internal delay lines in the pathways from left and right peripheries to central processing nuclei different binaural models for the formation of dichotic pitch employ these delay lines in different ways consequently the different models make different predictions for the relative strengths of dichotic pitches made with particular phase conditions the differences are magnified for dichotic pitches at low frequencies where especially long delay lines may be required data from four low frequency pitch strength experiments on pure tone like dichotic pitches two on huggins pitch and two on binaural coherence edge pitch are consistent with models of the equalization cancellation type and not consistent with the central activity pattern model

further evidence that fundamental frequency difference limens measure pitch discrimination difference limens for complex tones dlcs that differ in f0 are widely regarded as a measure of periodicity pitch discrimination however because f0 changes are inevitably accompanied by changes in the frequencies of the harmonics dlcs may actually reflect the discriminability of individual components to test this hypothesis dlcs were measured for complex tones the component frequencies of which were shifted coherently upward or downward by f 0 25 37 5 or 50 of the f0 yielding fully harmonic f 0 strongly inharmonic f 25 37 5 or odd harmonic f 50 tones if dlcs truly reflect periodicity pitch discriminability they should be larger worse for inharmonic tones than for harmonic and odd harmonic tones because inharmonic tones have a weaker pitch consistent with this prediction the results of two experiments showed a non monotonic dependence of dlcs on f with larger dlcs for f s of 25 or 37 5 than for f s of 0 or 50 of f0 these findings are consistent with

effects of contralateral presentation and of interaural time differences in segregating a harmonic from a vowel the extent to which the 500 hz component of a steady state vowel contributed to its phonemic category was measured by estimating the position of the i e phoneme boundary along a first formant f1 continuum shifts in the phoneme boundary were calibrated against shifts produced by physical changes in the level of the 500 hz component when the 500 hz component was presented contralateral to the rest of the vowel the phoneme boundary changed by an amount equivalent to a physical reduction in the level of the component of about 5 db experiment 1 however giving the 500 hz component an interaural time difference itd of 666 s and the remainder of the vowel an itd of 666 s did not reduce the component s contribution to vowel quality experiment 2 placing the 500 hz component of the vowel in a sequence of 500 hz tones substantially reduced the contribution of the 500 hz component the contribution was further reduced by giving both the tone sequence and the component an itd of 666 s and the re

on the determination of boundary collocation points for solving some problems for the laplace operator abstract boundary collocation is a method for obtaining approximate solutions of boundary problems for linear partial differential equations for which complete families of particular solutions are explicitly known the method contains various decisions which are important for its performance such as choice of solution subspace choice of basis for the subspace and choice of collocation points using a model problem some particular strategies for the determination of collocation points are investigated

mistuning detection and onset asynchrony in harmonic complexes in mongolian gerbils by applying a go nogo paradigm thresholds for detecting mistuning of components of a 200 hz complex were determined in the mongolian gerbil and compared with thresholds obtained in a previous study with an 800 hz complex frequency difference limens fdls for detecting mistuning decreased with increasing harmonic frequency and harmonic number 0 5 to 0 01 weber fraction it was furthermore examined how starting and ending the mistuned component earlier than the remaining complex affects the fdl duration of all components 400 ms time shift 30 to 500 ms large fdls that are similar to pure tone fdls between 21 and 6 7 were found for onset asynchronies of 300 ms and more indicating separate processing of the mistuned component small fdls that are similar to fdls of the synchronous condition were found if the temporal overlap between the mistuned component and the remaining complex was 100 ms or more these experimental data in combination with a simulation of processing of the harmonic complexe

separate mechanisms govern the selection of spectral components for perceptual fusion and for the computation of global pitch the perceptual fusion of harmonics is often assumed to result from the operation of a template mechanism that is also responsible for computing global pitch this dual role hypothesis was tested using frequency shifted complexes these sounds are inharmonic but preserve a regular pattern of equal component spacing the stimuli had a nominal fundamental f0 frequency of 200 hz 20 and were frequency shifted either by 25 0 or 37 5 of f0 three consecutive components 6 8 were removed and replaced with a sinusoidal probe located at one of a set of positions spanning the gap on any trial subjects heard a complex tone followed by an adjustable pure tone in a continuous loop subjects were well able to match the pitch of the probe unless it corresponded with a position predicted by the spectral pattern of the complex peripheral factors could not account for this finding in contrast hit rates were not depressed for probes positioned at integer multiples of the f0 s corresponding to the global pit

on zwicker tones and musical pitch in the likely absence of phase locking corresponding to the pitcha it was assessed whether zwicker tones zts an auditory afterimage produced by a band stop noise have a musical pitch first stage i musically trained subjects adjusted the frequency level and decay time of an exponentially decaying diotic sinusoid to sound similar to the zt they perceived following the presentation of diotic broadband noise for various band stop positions next stage ii subjects adjusted a sinusoid in frequency and level so that its pitch was a specified musical interval below that of either a preceding zt or a preceding sinusoid and so that it was equally loud for each subject the reference sinusoid corresponded to their adjusted sinusoid from stage i subjects selected appropriate frequency ratios for zts although the standard deviations of the adjustments were larger for the zts than for the equally salient sinusoids by a factor of 1 0 2 2 experiments with monaural stimuli led to similar results although the pitch of the zts could differ for monaural and diotic presentation of the zt exciting noise the results suggest that a weak musical pitch may exist in the absence of phase locking in the auditory nerve to the frequency corresponding to the pitch or harmonics thereof at the time of the percept

a stable richardson iteration method for complex linear systems the richardson iteration method is conceptually simple as well as easy to program and parallelize this makes the method attractive for the solution of large linear systems of algebraic equations with matrices with complex eigenvalues we change the ordering of the relaxation parameters of a richardson iteration method proposed by eiermann niethammer and varga for the solution of such problems the new method obtained is shown to be stable and to have better convergence properties

the solvability conditions for the inverse eigenvalue problem of the symmetrizable matrices the necessary and sufficient conditions for the solvability of the inverse eigenvalue problem ax x over the class of the symmetrizable matrices are discussed the general expression of the solution is given moreover the related optimal approximation problem to a given matrix over the solution set is solved

perceptual separation of concurrent speech sounds absence of across frequency grouping by common interaural delay three experiments and a computational model explored the role of within channel and across channel processes in the perceptual separation of competing complex broadband sounds which differed in their interaural phase spectra in each experiment two competing vowels whose first and second formants were represented by two discrete bands of noise were presented concurrently for identification experiments 1 and 2 showed that listeners were able to identify the vowels accurately when each was presented to a different ear but were unable to identify the vowels when they were presented with different interaural time delays itds i e listeners could not group the noisebands in different frequency regions with the same itd and thereby separate them from bands in other frequency regions with a different itd experiment 3 demonstrated that while listeners were unable to exploit a difference in interaural delay between the pairs of noisebands listeners could identify a vowel defined by interaurally decorrelated noisebands when the other two noisebands were interaurally correlated a computational model based upon that of durlach j acoust soc am 32 1075 1076 1960 showed that the results of these and other experiments can be interpreted in terms of a within channel mechanism which is sensitive to interaural decorrelation thus the across frequency integration which occurs in the lateralization of complex sounds may play little role in segregating concurrent sounds

the frequency range applicable to pitch identification based upon the auto correlation function model abstract pitch identification experiments were conducted to determine the upper boundary of the frequency range within which the autocorrelation function acf model described by ando see reference 16 is applicable to the phenomenon of the missing fundamental of a complex tone pitch matching tests were conducted using 1 complex tones consisting of 2 f 3 f and 4 f where f denotes the fundamental frequencies of 0 5 1 0 1 2 1 6 2 0 or 3 0 khz and 2 complex tones consisting of 2 f and 3 f these tests showed that for both kinds of complex tones the acf model can account for the perception of pitch when the fundamental frequency is below 1200 hz

numerical conformal mappings of bounded multiply connected domains by the charge simulation method we present here a simple method of numerical conformal mappings from bounded multiply connected domains onto the bounded canonical slit domains of nehari i e a disk with concentric circular slits and an annulus with concentric circular slits in this method we express the mapping functions in terms of a pair of conjugate harmonic functions and approximate them using the charge simulation method by a linear combination of complex logarithmic functions some numerical examples show the effectiveness of the method

cancellation model of pitch perception a model of pitch perception is presented involving an array of delay lines and inhibitory gating neurons in response to a periodic sound a minimum appears in the pattern of outputs of the inhibitory neurons at a lag equal to the period of the sound the position of this minimum is the cue to pitch the model is similar to the autocorrelation model of pitch multiplication being replaced by an operation similar to subtraction and maxima by minima the two models account for a wide class of pitch phenomena in very much the same way the principal goal of this paper is to demonstrate this fact several features of the cancellation model may be to its advantage it is closely related to the operation of harmonic cancellation that can account for segregation of concurrent harmonic stimuli it can be generalized to explain the perception of multiple pitches and it shows a greater degree of sensitivity to phase than autocorrelation which may allow it to explain certain phenomena that autocorrelation cannot account for

orthogonal polynomials of equilibrium measures supported on cantor sets the equilibrium measure of a compact set is a fundamental object in logarithmic potential theory we compute numerically this measure and its orthogonal polynomials when the compact set is a cantor set defined by an iterated function system we first construct sequences of discrete measures via the solution of large systems of non linear equations that converge weakly to the equilibrium measure successively we compute their jacobi matrices via standard procedures enhanced for the scope numerical estimates of the convergence rate to the limit jacobi matrix are provided which show stability and efficiency of the whole procedure as a companion result we also compute jacobi matrices in two other cases equilibrium measures on finite sets of intervals and balanced measures of iterated function systems these algorithms can reach large polynomial orders therefore we study the asymptotic behavior of the orthogonal polynomials and by a natural extension of the concept of regular root asymptotics we derive an efficient scheme for the computation of complex green s functions and of related conformal mappings

pitch shifts of mistuned partials a time domain model mistuning one partial of a complex harmonic tone makes that partial easier to hear as a tone separate from the complex at the same time two pitch shifts may be observed first the low pitch of the complex is shifted in the direction of the mistuning as if it were pulled by the partial second the mistuning of the partial is perceptually exaggerated as if the pitch of the partial were pushed away from the harmonic series defined by the complex this paper shows how the latter effect can emerge within a hypothetical neural circuit the circuit involves a gating neuron fed by three pathways one direct and excitatory and the other two delayed and inhibitory the neuron responds to any excitatory input spike unless it is accompanied by an inhibitory input spike on either delayed input thus acting as a kind of anticoincidence counter the first delay is fixed and tuned to the period of the background harmonic complex its purpose is to weaken correlates of in tune components and allow the mistuned partial to stand out the second delay is variable and used to estimate the period of the mistuned partial by searching for a minimum output as a function of delay with an appropriate choice of parameters the estimate is subject to shifts that are of the same sign as the mistuning and that peak at about 4 mistuning and decrease beyond as observed experimentally

perceptual fusion and fragmentation of complex tones made inharmonic by applying different degrees of frequency shift and spectral stretch global pitch depends on harmonic relations between components but the perceptual coherence of a complex tone cannot be explained in the same way instead it has been proposed that the auditory system responds to a common pattern of equal spacing between components but is only sensitive to deviations from this pattern over a limited range roberts and brunstrom j acoust soc am 104 2326 2338 1998 this hypothesis predicts that spectral fusion will be largely unaffected either by frequency shifting a harmonic stimulus because equal spacing is preserved or by small degrees of spectral stretch because significant deviations from equal spacing only cumulate over large spectral distances complex tones were either shifted by 0 50 of f0 200 hz 10 or stretched by 0 12 of f0 100 hz 10 subjects heard a complex followed by a pure tone in a continuous loop one of the components 2 11 was mistuned by 4 and subjects adjusted the pure tone to match its pitch broadly consistent with our hypothesis frequency shifts had relatively little effect on hit rates and only large degrees of stretch reduced them substantially the implications for simultaneous grouping are explored with reference to an autocorrelation model of auditory processing

missing data model of vowel identification vowel identity correlates well with the shape of the transfer function of the vocal tract in particular the position of the first two or three formant peaks however in voiced speech the transfer function is sampled at multiples of the fundamental frequency f0 and the short term spectrum contains peaks at those frequencies rather than at formants it is not clear how the auditory system estimates the original spectral envelope from the vowel waveform cochlear excitation patterns for example resolve harmonics in the low frequency region and their shape varies strongly with f0 the problem cannot be cured by smoothing lag domain components of the spectral envelope are aliased and cause f0 dependent distortion the problem is severe at high f0 s where the spectral envelope is severely undersampled this paper treats vowel identification as a process of pattern recognition with missing data matching is restricted to available data and missing data are ignored using an f0 dependent weighting functi

linear parameterized inverse eigenvalue problem of bisymmetric matrices abstract in this paper we consider the linear parameterized inverse eigenvalue problem of bisymmetric matrices which is described as follows problem i given real bisymmetric matrices b 0 b 1 b 2 b n and real numbers 1 2 n find values of c c 1 c 2 c n t such that the eigenvalues of the matrix b c b 0 c 1 b 1 c 2 b 2 c n b n are precisely 1 2 n we first establish the structure of bisymmetric matrices based on the newton type iterative method we then turn problem i into the inverse eigenvalue problems of symmetric matrices with small sizes and solve these problems finally we present numerical examples to illustrate our results

temporal dynamics of pitch strength in regular interval noises the pitch strength of rippled noise and iterated rippled noise has recently been fitted by an exponential function of the height of the first peak in the normalized autocorrelation function j acoust soc am 100 3329 3335 1996 the current study compares the pitch strengths and autocorrelation functions of rippled noise rn and another regular interval noise aabb rn is generated by delaying a copy of a noise sample and adding it to the undelayed version aabb with the same pitch is generated by taking a sample of noise a with the same duration as the rn delay and repeating it to produce aa and then concatenating many of these once repeated sequences to produce aabbccdd the height of the first peak h1 in the normalized autocorrelation function of aabb is 0 5 identical to that of rn the current experiments show the following 1 aabb and rn can be discriminated when the pitch is less than about 250 hz 2 for these low pitches the pitch strength of aabb is greater than that for rn

the role of excitation pattern temporal fine structure and envelope cues in the discrimination of complex tones the discrimination of bandpass filtered harmonic h from inharmonic i tones produced by shifting all components of the h tones upwards by a fixed amount in hz could be based on shifts in the pattern of ripples in the excitation pattern ep or on changes in the temporal fine structure evoked by the tones the predictions of two computational ep models were compared with measured performance one model used auditory filters with bandwidth values specified by glasberg and moore 1990 hear res 47 103 138 and one used filters that were twice as sharp stimulus variables were passband width fundamental frequency harmonic rank n of the lowest component within the passband component phase cosine or random signal to noise ratio snr and random perturbation in level of each component in the tones while the ep models correctly predicted the lack of an effect of phase and some of the trends in the data as a function of fundamental frequency and n neither model predicted the worsening in perfo

a fast method for solving certain integral equations of the first kind with application to conforma mapping abstract we describe a fast iterative method for solving fredholm integral equations of the first kind whose kernels have a logarithmic principal part the method is a fourier galerkin method and due to the singularity of the kernel the linear system of simultaneous equations is block diagonally dominant and can be solved rapidly by an iterative method we present examples of the computation of conformal mappings of simply and multiply connected domains

searching for the time constant of neural pitch extraction multichannel auditory models have been repeatedly used to explain many aspects of human pitch perception among the most successful ones are models where pitch is estimated based on an analysis of periodicity in the simulated auditory nerve firing this periodicity analysis is typically implemented as a running autocorrelation i e the autocorrelation is calculated within a temporal window which is shifted along the time axis the window was suggested to have an exponential decay with time constant estimates between 1 5 and 100 ms the window length determines the minimal integration time of pitch extraction the present experiments are designed to quantify the temporal window of pitch extraction using regular interval noises rins rins were generated by concatenating equal duration noise samples which produce a pitch corresponding to the reciprocal of the sample duration when the samples are identical periodic noise when the samples are independent the stimulus is gaussian noise and produces no pitch using rin stimuli where periodic portions interchange with aperiodic portions it is shown that the temporal window of pitch extraction cannot be modeled using a single time constant but that the size of the temporal window depends on the pitch itself

on polynomial approximation in the complex plane with application to conformal mapping we consider the selection of polynomial bases for polynomial approximation of analytic functions on bounded simply connected regions in the complex plane while a monomial basis may be very ill conditioned we show that a basis of lagrange polynomials with fejer points as nodes is well conditioned numerical examples where we compute polynomial approximations of conformal mappings conclude the paper

pitch discrimination of diotic and dichotic tone complexes harmonic resolvability or harmonic number three experiments investigated the relationship between harmonic number harmonic resolvability and the perception of harmonic complexes complexes with successive equal amplitude sine or random phase harmonic components of a 100 or 200 hz fundamental frequency f0 were presented dichotically with even and odd components to opposite ears or diotically with all harmonics presented to both ears experiment 1 measured performance in discriminating a 3 5 5 frequency difference between a component of a harmonic complex and a pure tone in isolation listeners achieved at least 75 correct for approximately the first 10 and 20 individual harmonics in the diotic and dichotic conditions respectively verifying that only processes before the binaural combination of information limit frequency selectivity experiment 2 measured fundamental frequency difference limens f0 dls as a function of the average lowest harmonic number similar results at both f0 s provide further evidence that harmonic number not absolute frequency underlies the order of magnitude increase observed in f0 dls when only harmonics above about the 10th are presented similar results under diotic and dichotic conditions indicate that the auditory system in performing f0 discrimination is unable to utilize the additional peripherally resolved harmonics in the dichotic case in experiment 3 dichotic complexes containing harmonics below the 12th or only above the 15th elicited pitches of the f0 and twice the f0 respectively together experiments 2 and 3 suggest that harmonic number regardless of peripheral resolvability governs the transition between two different pitch percepts one based on the frequencies of individual resolved harmonics and the other based on the periodicity of the temporal envelope