plurality voting based multiple classifier systems statistically independent with respect to dependent classifier sets abstract the simultaneous use of multiple classifiers has been shown to provide performance improvement in classification problems the selection of an optimal set of classifiers is an important part of multiple classifier systems and the independence of classifier outputs is generally considered to be an advantage for obtaining better multiple classifier systems in this paper the need for the classifier independence is interrogated from classification performance point of view the performance achieved with the use of classifiers having independent joint distributions is compared to some other classifiers which are defined to have best and worst joint distributions these distributions are obtained by formulating the combination operation as an optimization problem the analysis revealed several important observations about classifier selection which are then used to analyze the problem of selecting an additional classifier to be used with the available multiple classifier system

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

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

iterated rippled noise discrimination at long durations iterated rippled noise irn was used to study discrimination of irn stimuli with a lower number of iterations from irn stimuli with a higher number of iterations as a function of stimulus duration 100 2000 ms such irn stimuli differ in the strength of the repetition pitch in some cases the gain used to generate irn stimuli was adjusted so that both irn stimuli in the discrimination task had the same height of the first peak in the autocorrelation function or autocorrelogram in previous work involving short duration irn stimuli 500 ms listeners were not able to discriminate between irn stimuli that had different numbers of iterations but the same height of the first peak in the autocorrelation function in the current study irn discrimination performance improved with increases in duration even in cases when the height of the first peak in the autocorrelation was the same for the two irn stimuli thus future studies involving discrimination of irn stimuli may need to use longer durations 1 s or greater than those that have been used in the past

does fundamental frequency discrimination measure virtual pitch discrimination studies of pitch perception often involve measuring difference limens for complex tones dlcs that differ in fundamental frequency f0 these measures are thought to reflect f0 discrimination and to provide an indirect measure of subjective pitch strength however in many situations discrimination may be based on cues other than the pitch or the f0 such as differences in the frequencies of individual components or timbre brightness here dlcs were measured for harmonic and inharmonic tones under various conditions including a randomized or fixed lowest harmonic number with and without feedback the inharmonic tones were produced by shifting the frequencies of all harmonics upwards by 6 25 12 5 or 25 of f0 it was hypothesized that if dlcs reflect residue pitch discrimination these frequency shifted tones which produced a weaker and more ambiguous pitch than would yield larger dlcs than the harmonic tones however if dlcs reflect comparisons of component pitches or timbre they should no

a central spectrum model a synthesis of auditory nerve timing and place cues in monaural communication of frequency spectrum a probabilistic psychophysical model for monaural communication from the auditory nerve to the brain is given in the form of a tonotopic display of stimulus spectrum termed central spectrum the model builds upon prior research demonstrating the potential of neural timing cues from the auditory nerve for conveying information on complex spectra and was designed to meet the quantified demands of the psychophysics of frequency measurement the central spectrum magnitude at each frequency is determined by the response of the auditory nerve fiber with characteristic frequency matching that frequency an interval histogram from each fiber is passed through a filter matched to the characteristic frequency of the fiber this output versus characteristic frequency defines the central spectrum detailed analysis demonstrates that efficient probabilistic processing of the central spectrum describes known psychophysical properties of frequency measurement in discrimination and periodicity pitch experiments psycho

the relative strength of the tone and noise components in iterated rippled noise rippled noise is constructed by delaying a random noise and adding it back to the original iterated rippled noise irn is constructed by repeating the delay and add process irn produces a two component perception i e a buzzy tone with a pitch equal to the reciprocal of the delay and a background noise that sounds like the original random noise the perceived tone noise ratio increases with the number of iterations the effective tone noise ratio in irn sounds with 1 16 iterations was measured in a discrimination matching experiment each irn was paired with a range of standard sounds having varying proportions of a broadband noise and a complex tone to find the point where their perceived tone noise ratios are the same the experiment shows that the tone noise ratio of the matching standard increases 3 8 db per doubling of the number of iterations in the irn stimulus spectral models of auditory perception explain the pitch of irn in terms of peaks in the region of the first five to eight harmonic

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

pitch strength of iterated rippled noise when the pitch is ambiguous two versions of a cascade of delay gain following delay and add circuits 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 the repetition pitch of irn is different when the delayed noise is subtracted gain 0 to the undelayed noise in the case of subtraction irn pitch is often ambiguous having two or more pitches listeners were asked to use pitch strength to discriminate between various pairs of irn stimuli generated with different gains different network circuits and different number of iterations for most conditions the gain was less than one the data were described by a description based on an exponential function of the largest peak of the autocorrelation function of irn stimuli w a yost j acoust soc am 100 511 518 1996 processed such that the spectral dominance region is emphasized these results suggest that the strength of the pitch of irn stimuli can be described by temporal processing mechanisms as might be revealed by autocorrelation

perception of the pitch of unresolved harmonics by 3 and 7 month old human infants three month olds discriminate resolved harmonic complexes on the basis of missing fundamental mf pitch in view of reported difficulty in discriminating unresolved complexes at 7 months and striking changes in the organization of the auditory system during early infancy infants ability to discriminate unresolved complexes is of some interest this study investigated the ability of 3 month olds 7 month olds and adults to discriminate the pitch of unresolved harmonic complexes using an observer based method stimuli were mf complexes bandpass filtered with a 12 db octave slope combined in random phase presented at 70 db sound pressure level spl for 650 ms with a 50 ms rise fall with a pink noise at 65 db spl the conditions were 1 low unresolved harmonics 2500 4500 hz based on mfs of 160 and 200 hz and 2 high unresolved harmonics 4000 6000 hz based on mfs of 190 and 200 hz to demonstrate mf discrimination participants had to ignore spectral changes in complexes with the same fundamental and respond only when the fundamental changed nearly all infants tested categorized complexes by mf pitch suggesting discrimination of pitch extracted from unresolved harmonics by 3 months adults also categorized the complexes by mf pitch although musically trained adults were more successful than musically untrained adults

pitch discrimination of harmonic complex signals residue pitch or multiple component discriminations two models for pitch discrimination of harmonic complex sounds are discussed a multiple band probability summation model using comparisons among component frequencies and a model in which residue pitches are compared the second model is based on goldstein s optimum processor pitch theory j acoust soc am 54 1496 1516 1973 and is distinguished from the multiple band model by an internal noise process pitch difference limens from 2i2afc tasks show that when the test signals comprise corresponding harmonics relative pitch difference limens are less than the smaller relative difference limens for the component frequencies which is consistent with the multiple band model the absence of corresponding harmonics significantly reduces relative pitch discriminability this effect supports the model on goldstein s theory it appears that residue pitch comparisons are not used for pitch discrimination between sounds with corresponding components rather comparisons based on residue pitch are only employed where there are no common resolved components in the signals to be discriminated

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

convergence of numerical time averaging and stationary measures via poisson equations numerical approximation of the long time behavior of a stochastic differential equation sde is considered error estimates for time averaging estimators are obtained and then used to show that the stationary behavior of the numerical method converges to that of the sde the error analysis is based on using an associated poisson equation for the underlying sde the main advantages of this approach are its simplicity and universality it works equally well for a range of explicit and implicit schemes including those with simple simulation of random variables and for hypoelliptic sdes to simplify the exposition we consider only the case where the state space of the sde is a torus and we study only smooth test functions however we anticipate that the approach can be applied more widely an analogy between our approach and stein s method is indicated some practical implications of the results are discussed

pitch of iterated rippled noise iterated rippled noise irn stimuli are generated by a cascade of delay d gain g and add networks the matched pitch of irn stimuli was determined as a function of the type of network used to generate irn stimuli the delay d 2 4 and 8 ms the number of iterations n 1 2 3 4 6 8 of the delay and add networks and whether the delayed noise was added g 1 to or subtracted g 1 from the undelayed noise the matched pitch of irn stimuli did not depend on the type of network when g 1 addition the matched pitch did not depend on the number of stages of iterations n and was always equal to the reciprocal of the delay 1 d when g 1 subtraction the match pitch depended on n when n 1 the matched pitch of irn stimuli was ambiguous having two pitches in the region of 1 d 10 when n 8 the match pitch was equal to 1 2d this change in the pitch occurred between n 2 and 6 the results are discussed in terms of spectral and temporal models of complex pitch processing a temporal model based on autocorrelation was able to provide quantitative predictions for the pitch of these irn stimuli however a spectral type of model can also account for the pitch of these irn stimuli

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

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

perception of missing fundamental pitch by 3 and 4 month old human infants a hallmark of complex pitch perception is that the pitch of a harmonic complex is the same whether or not the fundamental frequency is present by 7 months infants appear to discriminate on the basis of the pitch of the missing fundamental mf although electrophysiological cortical responses to mf pitch changes have been recorded in infants younger than 7 months no psychophysical studies have been published this study investigated the ability of 3 and 4 month olds to perceive the pitch of mf harmonic complexes based on fundamentals of 160 hz and 200 hz using an observer based method in experiment i to demonstrate mf pitch discrimination 3 and 4 month olds were required to ignore spectral changes in complexes with the same fundamental and to respond only when the fundamental changed in experiment ii a 60 260 hz noise was presented with complexes to mask combination tones at the fundamental frequency in experiment iii complexes were bandpass filtered with a 12 db octave slope to limit use of

prediction of absolute thresholds and equal loudness contours using a modified loudness model the loudness model described by moore et al j audio eng soc 45 224 240 1997 forms the basis for a recent ansi standard for the calculation of the loudness of steady sounds however the model does not give accurate predictions of the absolute thresholds published in a recent iso standard here it is described how the assumed middle ear transfer function in the model can be modified to give more accurate absolute threshold predictions the modified model also gives reasonably accurate predictions of the equal loudness contours published in a recent iso standard

the perceptual tone noise ratio of merged iterated rippled noises iterated rippled noise irn is constructed by delaying a random noise by d ms adding it back to the same noise and repeating the process iteratively when two irns with the same power but slightly different delays are added together the perceptual tone noise ratio of the merged irn is markedly reduced with respect to that of either of the component irns in this paper the reduction in the perceptual tone noise ratio is measured for irns in which one of the delays is always 16 ms and the other is either 16 0 1 ms or 16 1 1 ms the component irns have the same number of iterations and the number varies across conditions from 4 to 256 the perceptual tone noise ratio is measured using a discrimination matching procedure developed for single irns each merged irn is compared with a range of standard stimuli having varying proportions of a complex tone and a broadband noise patterson et al j acoust soc am 100 3286 3294 1996 for single irns the function relating the signal to noise ratio of the matching standard to the number of iterations in the irn was found to be essentially straight this relationship was explained in terms of the height of the first peak in the autocorrelation of the stimulus wave or by the first peak in the summary autocorrelogram produced by a time domain auditory model for the merged irns in the current experiment the matching point functions are found to have pronounced downward curvature in addition to being well below the function for single irns to account for the reduction in the perceptual tone noise ratio of merged irns the autocorrelation model was extended to include a simple rule for combining adjacent peaks in the autocorrelation function of the wave and the autocorrelogram model was revised to improve the simulation of the loss of phase locking at higher frequencies in the autocorrelogram

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

moderate cochlear hearing loss leads to a reduced ability to use temporal fine structure information the ability of normally hearing and hearing impaired subjects to use temporal fine structure information in complex tones was measured subjects were required to discriminate a harmonic complex tone from a tone in which all components were shifted upwards by the same amount in hz in a three alternative forced choice task the tones either contained five equal amplitude components non shaped stimuli or contained many components but were passed through a fixed bandpass filter to reduce excitation pattern changes shaped stimuli components were centered at nominal harmonic numbers n 7 11 and 18 for the shaped stimuli hearing impaired subjects performed much more poorly than normally hearing subjects with most of the former scoring no better than chance when n 11 or 18 suggesting that they could not access the temporal fine structure information performance for the hearing impaired subjects was significantly improved for the non shaped stimuli presumably because they could benefit from spectral cues it is proposed that normal hearing subjects can use temporal fine structure information provided the spacing between fine structure peaks is not too small relative to the envelope period but subjects with moderate cochlear hearing loss make little use of temporal fine structure information for unresolved components

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