on stability of fuzzy systems expressed by fuzzy rules with singleton consequents addresses the issue of stability of a fuzzy system described by fuzzy rules with singleton consequents it first presents two canonical forms of a fuzzy system a parametric expression and a state space expression a fuzzy system with singleton consequents is found to be a piecewise polytopic affine system then the paper gives stability theorems for a discrete time system as well as for a continuous time system it also gives a brief survey on the stability issues of fuzzy control systems

frequency and intensity difference limens for harmonics within complex tones a two interval two alternative forced choice task was used to estimate frequency difference limens dls for individual harmonics within complex tones and dls for the periodicity i e number of periods per s of the whole complexes for complex tones with equal amplitude harmonics the dls for the lowest harmonics were small less than one percent the dls increased rather abruptly around the fifth to seventh harmonic the highest harmonic in each complex was also well discriminated and the discriminability of a single high harmonic was markedly improved by increasing its level relative to the other components the dl for a complex tone was generally smaller than the frequency dl of its most discriminable component the dl for a complex was found to be predictable from the dls of the harmonics comprising the complex using a formula derived by goldstein j acoust soc am 54 1496 1516 1973 from his optimum processor theory for the formation of the pitch of complex tones the dl for a complex i

stability analysis and control of discrete type 1 and type 2 tsk fuzzy systems part i stability analysis this paper introduces sufficient conditions for the exponential stability of type 1 and type 2 takagi sugeno kang tsk fuzzy systems a major advantage of the new conditions is that they do not require the existence of a common lyapunov function and are therefore applicable to systems with unstable consequents in addition our results include two classes of type 2 tsk systems with type 1 consequents for which no stability tests are available the use of the conditions in stability testing is demonstrated using simple numerical examples that include cases where methods that are based on a common lyapunov function fail the application of the stability test to develop new controller design methodologies is presented in a separate paper i e part ii

on asymmetrical performance of discrete cosine transform the discrete cosine transform dct is considered as a suboptimum transform for many practical source coding applications autoregressive order 1 ar 1 source models are good first approximations to several natural signals it is known that the performance of the dct depends on the sign of the autocorrelation coefficient of the ar 1 source the authors explain theoretically this asymmetrical performance of the dct as well as the behavior of the modified hermite transform mht and the discrete hadamard transform dht which perform symmetrically regardless of the sign of the autocorrelation coefficient

sensory constraints on auditory identification of the material and geometric properties of struck bars a computational formula is derived for estimating the constraints limited auditory sensitivity imposes on auditory identification of the material and geometric properties of struck bars the formula combines a model of the transverse motion of the bar with empirical psychometric functions to map out null regions in the bar s physical parameter space where changes in the frequency amplitude and decay of partials are likely below threshold for detection parameters of the physical space include bar density young s modulus fluid and viscoelastic damping factors bar length and bar cross sectional area as related to bar shape and hollowness the formula is used to estimate the possible effect of limited sensitivity in past studies on the auditory identification of bar attributes the results suggest that sensitivity may indeed have played a role in some studies and that apparent discrepancies in results may be understood based on whether the predominant source of damping was internal or external to the bar the formula identifies conditions representing an expected bound on identification performance and thereby may be used to aid in the design of future studies for which the struck bar is the sound source of choice

quadratic stability analysis of fuzzy model based control systems using staircase membership functions this paper presents the stability analysis of fuzzy model based fmb control systems staircase membership functions are introduced to facilitate the stability analysis through the staircase membership functions approximating those of the fuzzy model and fuzzy controller the information of the membership functions can be brought into the stability analysis based on the lyapunov stability theory stability conditions in terms of linear matrix inequalities lmis are derived in a simple and easy to understand manner to guarantee the system stability the proposed stability analysis approach offers a nice property that includes the membership functions of both fuzzy model and fuzzy controller in the lmi based stability conditions for a dedicated fmb control system furthermore the proposed stability analysis approach can be applied to the fmb control systems of which the membership functions of both fuzzy model and fuzzy controller are not necessarily the same greater design flexibility is allowed to choose the membership functions during the design of fuzzy controllers by employing membership functions with simple structure it is possible to lower the structural complexity and the implementation cost simulation examples are given to illustrate the merits of the proposed approach

a new orthogonal transform for signal coding the authors propose an orthogonal unitary transformation called the modified hermite transformation mht and its extension which is called the modular modified hermite transformation mmht the mht algorithm which is an efficient algorithm is explained and explored the mht is compared to the discrete cosine transform dct for various ar 1 input signal source models using the performance criterion of gain over pcm denoted by sup n g sub tc the mht algorithm requires only 2n real multiplications or divisions for a transformation of a signal block of n samples it is also used for the inverse transformation imht and makes this new transform attractive it is efficient computationally and comparable to the dct for ar 1 source models with positive correlation coefficients it is somewhat better than the dct for negative correlation coefficients

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

factorization of the coefficient variance matrix in orthogonal transforms the authors derive a matrix factorization of the coefficient variances for any fixed transformation this factorization formulation provides a better framework for understanding the role of transform on the one hand and the signal source model on the other it also greatly simplifies the number of computational operations required for each variance calculation a transform specific matrix which links the transform to the signal correlation model is derived this factorization provides a conceptual framework for understanding the behaviour of the transform for different source models it also significantly simplifies the calculation of the variance of each transform coefficient from a quadruple sum over four indices to a double sum over two indices this simplification can be used in adaptive transform coding which requires an estimate of the variances test results demonstrate that this mode based variance calculation provides an accurate basis for adaptive transform coding particularly at low bit rates

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

pitch discrimination by ferrets for simple and complex sounds although many studies have examined the performance of animals in detecting a frequency change in a sequence of tones few have measured animals discrimination of the fundamental frequency f0 of complex naturalistic stimuli additionally it is not yet clear if animals perceive the pitch of complex sounds along a continuous low to high scale here four ferrets mustela putorius were trained on a two alternative forced choice task to discriminate sounds that were higher or lower in f0 than a reference sound using pure tones and artificial vowels as stimuli average weber fractions for ferrets on this task varied from 20 to 80 across references 200 1200 hz and these fractions were similar for pure tones and vowels these thresholds are approximately ten times higher than those typically reported for other mammals on frequency change detection tasks that use go no go designs naive human listeners outperformed ferrets on the present task but they showed similar effects of stimulus type and refe

a new lmi based approach to relaxed quadratic stabilization of t s fuzzy control systems this paper proposes a new quadratic stabilization condition for takagi sugeno t s fuzzy control systems the condition is represented in the form of linear matrix inequalities lmis and is shown to be less conservative than some relaxed quadratic stabilization conditions published recently in the literature a rigorous theoretic proof is given to show that the proposed condition can include previous results as special cases in comparison with conventional conditions the proposed condition is not only suitable for designing fuzzy state feedback controllers but also convenient for fuzzy static output feedback controller design the latter design work is quite hard for t s fuzzy control systems based on the lmi based conditions derived one can easily synthesize controllers for stabilizing t s fuzzy control systems since only a set of lmis is involved the controller design is quite simple and numerically tractable finally the validity and applicability of the proposed approach are successfully demonstrated in the control of a continuous time nonlinear system

extended lapped transforms properties applications and fast algorithms the family of lapped orthogonal transforms is extended to include basis functions of arbitrary length within this new family the extended lapped transform elt is introduced as a generalization of the previously reported modulated lapped transform mlt design techniques and fast algorithms for the elt are presented as well as examples that demonstrate the good performance of the elt in signal coding applications therefore the elt is a promising substitute for traditional block transforms in transform coding systems and also a good substitute for less efficient filter banks in subband coding systems

structure identification of fuzzy model abstract the problems of structure identification of a fuzzy model are formulated a criterion for the verification of a structure is discussed using the criterion an algorithm for identifying a structure is suggested further a successive identification algorithm of the parameters is suggested the proposed methods are applied to an example

a new transform with symmetrical coding performance for markov 1 signals based on the dct and dst ii we present a new transform that provides a symmetrical performance for positively and negatively correlated markov 1 signals first order stationary markov process a fast computational algorithm is presented a sufficient condition of symmetrical transforms is also provided and the idea of constructing the discrete cosine sine transform dcst is then generalized to the karhunen loeve transform klt of any markov 1 signal

enhanced karnik mendel algorithms the karnik mendel km algorithms are iterative procedures widely used in fuzzy logic theory they are known to converge monotonically and superexponentially fast however several usually two to six iterations are still needed before convergence occurs methods to reduce their computational cost are proposed in this paper extensive simulations show that on average the enhanced km algorithms can save about two iterations which corresponds to more than a 39 reduction in computation time an additional at least 23 computational cost can be saved if no sorting of the inputs is needed

new approaches to relaxed quadratic stability condition of fuzzy control systems this paper deals with the quadratic stability conditions of fuzzy control systems that relax the existing conditions reported in the previous literatures two new conditions are proposed and shown to be useful in analyzing and designing fuzzy control systems the first one employs the s procedure to utilize information regarding the premise parts of the fuzzy systems the next one enlarges the class of fuzzy control systems whose stability is ensured by representing the interactions among the fuzzy subsystems in a single matrix and solving it by linear matrix inequality the relationships between the suggested stability conditions and the conventional well known stability conditions reported in the previous literatures are also discussed and it is shown in a rigorous manner that the second condition of this paper includes the conventional conditions finally some examples and simulation results are presented to illustrate the effectiveness of the stability conditions

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

a new fuzzy lyapunov function approach for a takagi sugeno fuzzy control system design in this paper a new fuzzy lyapunov function approach is presented for a class of continuous time takagi sugeno fuzzy control system the proposed fuzzy lyapunov function is formulated as a line integral of a fuzzy vector which is a function of the state and it can be regarded as the work done from the origin to the current state in the fuzzy vector field unlike the approaches using a fuzzy blending of multiple quadratic lyapunov functions the time derivatives of membership functions do not appear in the proposed approach the effectiveness of the proposed approach is shown through numerical examples

toward general type 2 fuzzy logic systems based on zslices higher order fuzzy logic systems flss such as interval type 2 flss have been shown to be very well suited to deal with the high levels of uncertainties present in the majority of real world applications general type 2 flss are expected to further extend this capability however the immense computational complexities associated with general type 2 flss have until recently prevented their application to real world control problems this paper aims to address this problem by the introduction of a complete representation framework which is referred to as zslices based general type 2 fuzzy systems the proposed approach will lead to a significant reduction in both the complexity and the computational requirements for general type 2 flss while it offers the capability to represent complex general type 2 fuzzy sets as a proof of concept application we have implemented a zslices based general type 2 fls for a two wheeled mobile robot which operates in a real world outdoor environment we have evaluated the computational performance of the zslices based general type 2 fls which is suitable for multiprocessor execution finally we have compared the performance of the zslices based general type 2 fls against type 1 and interval type 2 flss and a series of results is presented which is related to the different levels of uncertainty handled by the different types of flss

on the relative influence of individual harmonics on pitch judgment spectral weighting functions were estimated in a pitch comparison task to assess the relative influence of individual harmonics on listeners pitch judgment the stimuli were quasi harmonic complex tones composed of the first 12 components with fundamental frequencies ranging from 100 to 800 hz on each stimulus presentation the frequency of each harmonic was randomly jittered by a small amount the perceptual weight for each harmonic was calculated as the correlation coefficient between the binary responses of the listener and the frequency jitters for that harmonic although in general the present results conform to previous ones showing the predominant role of several low ranked harmonics discrepancies exist in details contrary to some previous reports that the dominant harmonics were of fixed harmonic ranks regardless of their frequencies the current results showed that the dominant harmonics were best described as close to a fixed absolute frequency of 600 hz

texture classification by modeling joint distributions of local patterns with gaussian mixtures texture classification generally requires the analysis of patterns in local pixel neighborhoods statistically the underlying processes are comprehensively described by their joint probability density functions jpdfs even for small neighborhoods however stable estimation of jpdfs by joint histograms jhsts is often infeasible since the number of entries in the jhst exceeds by far the number of pixels in a typical texture region moreover evaluation of distance functions between jhsts is often computationally prohibitive practically the number of entries in a jhst is therefore reduced by considering only two pixel patterns leading to 2d jhsts known as cooccurrence matrices or by quantization of the gray levels in local patterns to only two gray levels yielding local binary patterns lbps both approaches result in a loss of information we introduce here a framework for supervised texture classification which reduces or avoids this information loss local texture neighborhoods are first filtered by a filter bank without further quantization the jpdf of the filter responses is then described parametrically by gaussian mixture models gmms we show that the parameters of the gmms can be reliably estimated from small image regions moreover distances between the thus modelled jpdfs of different texture patterns can be computed efficiently in closed form from their model parameters we furthermore extend this texture descriptor to achieve full invariance to rotation we evaluate the framework for different filter banks on the brodatz texture set we first show that combining the lbp difference filters with the gmm based density estimator outperforms the classical lbp approach and its codebook extensions when replacing these rather elementary difference filters by the wavelet frame transform wft the performance of the framework on all 111 brodatz textures exceeds the one obtained more recently by spin image and rift descriptors by lazebnik et al

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

centroid of a type 2 fuzzy set abstract in this paper we introduce the centroid and generalized centroid of a type 2 fuzzy set both of which are essential for implementing a type 2 fuzzy logic system and explain how to compute them for practical use we show how to compute the centroid of interval and gaussian type 2 fuzzy sets an exact computation procedure is provided for an interval type 2 set whereas an approximation is provided for both interval and gaussian type 2 sets examples are given that compare the exact computational results with the approximate results

a multiple lyapunov function approach to stabilization of fuzzy control systems this paper addresses stability analysis and stabilization for takagi sugeno fuzzy systems via a so called fuzzy lyapunov function which is a multiple lyapunov function the fuzzy lyapunov function is defined by fuzzily blending quadratic lyapunov functions based on the fuzzy lyapunov function approach we give stability conditions for open loop fuzzy systems and stabilization conditions for closed loop fuzzy systems to take full advantage of a fuzzy lyapunov function we propose a new parallel distributed compensation pdc scheme that feedbacks the time derivatives of premise membership functions the new pdc contains the ordinary pdc as a special case a design example illustrates the utility of the fuzzy lyapunov function approach and the new pdc stabilization method

effect of noise on the detectability and fundamental frequency discrimination of complex tones percent correct performance for discrimination of the fundamental frequency 0 of a complex tone was measured as a function of the level of a background pink noise using fixed values of the difference in f0 deltaf0 and compared with percent correct performance for detection of the complex tone in noise again as a function of noise level the tone included some low resolvable components but not the fundamental component the results were used to test the hypothesis that the worsening in f0 discrimination with increasing noise level was caused by the reduced detectability of the tone rather than by reduced precision of the internal representation of f0 for small values of deltaf0 the hypothesis was rejected because measured performance fell below that predicted by the hypothesis however this was true only for high noise levels within 2 4 5 db of the level required for masked threshold the results indicate that the mechanism for extracting the f0 of a complex tone with resolved harmonics is remarkably robust they also indicate that adding a background noise to a complex tone containing resolved harmonics is not a good means for equating its pitch salience with that of a complex tone containing only unresolved harmonics

the effect of hearing loss on the resolution of partials and fundamental frequency discrimination the relationship between the ability to hear out partials in complex tones discrimination of the fundamental frequency f0 of complex tones and frequency selectivity was examined for subjects with mild to moderate cochlear hearing loss the ability to hear out partials was measured using a two interval task each interval included a sinusoid followed by a complex tone one complex contained a partial with the same frequency as the sinusoid while in the other complex that partial was missing subjects had to indicate the interval in which the partial was present in the complex the components in the complex were uniformly spaced on the erbn number scale performance was generally good for the two edge partials but poorer for the inner partials performance for the latter improved with increasing spacing f0 discrimination was measured for a bandpass filtered complex tone containing low harmonics the equivalent rectangular bandwidth erb of the auditory filter was estimated using the notched noise

stability analysis of discrete tsk type ii iii systems we propose a new approach for the stability analysis of discrete sugeno types ii and iii fuzzy systems the approach does not require the existence of a common lyapunov function we introduce the concept of fuzzy positive definite and fuzzy negative definite functions this new concept is used to replace classical positive and negative definite functions in arguments similar to those of traditional lyapunov stability theory we obtain the equivalent fuzzy system for a cascade of two type ii iii fuzzy systems we use the cascade of a system and a fuzzy lyapunov function candidate to derive new conditions for stability and asymptotic stability for discrete type ii and type iii fuzzy systems to demonstrate the new approach we apply it to numerical examples where no common lyapunov function exists

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

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

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

geometric type 1 and type 2 fuzzy logic systems this paper presents a novel approach to the representation of type 1 and type 2 fuzzy sets utilising computational geometry to achieve this our approach borrows ideas from the field of computational geometry and applies these techniques in the novel setting of fuzzy logic we provide new algorithms for various operations on type 1 and type 2 fuzzy sets and for defuzzification results of experiments indicate that this approach reduces the execution speed of these operations