a high resolution fundamental frequency determination based on phase changes of the fourier transform the constant q transform described recently j c brown and m s puckette an efficient algorithm for the calculation of a constant q transform j acoust soc am 92 2698 2701 1992 has been adapted so that it is suitable for tracking the fundamental frequency of extremely rapid musical passages for this purpose the calculation described previously has been modified so that it is constant frequency resolution rather than constant q for lower frequency bins this modified calculation serves as the input for a fundamental frequency tracker similar to that described by brown j c brown musical fundamental frequency tracking using a pattern recognition method j acoust soc am 92 1394 1402 1992 once the fast fourier transform fft bin corresponding to the fundamental frequency is chosen by the frequency tracker an approximation is used for the phase change in the fft for a time advance of one sample to obtain an extremely precise value for this frequency graphical examples are given for musical passages by a violin executing vibrato and glissando where the fundamental frequency changes are rapid and continuous

calculation of a constant q spectral transform the frequencies that have been chosen to make up the scale of western music are geometrically spaced thus the discrete fourier transform dft although extremely efficient in the fast fourier transform implementation yields components which do not map efficiently to musical frequencies this is because the frequency components calculated with the dft are separated by a constant frequency difference and with a constant resolution a calculation similar to a discrete fourier transform but with a constant ratio of center frequency to resolution has been made this is a constant q transform and is equivalent to a 1 24 oct filter bank thus there are two frequency components for each musical note so that two adjacent notes in the musical scale played simultaneously can be resolved anywhere in the musical frequency range this transform against log frequency to obtain a constant pattern in the frequency domain for sounds with harmonic frequency components has been plotted this is compared to the conventio

estimation of aquifer parameters under transient and steady state conditions 2 uniqueness stability and solution algorithms paper 2 of this three part series starts with a discussion of the question under what conditions is the aquifer inverse problem well posed after defining the terms uniqueness identifiability and stability theoretical considerations and synthetic examples are used to demonstrate that ill posedness can be mitigated by including prior information about the parameters in the estimation criterion to be minimized at the same time the inclusion of such information is shown to be insufficient to guarantee uniqueness and stability in all cases several test problems in the recent literature which have resulted in pessimistic conclusions about the solvability of the aquifer inverse problem are shown to be ill posed a question is thus raised about the validity of these conclusions in the general case various conjugate gradient algorithms coupled with the adjoint state finite element method for computing the gradient of the estimation criterion and with newton s method for determining the optimum step size downgradient are compared a marked improvement in the rate at which these algorithms converge is shown to be achieved by switching from one method to another when the former slows down or fails to converge

an extended identifiability in aquifer parameter identification and optimal pumping test design an extended identifiability called identifiability is developed for groundwater modeling and management some fundamental concepts are developed for establishing a criterion in connection with the problem of optimal experimental design such as the design of an optimum pumping test to assist aquifer parameter identification in practice the quantity and quality of data prohibits a unique solution of the inverse problem of parameter identification the proposed identifiability is based upon the concept of weak uniqueness the determination of the admissibility of a given design is formulated as a nonlinear programming problem the original constrained problem is transformed into solving a sequence of unconstrained problems by a penalty function method numerical experiments are conducted to illustrate the proposed concept and algorithm

computer identification of musical instruments using pattern recognition with cepstral coefficients as features cepstral coefficients based on a constant q transform have been calculated for 28 short 1 2 s oboe sounds and 52 short saxophone sounds these were used as features in a pattern analysis to determine for each of these sounds comprising the test set whether it belongs to the oboe or to the sax class the training set consisted of longer sounds of 1 min or more for each of the instruments a k means algorithm was used to calculate clusters for the training data and gaussian probability density functions were formed from the mean and variance of each of the clusters each member of the test set was then analyzed to determine the probability that it belonged to each of the two classes and a bayes decision rule was invoked to assign it to one of the classes results have been extremely good and are compared to a human perception experiment identifying a subset of these same sounds

uncertainty in dual permeability model parameters for structured soils 1 successful application of dual permeability models dpm to predict contaminant transport is contingent upon measured or inversely estimated soil hydraulic and solute transport parameters the difficulty in unique identification of parameters for the additional macropore and matrix macropore interface regions and knowledge about requisite experimental data for dpm has not been resolved to date therefore this study quantifies uncertainty in dual permeability model parameters of experimental soil columns with different macropore distributions single macropore and low and high density multiple macropores uncertainty evaluation is conducted using adaptive markov chain monte carlo amcmc and conventional metropolis hastings mh algorithms while assuming 10 out of 17 parameters to be uncertain or random results indicate that amcmc resolves parameter correlations and exhibits fast convergence for all dpm parameters while mh displays large posterior correlations for various parameters this study demonstrates that the choice of parameter sampling algorithms is paramount in obtaining unique dpm parameters when information on covariance structure is lacking or else additional information on parameter correlations must be supplied to resolve the problem of equifinality of dpm parameters this study also highlights the placement and significance of matrix macropore interface in flow experiments of soil columns with different macropore densities histograms for certain soil hydraulic parameters display tri modal characteristics implying that macropores are drained first followed by the interface region and then by pores of the matrix domain in drainage experiments results indicate that hydraulic properties and behavior of the matrix macropore interface is not only a function of saturated hydraulic conductivity of the macroporematrix interface ksa and macropore tortuosity lf but also of other parameters of the matrix and macropore domains

reproducibility of soil moisture ensembles when representing soil parameter uncertainty using a latin hypercube based approach with correlation control 1 representation of model input uncertainty is critical in ensemble based data assimilation monte carlo sampling of model inputs produces uncertainty in the hydrologic state through the model dynamics small monte carlo ensemble sizes are desirable because of model complexity and dimensionality but potentially lead to sampling errors and correspondingly poor representation of probabilistic structure of the hydrologic state we compare two techniques to sample soil hydraulic and thermal properties shtps 1 latin hypercube lh based sampling with correlation control and 2 random sampling from shtp marginal distributions a hydrology model is used to project shtp uncertainty onto the soil moisture state for given forcings for statistical comparison we generate 20 ensembles for 7 ensemble sizes variance in ensemble moment estimates decreases with increasing ensemble size the lh based approach yields less variance in the estimate of ensemble moments at all ensemble sizes an advantage greatest with small ensembles implications for hydrologic uncertainty assessment data assimilation and parameter estimation are discussed

the least squares invertible constant q spectrogram and its application to phase vocoding this paper discusses the development of a constant q spectrogram representation that is invertible in a least squares sense a good quality inverse is possible because this modified transform method unlike the usual sliding window constant q spectrogram does not discard data samples when performing the variable length discrete fourier transforms on the signal the development of a phase vocoder application using this modified technique is also discussed it is shown that a phase vocoder constructed using the least squares invertible constant q spectrogram lsicqs is not a trivial extension of the regular fft based phase vocoder algorithm and some of the mathematical subtleties related to phase reassignment are addressed

higher spectral flow for a continuous curve of families of dirac type operators we define a higher spectral flow as ak group element we show that this higher spectral flow can be computed analytically by forms and is related to the family index in the same way as the spectral flow is related to the index we introduce a notion of toeplitz family and relate its index to the higher spectral flow applications to family indices for manifolds with boundary are also given

markov chain monte carlo convergence diagnostics a comparative review abstract a critical issue for users of markov chain monte carlo mcmc methods in applications is how to determine when it is safe to stop sampling and use the samples to estimate characteristics of the distribution of interest research into methods of computing theoretical convergence bounds holds promise for the future but to date has yielded relatively little of practical use in applied work consequently most mcmc users address the convergence problem by applying diagnostic tools to the output produced by running their samplers after giving a brief overview of the area we provide an expository review of 13 convergence diagnostics describing the theoretical basis and practical implementation of each we then compare their performance in two simple models and conclude that all of the methods can fail to detect the sorts of convergence failure that they were designed to identify we thus recommend a combination of strategies aimed at evaluating and accelerating mcmc sampler convergence including ap

incorporation of prior information on parameters into nonlinear regression groundwater flow models 1 theory prior information on the parameters of a groundwater flow model can be used to improve parameter estimates obtained from nonlinear regression solution of a modeling problem two scales of prior information can be available 1 prior information having known reliability that is bias and random error structure and 2 prior information consisting of best available estimates of unknown reliability a regression method that incorporates the second scale of prior information assumes the prior information to be fixed for any particular analysis to produce improved although biased parameter estimates approximate optimization of two auxiliary parameters of the formulation is used to help minimize the bias which is almost always much smaller than that resulting from standard ridge regression it is shown that if both scales of prior information are available then a combined regression analysis may be made

evaluation of maximum likelihood parameter estimation techniques for conceptual rainfall runoff models influence of calibration data variability and length on model credibility the success of an automatic calibration procedure is highly dependent on the choice of the objective function and the nature quantity and quality of the data used the objective function should be selected on the basis of the stochastic properties of the errors present in the data and in the model also the data should be chosen so as to contain as much valuable information about the process as possible in this paper we compare the performance of two maximum likelihood estimators the amle which assumes the presence of first lag autocorrelated homogeneous variance errors and the hmle which assumes the presence of uncorrelated inhomogeneous variance errors to the commonly used simple least squares criterion sls the model calibrated was the soil moisture accounting model of the u s national weather service s river forecast system sma nwsrfs the results indicate that a properly chosen objective function can enhance the possibility of obtaining unique and conceptually realistic parameter estimates furthermore the sensitivity of the estimation results to various characteristics of the calibration data such as hydrologic variability and length are substantially reduced

an analytic wavelet transform with a flexible time frequency covering we develop a rational dilation wavelet transform for which the dilation factor the q factor and the redundancy can be easily specified the introduced transform contains hilbert transform pairs of atoms therefore it is also suitable for oscillatory signal processing the transform may be modified to obtain a tight chirplet frame for discrete time signals a fast implementation that makes use of an equivalent filter bank makes the transform suitable for long signals examples on natural signals are provided to demonstrate the utility of the transform

estimation of aquifer parameters under transient and steady state conditions 1 maximum likelihood method incorporating prior information in this series of three papers a method is presented to estimate the parameters of groundwater flow models under steady and nonsteady state conditions the parameters include values and directions of principal hydraulic conductivities or transmissivities in anisotropic media specific storage or storativity interior and boundary recharge or leakage rates coefficients of head dependent interior and boundary sources and boundary heads in transient situations the initial head distribution can also be estimated if the system is originally at a steady state paper 1 of the series discusses some of the advantage in treating the inverse problem statistically and in regularizing its solution by means of penalty criteria based on prior estimates of the parameters the inverse problem is posed in the framework of maximum likelihood theory cast in a manner that accounts for prior information about the parameters since not all the factors which contribute to the prior errors can be quantified statistically at the outset the covariance matrices of these errors are expressed in terms of several parameters which if unknown can be estimated jointly with the hydraulic parameters by a stagewise optimization process when transient head data are separated by a fixed time interval the temporal structure of these data is approximated by a lag one autoregressive model with a correlation coefficient that can be treated as another unknown parameter estimation errors are analyzed by examining the lower bound of their covariance matrix in the eigenspace paper 1 concludes by suggesting that certain model identification criteria developed in the time series literature all of which are based on the maximum likelihood concept might be useful for selecting the best groundwater model or the best method of parameterizing a particular model among a number of given alternatives

independent component analysis for automatic note extraction from musical trills the method of principal component analysis which is based on second order statistics or linear independence has long been used for redundancy reduction of audio data the more recent technique of independent component analysis enforcing much stricter statistical criteria based on higher order statistical independence is introduced and shown to be far superior in separating independent musical sources this theory has been applied to piano trills and a database of trill rates was assembled from experiments with a computer driven piano recordings of a professional pianist and commercially available compact disks the method of independent component analysis has thus been shown to be an outstanding effective means of automatically extracting interesting musical information from a sea of redundant data

wavelet transform with tunable q factor this paper describes a discrete time wavelet transform for which the q factor is easily specified hence the transform can be tuned according to the oscillatory behavior of the signal to which it is applied the transform is based on a real valued scaling factor dilation factor and is implemented using a perfect reconstruction over sampled filter bank with real valued sampling factors two forms of the transform are presented the first form is defined for discrete time signals defined on all of z the second form is defined for discrete time signals of finite length and can be implemented efficiently with ffts the transform is parameterized by its q factor and its oversampling rate redundancy with modest oversampling rates e g three to four times overcomplete being sufficient for the analysis synthesis functions to be well localized

the eta invariant and parity conditions abstract we give a formula for the invariant of odd order operators on even dimensional manifolds and even order operators on odd dimensional manifolds second order operators with nontrivial invariants are found this solves a problem posed by gilkey

an efficient algorithm for the calculation of a constant q transform an efficient method of transforming a discrete fourier transform dft into a constant q transform where q is the ratio of center frequency to bandwidth has been devised this method involves the calculation of kernels that are then applied to each subsequent dft only a few multiples are involved in the calculation of each component of the constant q transform so this transformation adds a small amount to the computation in effect this method makes it possible to take full advantage of the computational efficiency of the fast fourier transform fft graphical examples of the application of this calculation to musical signals are given for sounds produced by a clarinet and a violin

bayesian density estimation and inference using mixtures abstract we describe and illustrate bayesian inference in models for density estimation using mixtures of dirichlet processes these models provide natural settings for density estimation and are exemplified by special cases where data are modeled as a sample from mixtures of normal distributions efficient simulation methods are used to approximate various prior posterior and predictive distributions this allows for direct inference on a variety of practical issues including problems of local versus global smoothing uncertainty about density estimates assessment of modality and the inference on the numbers of components also convergence results are established for a general class of normal mixture models

the residue of the global η function at the origin where i dvol x l denotes the riemannian measure on m using the calculus of pseudo differential operators depending upon a complex parameter which was developed by seeley 9 one can show that both q s x p and r s p can be meromorphically extended to the complex plane with simple poles at s m n u for n 0 the residues of l s x p at the poles for n 0 m are given by local formulas in the jets of the total symbol of p we define

theory implementation and applications of nonstationary gabor frames signal analysis with classical gabor frames leads to a fixed time frequency resolution over the whole time frequency plane to overcome the limitations imposed by this rigidity we propose an extension of gabor theory that leads to the construction of frames with time frequency resolution changing over time or frequency we describe the construction of the resulting nonstationary gabor frames and give the explicit formula for the canonical dual frame for a particular case the painless case we show that wavelet transforms constant q transforms and more general filter banks may be modeled in the framework of nonstationary gabor frames further we present the results in the finite dimensional case which provides a method for implementing the above mentioned transforms with perfect reconstruction finally we elaborate on two applications of nonstationary gabor frames in audio signal processing namely a method for automatic adaptation to transients and an algorithm for an invertible constant q transform

a dual tree rational dilation complex wavelet transform in this correspondence we introduce a dual tree rational dilation complex wavelet transform for oscillatory signal processing like the short time fourier transform and the dyadic dual tree complex wavelet transform the introduced transform employs quadrature pairs of time frequency atoms which allow to work with the analytic signal the introduced wavelet transform is a constant q transform a property lacked by the short time fourier transform which in turn makes the introduced transform more suitable for models that depend on scale also the frequency resolution can be as high as desired a property lacked by the dyadic dual tree complex wavelet transform which makes the introduced transform more suitable for processing oscillatory signals like speech audio and various biomedical signals

frequency domain design of overcomplete rational dilation wavelet transforms the dyadic wavelet transform is an effective tool for processing piecewise smooth signals however its poor frequency resolution its low q factor limits its effectiveness for processing oscillatory signals like speech eeg and vibration measurements etc this paper develops a more flexible family of wavelet transforms for which the frequency resolution can be varied the new wavelet transform can attain higher q factors desirable for processing oscillatory signals or the same low q factor of the dyadic wavelet transform the new wavelet transform is modestly overcomplete and based on rational dilations like the dyadic wavelet transform it is an easily invertible constant q discrete transform implemented using iterated filter banks and can likewise be associated with a wavelet frame for l2 r the wavelet can be made to resemble a gabor function and can hence have good concentration in the time frequency plane the construction of the new wavelet transform depends on the judicious use of both the transform s redundancy and the flexibility allowed by frequency domain filter design