an algebro geometric proof of witten s conjecture we present a new proof of witten s conjecture the proof is based on the analysis of the relationship between intersection indices on moduli spaces of complex curves and hurwitz numbers enumerating ramified coverings of the 2 sphere

minimum mean squared error transform coding and subband coding knowledge of the power spectrum of a stationary random sequence can be used for quantizing the signal efficiently and with minimum mean squared error a multichannel filter is used to transform the random sequence into an intermediate set of variables that are quantized using independent scalar quantizers and then inverse filtered producing a quantized version of the original sequence equal word length and optimal word length quantization at high bit rates is considered an analytical solution for the filter that minimizes the mean squared quantization error is obtained in terms of its singular value decomposition the performance is characterized by a set of invariants termed second order modes which are derived from the eigenvalue decomposition of the matrix valued power spectrum a more general rank reduced model is used for decreasing distortion by introducing bias the results are specialized to the case when the vector valued time series is obtained from a scalar random sequence which gives rise to a filter bank model for quantization the asymptotic performance of such a subband coder is derived and shown to coincide with the asymptotic bound for transform coding quantization employing a single scalar pre and postfilter traditional transform coding using a square linear transformation and subband coding in filter banks arise as special cases of the structure analyzed here

smooth wavelets transform coding and markov 1 processes this paper compares the energy compacting properties of unitary transforms from transform coders and two band paraunitary filter banks from subband coders using a cost criterion that is proposed stationary processes for which paraunitary filters have better energy compaction than unitary filters are denoted as subband optimal and all subband optimal processes are analytically characterized for the case of length 4 filters it is shown analytically for length 4 filters and empirically for longer length filters that markov 1 processes are subband optimal and that the daubechies 1988 maximally smooth wavelet sequences achieve better energy compaction than the best unitary filters for markov 1 inputs

the role of linear semi infinite programming in signal adapted qmf bank design we consider the problem of designing a perfect reconstruction fir quadrature mirror filter qmf bank h g adapted to input signal statistics with the coding gain as the adaptation criterion maximization of the coding gain has so far been viewed as a difficult nonlinear constrained optimization problem it is shown that the coding gain depends only on the product filter p z h z h z sup 1 and this transformation leads to a stable class of linear optimization problems having finitely many variables and infinitely many constraints termed linear semi infinite programming sip problems the sought for original filter h z is obtained by deflation and spectral factorization of p z with the sip formulation every locally optimal solution is also globally optimal and can be computed using reliable numerical algorithms the natural regularity properties inherent in the sip formulation enhance the performance of these algorithms we present a comprehensive theoretical analysis of the sip problem and its dual characterize the optimal filters and analyze uniqueness and sensitivity issues all these properties are intimately related to those of the input signal and bring considerable insight into the nature of the adaptation process we present discretization and cutting plane algorithms and apply both methods to several examples

two dimensional filter bank design for optimal reconstruction using limited subband information in this correspondence we propose design techniques for analysis and synthesis filters of 2 d perfect reconstruction filter banks prfb s that perform optimal reconstruction when a reduced number of subband signals is used based on the minimization of the squared error between the original signal and some low resolution representation of it the 2 d filters are optimally adjusted to the statistics of the input images so that most of the signal s energy is concentrated in the first few subband components this property makes the optimal prfb s efficient for image compression and pattern representations at lower resolutions for classification purposes by extending recently introduced ideas from frequency domain principal component analysis to two dimensions we present results for general 2 d discrete nonstationary and stationary second order processes showing that the optimal filters are nonseparable particular attention is paid to separable random fields proving that only the first and last filters of the optimal prfb are separable in this case simulation results that illustrate the theoretical achievements are presented

on the optimality of ideal filters for pyramid and wavelet signal approximation the reconstructed lowpass component in a quadrature mirror filter qmf bank provides a coarser resolution approximation of the input signal since the outputs of the two qmf branches are orthogonal the transformation that provides the maximum energy compaction in the lowpass channel is also the one that results in the minimum approximation error this property is used as a common strategy for the optimization of qmf banks orthogonal wavelet transforms and least squares pyramids a general solution is derived for the qmf bank that provides the optimal decomposition of an arbitrary wide sense stationary process this approach is extended to the continuous case to obtain the minimum error approximation of a signal at a given sampling rate in particular it is shown that the sine wavelet transform is optimal for the representation at all scales of signals with non increasing spectral density

landau ginzburg calabi yau correspondence for quintic three folds via symplectic transformations we compute the recently introduced fan jarvis ruan witten theory of w curves in genus zero for quintic polynomials in five variables and we show that it matches the gromov witten genus zero theory of the quintic three fold via a symplectic transformation more specifically we show that the j function encoding the fan jarvis ruan witten theory on the a side equals via a mirror map the i function embodying the period integrals at the gepner point on the b side this identification inscribes the physical landau ginzburg calabi yau correspondence within the enumerative geometry of moduli of curves matches the genus zero invariants computed by the physicists huang klemm and quackenbush at the gepner point and yields via givental s quantization a prediction on the relation between the full higher genus potential of the quintic three fold and that of fan jarvis ruan witten theory

design of fir paraunitary filter banks for subband coding using a polynomial eigenvalue decomposition the problem of paraunitary pu filter bank design for subband coding has received considerable attention in recent years not least because of the energy preserving property of this class of filter banks in this paper we consider the design of signal adapted finite impulse response fir pu filter banks using polynomial matrix evd pevd techniques modifications are proposed to an iterative time domain pevd method known as the sequential best rotation sbr2 algorithm which enables its effective application to the problem of fir orthonormal filter bank design for efficient subband coding by choosing an optimization scheme that maximizes the coding gain at each stage of the algorithm it is shown that the resulting filter bank behaves more and more like the infinite order principle component filter bank pcfb the proposed method is compared to state of the art techniques namely the iterative greedy algorithm iga the approximate evd aevd standard sbr2 and a fast algorithm for fir compaction filter design called the window method wm we demonstrate that for the calculation of the subband coder the wm approach offers a low cost alternative at lower coding gains while at moderate to high complexity the proposed approach outperforms the benchmarkers in terms of run time complexity aevd performs well at low orders while the proposed algorithm offers a better coding gain than the benchmarkers at moderate to high filter order for a number of simulation scenarios

multidimensional paraunitary principal component filter banks in this correspondence the one dimensional 1 d principal component filter banks pcfb s derived by tsatsatsanis and giannakis 1995 are generalized to higher dimensions as presented by tsatsatsanis and giannakis pcfb s minimize the mean squared error mse when only q out of p subbands are retained previously two dimensional 2 d pcfb s were proposed by tirakis et al 1995 the work by tirakis et al was limited to 2 d signals and separable resampling operators the formulation presented here is general in that it can easily accommodate signals of arbitrary yet finite dimension and nonseparable sampling a major result presented in this paper is that in addition to minimizing mse when reconstructing from q out of p subbands the pcfb s result in maximizing theoretical coding gain tcg thereby performing optimally in a energy compaction sense

efficient large scale filter filterbank design via lmi characterization of trigonometric curves many filter and filterbank design problems can be posed as the optimization of linear or convex quadratic objectives over trigonometric semi infinite constraints recent advances in design methodology are based on various linear matrix inequality lmi characterizations of the semi infinite constraints and semidefinite programming sdp solutions despite these advances the design of filters of several hundredth order which typically arise in multicarrier communication and signal compression cannot be accommodated this hurdle is due mainly to the large number of additional variables incurred in the lmi characterizations this paper proposes a novel lmi characterization of the semi infinite constraints that involves additional variables of miminal dimensions consequently the design of high order filters required in practical applications can be achieved examples of designs of up to 1200 tap filters are presented to verify the viability of the proposed approach

proper efficiency in a linear fractional vector maximum problem with generalized convex constraints abstract in the present paper a vector maximum problem vmp with linear fractional objectives and generalized convex constraints is considered a necessary and sufficient condition for an efficient solution of vmp is derived in kuhn tucker s form moreover it is proved that under a certain boundedness assumption an efficient solution is properly efficient this extends the results of choo 3 for a linear fractional vector maximum problem with linear constraints to generalized convex constraints an example is given to illustrate the results

equivalence of elsv and bouchard marino conjectures for r spin hurwitz numbers we propose two conjectures on hurwitz numbers with completed r 1 cycles or equivalently on certain relative gromov witten invariants of the projective line the conjectures are analogs of the elsv formula and of the bouchard marino conjecture for ordinary hurwitz numbers our r elsv formula is an equality between a hurwitz number and an integral over the space of r spin structures that is the space of stable curves with an r th root of the canonical bundle our r bm conjecture is the statement that n point functions for hurwitz numbers satisfy the topological recursion associated with the spectral curve x y r log y in the sense of chekhov eynard and orantin we show that the r elsv formula and the r bm conjecture are equivalent to each other and provide some evidence for both

a state space approach to the design of globally optimal fir energy compaction filters we introduce a new approach for the least squared optimization of a weighted fir filter of arbitrary order n under the constraint that its magnitude squared response be nyquist m although the new formulation is general enough to cover a wide variety of applications the focus of the paper is on optimal energy compaction filters the optimization of such filters has received considerable attention in the past due to the fact that they are the main building blocks in the design of principal component filter banks pcfbs the newly proposed method finds the optimum product filter f sub opt z h sub opt z h sub opt z sup 1 corresponding to the compaction filter h sub opt z by expressing f z in the form d z d z sup 1 we show that the compaction problem can be completely parameterized in terms of the state space realization of the causal function d z for a given input power spectrum the resulting filter f sub opt z is guaranteed to be a global optimum solution due to the convexity of the new formulation the new algorithm is universal in the sense that it works for any m arbitrary filter length n and any given input power spectrum furthermore additional linear constraints such as wavelets regularity constraints can be incorporated into the design problem finally obtaining h sub opt z from f sub opt z does not require an additional spectral factorization step the minimum phase spectral factor h sub min z can be obtained automatically by relating the state space realization of d sub opt z to that of h sub opt z

synthesis of extremal wavelet generating filters using gaussian quadrature orthogonal wavelets can be generated from finite impulse response quadrature mirror filters these filters are also used in perfect reconstruction filter banks this paper addresses the problem of efficiently synthesizing such filters a class of extremal filters is defined by the property that their magnitude spectrum maximizes an integral criterion it is found that these filters are characterized by their zeros on the unit circle which frequently can be obtained from a set of orthogonal polynomials a family of filters is constructed that minimize the subband aliasing energy and can generate wavelets with an arbitrary number of vanishing moments the algorithm for generating these filters makes use of the levinson recursions gaussian quadrature and a fast version of euclid s algorithm similar to other methods for constructing quadrature mirror filters the spectral factorization of a polynomial is the computationally expensive part of this algorithm

signal analysis using a multiresolution form of the singular value decomposition this paper proposes a multiresolution form of the singular value decomposition svd and shows how it may be used for signal analysis and approximation it is well known that the svd has optimal decorrelation and subrank approximation properties the multiresolution form of svd proposed here retains those properties and moreover has linear computational complexity by using the multiresolution svd the following important characteristics of a signal may he measured at each of several levels of resolution isotropy sphericity of principal components self similarity under scaling and resolution of mean squared error into meaningful components theoretical calculations are provided for simple statistical models to show what might be expected results are provided with real images to show the usefulness of the svd decomposition

principal component filter banks for optimal multiresolution analysis an important issue in multiresolution analysis is that of optimal basis selection an optimal p band perfect reconstruction filter bank prfb is derived in this paper which minimizes the approximation error in the mean square sense between the original signal and its low resolution version the resulting prfb decomposes the input signal into uncorrelated low resolution principal components with decreasing variance optimality issues are further analyzed in the special case of stationary and cyclostationary processes by exploiting the connection between discrete time filter banks and continuous wavelets an optimal multiresolution decomposition of l sub 2 r is obtained analogous results are also derived for deterministic signals some illustrative examples and simulations are presented

a multirate dsp model for estimation of discrete probability density functions the problem of estimating a probability density function pdf from measurements has been widely studied by many researchers even though much work has been done in the area of pdf estimation most of it was focused on the continuous case we propose a new model based approach for modeling and estimating discrete probability density functions or probability mass functions this approach is based on multirate signal processing theory and it has several advantages over the conventional histogram method we illustrate the pdf estimation procedure and analyze the statistical properties of the pdf estimates based on this model a novel scheme is introduced that can be used for estimating the pdf in the presence of noise furthermore the proposed ideas are extended to the more general case of estimating multivariate pdfs finally we also consider practical issues such as optimizing the coefficients of a digital filter which is an integral part of the model this allows us to apply the proposed model to solve real world problems simulation results are given where appropriate in order to demonstrate the ideas

the role of gtd in optimizing perfect reconstruction filter banks filter bank optimization for specific input statistics has been of great interest in both theory and practice in many signal processing applications in this paper we propose gtd generalized triangular decomposition filter banks as a subband coder for optimizing the theoretical coding gain we focus on perfect reconstruction orthonormal gtd filter banks and biorthogonal gtd filter banks we show that in both cases there are two fundamental properties in the optimal solutions namely total decorrelation and spectrum equalization the optimal solutions can be obtained by performing the frequency dependent gtd on the cholesky factor of the input power spectrum density matrices we also show that in both theory and numerical simulations the optimal gtd subband coders have superior performance than optimal traditional subband coders in addition the uniform bit loading scheme can with no loss of optimality be used in the optimal biorthogonal gtd coders which solves the granularity problem in the conventional optimum bit loading formula we then extend the use of gtd filter banks to wireless communication systems where linear precoding and zero forcing decision feedback equalization is used in frequency selective channels we consider the quality of service qos problem of minimizing the transmitted power subject to the bit error rate and total bit rate constraints optimal systems with orthonormal precoder and unconstrained precoder are both derived and shown to be related to the frequency dependent gtd of the channel frequency response

a newton raphson method for moving average spectral factorization using the euclid algorithm an implementation of the newton raphson approach to compute the minimum phase moving average spectral factor of a finite positive definite correlation sequence is presented each step in the successive approximation method involves a system of linear equations that is solved using either the levinson algorithm backwards the jury stability test or a symmetrized version of the euclid algorithm various properties of the newton raphson map are studied the algorithm is generalized to other symmetries other than with respect to the unit circle the special case of the symmetry with respect to the imaginary axis is presented and related to the routh hurwitz stability test for continuous time transfer function

optimum fir transmitter and receiver filters for data transmission over band limited channels the paper deals with the design of digital transmitter and receiver filters with finite impulse response fir for data transmission over band limited channels the filters are matched and satisfy a zero intersymbol interference constraint when cascaded for baseband transmission the filters achieve optimum spectral concentration in the frequency range 1 beta 2t 1 beta 2t mathematically the filter design leads to a generalized eigenvalue problem which is solved numerically by a projected gradient procedure for transmission over bandpass channels by combined amplitude and phase modulation the design technique is modified so that filters with complex valued impulse response and optimum spectral concentration in the range of positive bandpass frequencies f c 1 beta 2t f c 1 beta 2t are obtained in addition the complex formulation allows the design of impulse responses with enhanced spectral attenuation in the corresponding range of negative frequencies in order to minimize imageband interference results are shown in terms of filter coefficients signal spectra and spectral concentrations obtained for example filters designed for a voiceband data modem operating at a symbol rate of 2400 baud achieve a spectral concentration of 98 5 percent with 24 coefficients and beta 0 1 and with only 0 001 percent of the total energy in the imageband region

results on principal component filter banks colored noise suppression and existence issues we have made explicit the precise connection between the optimization of orthonormal filter banks fbs and the principal component property the principal component filter bank pcfb is optimal whenever the minimization objective is a concave function of the subband variances of the fb this explains pcfb optimality for compression progressive transmission and various hitherto unnoticed white noise suppression applications such as subband wiener filtering the present work examines the nature of the fb optimization problems for such schemes when pcfbs do not exist using the geometry of the optimization search spaces we explain exactly why these problems are usually analytically intractable we show the relation between compaction filter design i e variance maximization and optimum fbs a sequential maximization of subband variances produces a pcfb if one exists but is otherwise suboptimal for several concave objectives we then study pcfb optimality for colored noise suppression unlike the case when the noise is white here the minimization objective is a function of both the signal and the noise subband variances we show that for the transform coder class if a common signal and noise pcfb klt exists it is optimal for a large class of concave objectives common pcfbs for general fb classes have a considerably more restricted optimality as we show using the class of unconstrained orthonormal fbs for this class we also show how to find an optimum fb when the signal and noise spectra are both piecewise constant with all discontinuities at rational multiples of spl pi

technical note proper efficiency and the linear fractional vector maximum problem a vector maximum problem arises when two or more criterion functions are to be simultaneously maximized over a feasible region we prove that in linear fractional vector maximum problems every efficient solution satisfies the requirements of a restricted concept of efficiency the notion of proper efficiency

cyclostationary modeling analysis and optimal compensation of quantization errors in subband codecs the paper is concerned with the analysis and modeling of the effects of quantization of subband signals in subband codecs using cyclostationary representations the authors derive equations for the autocorrelation and power spectral density psd of the reconstructed signal y n in terms of the analysis synthesis filters the psd of the input and the pdf optimized quantizer model formulas for the mean square error mse and for compaction gain are obtained in terms of these parameters the authors constrain the filter bank to be perfect reconstruction pr but not necessarily paraunitary in the absence of quantization and transmission errors these formulas set the stage for filter optimization maximization of compaction gain and minimization of mse subject to pr and bit constraints optimal filters are designed optimal compensation is performed and the theoretical results are confirmed with simulations the floating point quantizer wherein only the mantissa is uniformly quantized is also analyzed and compared with the fixed point pdf optimized filter bank for high bit rates their performance is comparable

oversampling pcm techniques and optimum noise shapers for quantizing a class of nonbandlimited signals we consider the efficient quantization of a class of nonbandlimited signals namely the class of discrete time signals that can be recovered from their decimated version the signals are modeled as the output of a single fir interpolation filter single band model or more generally as the sum of the outputs of l fir interpolation filters multiband model these nonbandlimited signals are oversampled and it is therefore reasonable to expect that we can reap the same benefits of well known efficient a d techniques that apply only to bandlimited signals we first show that we can obtain a great reduction in the quantization noise variance due to the oversampled nature of the signals we can achieve a substantial decrease in bit rate by appropriately decimating the signals and then quantizing them to further increase the effective quantizer resolution noise shaping is introduced by optimizing prefilters and postfilters around the quantizer we start with a scalar time invariant quantizer and study two important cases of linear time invariant lti filters namely the case where the postfilter is the inverse of the prefilter and the more general case where the postfilter is independent from the prefilter closed form expressions for the optimum filters and average minimum mean square error are derived in each case for both the single band and multiband models the class of noise shaping filters and quantizers is then enlarged to include linear periodically time varying lptv sub m filters and periodically time varying quantizers of period m we study two special cases in great detail

pseudolinearity and efficiency first order and second order characterizations of pseudolinear functions are derived for a nonlinear programming problem involving pseudolinear functions only it is proved that every efficient solution is properly efficient under some mild conditions

minlab minimum noise structure for ladder based biorthogonal filter banks we introduce a minimum noise structure for ladder based biorthogonal minlab filter bank the minimum noise structure ensures that the quantization error has a unity noise gain even though the filter bank is biorthogonal the coder has a very low design and implementation cost the perfect reconstruction property is structurally preserved optimal bit allocation and coding gain formulas are derived we show that the coding gain of the optimal minlab coder is always greater than or equal to unity for both ar 1 process and ma 1 process the minlab coder with two taps has a higher coding gain than the optimal orthonormal coder with an infinite number of taps in addition to its superior decorrelation ability it has many other desired features that make it a potentially valuable and attractive alternative to the orthonormal coder especially for a high fidelity compression

signal adapted multiresolution transform for image coding the authors consider the problem of designing multiresolution transforms that are adapted to the given image signal in the sense that they maximize the coding gain at each resolution level a simple alternating optimization algorithm is derived for solving this problem in the framework of the lattice realization of para unitary quadrature mirror filters the resulting large coding scheme is discussed in some detail and its performance is compared with that of the discrete cosine transform jpeg technique and with that of some nonadapted multiresolution transforms

theory and design of optimum fir compaction filters the problem of optimum fir energy compaction filter design for a given number of channels m and a filter order n is considered the special cases where n m and n spl infin have analytical solutions that involve eigenvector decomposition of the autocorrelation matrix and the power spectrum matrix respectively we deal with the more difficult case of m n spl infin for the two channel case and for a restricted but important class of random processes we give an analytical solution for the compaction filter that is characterized by its zeros on the unit circle this also corresponds to the optimal two channel fir filter bank that maximizes the coding gain under the traditional quantization noise assumptions with a minor extension this can also be used to generate optimal wavelets for the arbitrary m channel case we provide a very efficient suboptimal design method called the window method the method involves two stages that are associated with the above two special cases as the order increases the suboptimality becomes negligible and the filter converges to the ideal optimal solution we compare the window method with a previously introduced technique based on linear programming

on pseudolinear functions abstract in this paper the structure of a smooth pseudolinear function is investigated and the general form of the gradient is given explicitly

time varying system identification and model validation using wavelets parametric identification of time varying tv systems is possible if each tv coefficient can be expanded onto a finite set of basis sequences the problem then becomes time invariant with respect to the parameters of the expansion the authors address the question of selecting this set of basis sequences they advocate the use of a wavelet basis because of its flexibility in capturing the signal s characteristics at different scales and discuss how to choose the optimal wavelet basis for a given system trajectory they also develop statistical tests to keep only the basis sequences that significantly contribute to the description of the system s time variation by formulating the problem as a regressor selection problem they apply an p test and an aic based approach for multiresolution analysis of tv systems the resulting algorithm can estimate tv ar or armax models and determine their orders they apply this algorithm to both synthetic and real speech data and compare it with the kalman filtering tv parameter estimator

analytical optimization of cqf filter banks the optimization of subband filter banks for signal and image coding is normally dealt with by numerical means it is shown that this optimization can be done analytically in the case of the prototype four tap causal conjugate quadrature filter cqf the coding gain and aliasing energy are considered in the optimization using parametrizations of the prototype filter coefficients it was found that the optimal filter is the regular daubechies d sub 2 wavelet filter

on the existence and uniqueness of the eigenvalue decomposition of a parahermitian matrix this paper addresses the extension of the factorization of a hermitian matrix by an eigenvalue decomposition evd to the case of a parahermitian matrix that is analytic at least on an annulus containing the unit circle such parahermitian matrices contain polynomials or rational functions in the complex variable z and arise e g as cross spectral density matrices in broadband array problems specifically conditions for the existence and uniqueness of eigenvalues and eigenvectors of a parahermitian matrix evd are given such that these can be represented by a power or laurent series that is absolutely convergent at least on the unit circle permitting a direct realization in the time domain based on an analysis of the unit circle we prove that eigenvalues exist as unique and convergent but likely infinite length laurent series the eigenvectors can have an arbitrary phase response and are shown to exist as convergent laurent series if eigenvalues are selected as analytic functions on the unit circle and if the phase response is selected such that the eigenvectors are holder continuous with alpha frac 1 2 on the unit circle in the case of a discontinuous phase response or if spectral majorisation is enforced for intersecting eigenvalues an absolutely convergent laurent series solution for the eigenvectors of a parahermitian evd does not exist we provide some examples comment on the approximation of a parahermitian matrix evd by laurent polynomial factors and compare our findings to the solutions provided by polynomial matrix evd algorithms

a direct approach to h sub 2 optimal deconvolution of periodic digital channels this paper studies the h sub 2 optimal deconvolution problem for periodic finite impulse response fir and infinite impulse response iir channels it shows that the h sub 2 norm of a periodic filter can be directly quantified in terms of periodic system matrices and linear matrix inequalities lmis without resorting to the commonly used lifting technique the optimal signal reconstruction problem is then formulated as an optimization problem subject to a set of matrix inequality constraints under this framework the optimization of both the fir and iir periodic deconvolution filters can be made convex solved using the interior point method and computed by using the matlab lmi toolbox the robust deconvolution problem for periodic fir and iir channels with polytopic uncertainties are further formulated and solved also by convex optimization and the lmis compared with the lifting approach to the design of periodic filters the proposed approach is simpler yet more powerful in dealing with multiobjective deconvolution problems and channel uncertainties especially for iir deconvolution filter design the obtained solutions are applied to the design of an optimal filterbank yielding satisfactory performance

recursive biorthogonal interpolating wavelets and signal adapted interpolating filter banks in this paper by combining the ideas of the recursive wavelets with second generation wavelets a family of recursive biorthogonal interpolating wavelets rbiws is developed the rbiws have simple shape parameter vectors on each level which allows a multichannel decomposition algorithm and provides a flexible structure for designing signal adapted interpolating filter banks in the single level case an efficient approach to design an optimum two channel biorthogonal interpolating filter bank is proposed which maximizes the coding gain under the traditional quantization noise assumption furthermore in the multilevel case using level wise optimization of the shape parameter vectors signal adapted tree structured recursive biorthogonal interpolating filter banks rbifbs are designed which are efficient in computation and can remarkedly improve the coding gain finally numerical results demonstrate the effectiveness of the proposed methods

improved technique for design of perfect reconstruction fir qmf banks with lossless polyphase matrices a technique is developed for the design of analysis filters in an m channel maximally decimated perfect reconstruction finite impulse response quadrature mirror filter fir qmf bank that has a lossless polyphase component matrix e z the aim is to optimize the parameters characterizing e z until the sum of the stopband energies of the analysis filters is minimized there are four novel elements in the procedure reported here the first is a technique for efficient initialization of one of the m analysis filters as a spectral factor of an mth band filter the factorization itself is done in an efficient manner using the eigenfilters approach without the need for root finding techniques the second element is the initialization of the internal parameters which characterize e z based on the above spectral factor the third element is a modified characterization mostly free from rotation angles of the fir e z the fourth is the incorporation of symmetry among the analysis filters so as to minimize the number of unknown parameters being optimized the resulting design procedure always gives better filter responses than earlier ones for a given filter length and converges much faster

prediction based lower triangular transform a new nonunitary transform called the prediction based lower triangular transform plt is introduced for signal compression the new transform has the same decorrelation property as the kahurnen loeve transform klt but its implementational cost is less than one half of klt compared with the klt the design cost of an m spl times m plt is much lower and is only of the order of o m sup 2 moreover the plt can be factorized into simple building blocks using two different factorizations we introduce two minimum noise structures that have roughly the same complexity as the direct implementation of plt these minimum noise structures have the following properties 1 its noise gain is unity even though the transform is nonunitary 2 perfect reconstruction is structurally guaranteed 3 it can be used for both lossy lossless compression we show that the coding gain of plt implemented using the minimum noise structure is the same as that of klt furthermore universal transform coders using plt are derived for ar 1 process the m spl times m plt has a closed form and needs only m 1 multiplications and additions

moduli of roots of line bundles on curves we treat the problem of completing the moduli space for roots of line bundles on curves special attention is devoted to higher spin curves within the universal picard scheme two new different constructions both using line bundles on nodal curves as boundary points are carried out and compared with pre existing ones

hurwitz numbers and intersections on moduli spaces of curves 1 department of mathematics university of stockholm s 10691 stockholm sweden e mail teke matematik su se 2 higher college of mathematics independent university of moscow and institute for system research ras moscow russia e mail lando mccme ru 3 department of mathematics royal institute of technology s 10044 stockholm sweden e mail mshapiro math kth se 4 department of mathematics and department of computer science university of haifa haifa 31905 israel e mail alek mathcs haifa ac il

identification of the givental formula with the spectral curve topological recursion procedure we identify the givental formula for the ancestor formal gromov witten potential with a version of the topological recursion procedure for a collection of isolated local germs of the spectral curve as an application we prove a conjecture of norbury and scott on the reconstruction of the stationary sector of the gromov witten potential of mathbb c rm p 1 via a particular spectral curve

polynomiality of hurwitz numbers bouchard marino conjecture and a new proof of the elsv formula in this paper we give a new proof of the elsv formula first we refine an argument of okounkov and pandharipande in order to prove quasi polynomiality of hurwitz numbers without using the elsv formula the only way to do that before used the elsv formula then using this polynomiality we give a new proof of the bouchard marino conjecture after that using the correspondence between the givental group action and the topological recursion coming from matrix models we prove the equivalence of the bouchard marino conjecture and the elsv formula it is a refinement of an argument by eynard c 2015 elsevier inc all rights reserved

algebraic theory of optimal filterbanks we introduce an optimality theory for finite impulse response fir filterbanks using a general algebraic point of view we consider an admissible set spl lscr of fir filterbanks and use scalability as the main notion based on which performance of the elements in spl lscr are compared we show that quantification of scalability leads naturally to a partial ordering on the set spl lscr an optimal solution is therefore represented by the greatest element in spl lscr it turns out that a greatest element does not necessarily exist in spl lscr hence one has to settle with one of the maximal elements that exist in spl lscr we provide a systematic way of finding a maximal element by embedding the partial ordering at hand in a total ordering this is done by using a special class of order preserving functions known as schur convex there is however a price to pay for achieving a total ordering there are infinitely many possible choices for schur convex functions and the optimal solution specified in spl lscr depends on this subjective choice an interesting aspect of the presented algebraic theory is that the connection between several concepts namely principal component filterbanks pcfbs filterbanks with maximum coding gain and filterbanks with good scalability is clearly revealed we show that these are simply associated with different extremal elements of the partial ordering induced on spl lscr by scalability