optimal design of magnitude responses of rational infinite impulse response filters this correspondence considers a design of magnitude responses of optimal rational infinite impulse response iir filters the design problem is formulated as an optimization problem in which a total weighted absolute error in the passband and stopband of the filters the error function reflects a ripple square magnitude is minimized subject to the specification on this weighted absolute error function defined in the corresponding passband and stopband as well as the stability condition since the cost function is nonsmooth and nonconvex while the constraints are continuous this kind of optimization problem is a nonsmooth nonconvex continuous functional constrained problem to address this issue our previous proposed constraint transcription method is applied to transform the continuous functional constraints to equality constraints then the nonsmooth problem is approximated by a sequence of smooth problems and solved via a hybrid global optimization method the solutions obtained from these smooth problems converge to the global optimal solution of the original optimization problem hence small transition bandwidth filters can be obtained

allpass vfd filter design this correspondence proposes a general design for allpass variable fractional delay vfd digital filters with minimum weighted integral squared error subject to constraints on maximum error deviation from the desired response the resulting optimization problem is nonlinear and nonconvex with a nonlinear continuous inequality constraint stability of the designed filters are discussed an effective procedure is proposed for solving the optimization problem firstly a constraint transcription method and a smoothing technique are employed to transform the continuous inequality constraint into one equality constraint then by using the concept of a penalty function the transformed constraint is incorporated into the cost function to form a new cost function the nonlinear optimization problem subject to continuous inequality constraints is then approximated by a sequence of unconstraint optimization problems finally a global optimization method using a filled function is employed to solve the unconstraint optimization problem design example shows that a trade off can be achieved between the integral squared error and the maximum error deviation for the design of allpass vfd filters

markovianizing cost of tripartite quantum states we introduce and analyze a task that we call markovianization in which a tripartite quantum state is transformed to a quantum markov chain by a randomizing operation on one of the three subsystems we consider cases where the initial state is the tensor product of n copies of a tripartite state rho abc and is transformed to a quantum markov chain conditioned by b n with a small error using a random unitary operation on a n in an asymptotic limit of infinite copies and vanishingly small error we analyze the markovianizing cost that is the minimum cost of randomness per copy required for markovianization for tripartite pure states we derive a single letter formula for the markovianizing costs counterintuitively the markovianizing cost is not a continuous function of states and can be arbitrarily large even if the state is close to a quantum markov chain our results have an application in analyzing the cost of resources for simulating a bipartite unitary gate by local operations and classical communication

digital filter design using root moments for sum of all pass structures from complete and partial specifications this paper is concerned with the development of digital filter design procedures for transfer functions in the form of sum of all pass in which the requirements may be partially specified specifically the requirements for a digital filter or equalizer in amplitude a spl theta or phase spl phi spl theta or possibly group delay response spl tau spl theta may be specified from measurements over a limited a set of frequencies spl theta sub 1 spl theta sub 2 the problem is to develop techniques for the design a transfer function h z satisfying these specifications and constrained to be in the form of a sum of two all pass functions the proposed solution is based on the use of root moments the companion problem concerned with the estimation of the orders of the required all pass filters is also examined and a solution proposed based on the same context of root moments

eigenfilter design of 1 d and 2 d iir digital all pass filters the eigenfilter approach is extended to design 1d and 2d iir digital all pass filters instead of the integration of the filter magnitude error the integration of phase error is minimized such that the design problem can be characterized by an eigenformulation the stability is obtained by constraining the phase specification

a technique for realizing linear phase iir filters a real time iir filter structure is presented that possesses exact phase linearity with 10 approximately 1000 times fewer general multiplies than conventional fir filters of similar performance and better magnitude characteristics than equiripple or maximally flat group delay iir filters this structure is based on a technique using local time reversal and single pass sectioned convolution methods to realized a real time recursive implementation of the noncausal transfer function h z sup 1 the time reversed section technique used to realize exactly linear phase iir filters is described the effects of finite section length on the sectional convolution are analyzed a simulation methodology is developed to address the special requirements of simulating a time reversed section filter a design example is presented with computer simulation to illustrate performance in terms of overall magnitude response and phase linearity as a function of finite section length nine example filter specifications are used to compare the performance and complexity of the time reversed section technique to those of a direct fir implementation

optimal design of fir filters with the complex chebyshev error criteria we present an improved algorithm for an established filter design problem the design of an fir filter that best approximates in the complex chebyshev sense a desired complex valued frequency response the algorithm is a variant of the simplex algorithm of linear programming which has an interpretation as an implicit multiple exchange it is iterative robust and exhibits good convergence speed global optimum convergence is guaranteed both complex and real valued impulse responses can be designed with it the design of complex coefficient filters is new an example is given for each case the design of noncausal filters is new in addition to these new applications we conjecture that this new algorithm may have important advantages over existing techniques with respect to the maximum filter length possible speed and stability of convergence accuracy and memory requirements the ability to design long filters is among the more significant improvements over previous work filters of length 1000 have been designed with the new method

allpass filter design and applications the problem of allpass filter design for phase approximation and equalization in the chebyshev sense is solved by using a generalized remez algorithm convergence to the unique optimum is guaranteed and is achieved rapidly in the actual implementation the well known numerical problems for higher degree filters are analyzed and solved by a simple approach the algorithm yields a solution to a variety of filter design problems such as the design of filters with a desired phase response e g a delay element the design of phase equalizers or the design of recursive filters with magnitude prescriptions using parallel allpass filters for the latter the algorithm can be modified to allow arbitrary tolerance schemes for the magnitude response

design of fir digital phase networks the problem of the minimax design of fir digital filters with prescribed phase characteristics and unit magnitude is a nonlinear optimization problem in this paper it is approximated by a linear programming problem and it is shown that the solution of this linear program is optimal to first order that is if 0 and e 0 are optimal deviations of magnitude and phase characteristics then the actual deviations obtained from the linear program solution satisfy delta leq delta 0 epsilon min 0 max 2 and epsilon leq epsilon 0 1 delta 0 1 delta 0 numerical examples are given including design results for full band m term chirp filters which like linear phase filters can be implemented with m 1 2 multiplications per point

iir discrete time hilbert transformers a procedure for obtaining iir hilbert transformers from generalized halfband filters 5 is described the solution is shown to be suited for specifications where the care band for the hilbert transformers is centered at 0 5 even when this condition is not satisfied the proposed hilbert transformers obtained by overdesign may often be preferable for implementation to those obtained from a general design procedure 6 analytic solutions for noncausal hilbert transformers and 90 phase shifters can be derived from special classes of classical low pass filters the design procedure described by gold et al 6 is shown to be equivalent to applying a transformation on hilbert transformers derived from elliptic low pass filters numerical approximation can be used for designing iir hilbert transformers with a right sided impulse response this gives us a single causal iir filter instead of a pair of 90 phase shifters whose output is the approximate hilbert transform of the delayed version of the input

h infty optimal fractional delay filters fractional delay filters are digital filters to delay discrete time signals by a fraction of the sampling period since the delay is fractional the intersample behavior of the original analog signal becomes crucial in contrast to the conventional designs based on the shannon sampling theorem with the band limiting hypothesis the present paper proposes a new approach based on the modern sampled data h optimization that aims at restoring the intersample behavior beyond the nyquist frequency by using the lifting transform or continuous time blocking the design problem is equivalently reduced to a discrete time h optimization which can be effectively solved by numerical computation softwares moreover a closed form solution is obtained under an assumption on the original analog signals design examples are given to illustrate the advantage of the proposed method

sufficient subalgebras and the relative entropy of states of a von neumann algebra a subalgebram 0 of a von neumann algebram is called weakly sufficient with respect to a pair of states if the relative entropy of and coincides with the relative entropy of their restrictions tom 0 the main result says thatm 0 is weakly sufficient for if and only ifm 0 contains the radon nikodym cocycle d d t other conditions are formulated in terms of generalized conditional expectations and the relative hamiltonian

weighted least squares design of recursive allpass filters a method for the design of allpass filters is described in this method an error reflecting the difference between the desired phase response and the phase response of the practical allpass filter is formulated in a quadratic form the coefficients are obtained by solving a system of linear equations involving the sum of a toeplitz and an hankel matrix

conditional decoupling of quantum information insights from quantum information theory show that correlation measures based on quantum entropy are fundamental tools that reveal the entanglement structure of multipartite states in that spirit groisman popescu and winter phys rev a 72 032317 2005 showed that the quantum mutual information i a b quantifies the minimal rate of noise needed to erase the correlations in a bipartite state of quantum systems ab here we investigate correlations in tripartite systems abe in particular we are interested in the minimal rate of noise needed to apply to the systems ae in order to erase the correlations between a and b given the information in system e in such a way that there is only negligible disturbance on the marginal be we present two such models of conditional decoupling called deconstruction and conditional erasure cost of tripartite states abe our main result is that both are equal to the conditional quantum mutual information i a b e establishing it as an operational measure for tripartite quantum correlations

design of iir digital allpass filters based on eigenvalue problem a new method is proposed for designing iir digital allpass filters with an equiripple phase response that can be proven to be optimal in the chebyshev sense the proposed procedure is based on the formulation of an eigenvalue problem by using the remez exchange algorithm since there exists more than one eigenvalue in the general eigenvalue problem we introduce a new and very simple selection rule for the eigenvalue to be searched for where the rational interpolation is performed if and only if the real maximum eigenvalue is chosen therefore the solution of the rational interpolation problem can be gotten by computing only one eigenvector corresponding to the real maximum eigenvalue and the optimal filter coefficients are easily obtained through a few iterations without any initial guess of the solution the design algorithm proposed not only retains the speed inherent in the remez exchange algorithm but also simplifies the interpolation step because it has been reduced to the computation of the real maximum eigenvalue two examples are designed to demonstrate the effectiveness of this method

quantum to classical randomness extractors the goal of randomness extraction is to distill almost perfect randomness from a weak source of randomness when the source yields a classical string x many extractor constructions are known yet when considering a physical randomness source x is itself ultimately the result of a measurement on an underlying quantum system when characterizing the power of a source to supply randomness it is hence natural to ask how much classical randomness we can extract from a quantum system to tackle this question we here take on the study of quantum to classical randomness extractors qc extractors we provide constructions of qc extractors based on measurements in a full set of mutually unbiased bases mubs and certain single qubit measurements the latter are particularly appealing since they are not only easy to implement but also appear throughout quantum cryptography we proceed to prove an upper bound on the maximum amount of randomness that we could hope to extract from any quantum state some of our qc extractors almost match this bound we show two applications of our results first we show that any qc extractor gives rise to entropic uncertainty relations with respect to quantum side information such relations were previously only known for two measurements in particular we obtain strong relations in terms of the von neumann shannon entropy as well as the min entropy for measurements in almost unitary two designs a full set of mubs and single qubit measurements in three mubs each second we resolve the central open question in the noisy storage model by linking security to the quantum capacity of the adversary s storage device more precisely we show that any two party cryptographic primitives can be implemented securely as long as the adversary s storage device has sufficiently low quantum capacity our protocol does not need any quantum storage to implement and is technologically feasible using present day technology

a coding theorem for bipartite unitaries in distributed quantum computation we analyze implementations of bipartite unitaries by means of local operations and classical communication locc assisted by shared entanglement we employ concepts and techniques developed in the quantum shannon theory to study an asymptotic scenario in which two distant parties perform the same bipartite unitary on infinitely many pairs of inputs we analyze minimum cost of entanglement and classical communication per copy for two round locc protocols we derive a single letter formula for the minimum cost of entanglement and classical communication under an additional requirement that the error converges to zero faster than 1 n 4 where n is the number of input pairs the formula is given by the markovianizing cost of a tripartite state associated with the unitary which can be computed by a finite step algorithm we also derive a lower bound on the minimum cost of resources which applies for protocols with arbitrary number of rounds

complex chebyshev approximation for fir digital filters an adaptive approach to fir finite impulse response filter design is applied to a fully general complex specification showing it to be capable of giving an optimum chebyshev solution it is thought to be one of the first practical approaches to achieve this in the case of a complex function design examples include a bandpass filter with nearly linear phase and all pass filters with general shaping phase comparisons are drawn with equivalent results from other algorithms

velocity filtering of acoustic well logging waveforms a velocity filter that is based on a particularly convenient and effective combination of an up down filter and slanting time shift operations is presented the up down filter is based on a cascade of spatial and temporal hilbert transform filters the hilbert transform filters and the time shift operators are finite duration impulse response fir filters designed according to the minimax criterion the velocity filter is applied to acoustic well logging waveforms to isolate the initial p s and stoneley waves from their reflected and converted waves at bed boundaries to achieve this objective the waveforms are time shifted to align the primary wave of interest before the velocity filter is applied examples demonstrate the effectiveness of this procedure in separating the primary waves from their reflected and converted waves

design of recursive group delay filters by autoregressive modeling a new method of design of recursive group delay filters is presented in this paper the method uses autoregressive modeling to derive parameters of the filter the design is based on the following line of argument the desired group delay characteristics are to be realized through a stable all pass filter the transfer function of an all pass filter is completely determined by the coefficients of either the numerator or the denominator polynomial for a stable all pass filter the denominator polynomial must be a minimum phase polynomial for a minimum phase polynomial the magnitude function and the group delay function are related through cepstral coefficients therefore from the given group delay specification the cepstral coefficients corresponding to the pole part inverse of the denominator polynomial of the desired filter are first determined the magnitude spectrum corresponding to these cepstral coefficients is approximated using autoregressive modeling a wide variety of group delay filters can be realized by the proposed method depending on the nature of approximation used and the accuracy desired the design procedure is illustrated through examples

eigenfilter design of higher order digital differentiators an effective approach is proposed for designing higher order differentiators by the eigenfilter method by minimizing a quadratic measure of the error in the frequency band an eigenvector of an appropriate matrix is computed to get the filter coefficients this method is not only simple and fast but also optimal in the least squares sense comparison to the mcclellan parks algorithm for minimax equiripple filters shows that both are optimal in the sense of different minimum norms of the error function but much better performance is obtained with the proposed approach in most of the frequency band except in the narrowband region near the cutoff edge

eigenfilter approach for the design of allpass filters approximating a given phase response we apply the eigenfilter method to design an allpass filter that approximates a given phase response in the least squares ls sense as it is not possible to express the exact ls phase error as a quadratic form suitable for eigenfilter formulation alternative error measures that approximate the ideal ls error are proposed for each of these new formulations the allpass coefficients are obtained as the elements of the eigenvector corresponding to the minimum eigenvalue of a real symmetric and positive definite matrix we propose a fast converging iterative technique to approximate the ideal ls phase error solution by employing an iterative weighting technique the phase error can he made approximately equiripple the design methods are illustrated with various practical examples and the results are compared to allpass filters designs reported in the literature

the fidelity of recovery is multiplicative fawzi and renner recently established a lower bound on the conditional quantum mutual information cqmi of tripartite quantum states abc in terms of the fidelity of recovery for i e the maximal fidelity of the state abc with a state reconstructed from its marginal bc by acting only on the c system the for measures quantum correlations by the local recoverability of global states and has many properties similar to the cqmi here we generalize the for and show that the resulting measure is multiplicative by utilizing semi definite programming duality this allows us to simplify an operational proof by brandao et al of the above mentioned lower bound that is based on quantum state redistribution in particular in contrast to the previous approaches our proof does not rely on de finetti reductions

quantum conditional mutual information and approximate markov chains a state on a tripartite quantum system a otimes b otimes c forms a markov chain if it can be reconstructed from its marginal on a otimes b by a quantum operation from b to b otimes c we show that the quantum conditional mutual information i a c b of an arbitrary state is an upper bound on its distance to the closest reconstructed state it thus quantifies how well the markov chain property is approximated

design of iir digital filters based on eigenvalue problem this paper presents a new method for designing iir digital filters with optimum magnitude response in the chebyshev sense and different order numerator and denominator the proposed procedure is based on the formulation of a generalized eigenvalue problem by using remez exchange algorithm since there exist more than one eigenvalue in the general eigenvalue problem we introduce a very simple selection rule for the eigenvalue to be sought for where the rational interpolation is performed if and only if the positive minimum eigenvalue is chosen therefore the solution of the rational interpolation problem can be obtained by computing only one eigenvector corresponding to the positive minimum eigenvalue and the optimal filter coefficients are easily obtained through a few iterations the design algorithm proposed in this paper not only retains the speed inherent in the remez exchange algorithm but also simplifies the interpolation step because it has been reduced to the computation of the positive minimum eigenvalue some properties of the filters such as lowpass filters bandpass filters and so on are discussed and several design examples are presented to demonstrate the effectiveness of this method

quantum discord a measure of the quantumness of correlations two classically identical expressions for the mutual information generally differ when the systems involved are quantum this difference defines the quantum discord it can be used as a measure of the quantumness of correlations separability of the density matrix describing a pair of systems does not guarantee vanishing of the discord thus showing that absence of entanglement does not imply classicality we relate this to the quantum superposition principle and consider the vanishing of discord as a criterion for the preferred effectively classical states of a system i e the pointer states

the cost of randomness for converting a tripartite quantum state to be approximately recoverable we introduce and analyze a task in which a tripartite quantum state is transformed to an approximately recoverable state by a randomizing operation on one of the three subsystems we consider cases where the initial state is a tensor product of n copies of a tripartite state rho abc and is transformed by a random unitary operation on a n to another state which is approximately recoverable from its reduced state on a n b n case 1 or b n c n case 2 we analyze the minimum cost of randomness per copy required for the task in an asymptotic limit of infinite copies and vanishingly small error of recovery mainly focusing on the case of pure states we prove that the minimum cost in case 1 is equal to the markovianizing cost of the state for which a single letter formula is known with an additional requirement on the convergence speed of the recovery error we prove that the minimum cost in case 2 is also equal to the markovianizing cost our results have an application for distributed quantum computation

parabolic equations for curves on surfaces 2 intersections blow up and generalized solutions we describe a theory for parabolic equations for immersed curves on surfaces which generalizes the curve shortening or flow by mean curvature problem as well as several models in the theory of phase transitions in two dimensions a class of equations is described for which the initial value problem is well posed for rough initial data for which one can give a description of the way a smooth solution becomes singular and for which one can define generalized solutions i e solutions which are smooth except at a discrete set of times the methods which are used in this paper are more geometrical than those of part i by comparing arbitrary solutions with certain special solutions and by considering the way they intersect we derive estimates for the curvature and the tangent which allow one to study the initial value problem and the way solutions become singular

a new method for digital all pass filter design a new method for the design of digital all pass filters using chebyshev criterion is introduced it is based on a phase approximation algorithm for polynomial transfer functions the algorithm exploits a scheme of iteratively linearizing the nonlinear constraints in a nonlinear programming and converges theoretically the design method has the advantage that it finds the best uniform phase approximation to an arbitrarily specified phase response without any initial guess of the solution design examples of orders up to 80 obtained on an ibm pc xt personal computer are given to show the practicability of the method

design of fir filters in the complex domain the design of fir digital filters with a complex valued desired frequency response using the chebyshev error is investigated the complex approximation problem is converted into a real approximation problem which is nearly equivalent to the complex problem a standard linear programming algorithm for the chebyshev solution of overdetermined equations is used to solve the real approximation problem additional constraints are introduced which allow weighting of the phase and or group delay of the approximation digital filters are designed which have nearly constant group delay in the passbands the desired constant group delay which gives the minimum chebyshev error is found to be smaller than that of a linear phase filter of the same length these filters in addition to having a smaller approximately constant group delay have better magnitude characteristics than exactly linear phase filters with the same length the filters have nearly equiripple magnitude and group delay

the design of arbitrary fir digital filters using the eigenfilter method the design of finite impulse response fir digital filters for approximating an arbitrary function in both magnitude and phase in the least square sense is studied the design method is based on the computation of an eigenvector of an appropriate real symmetric and positive definite matrix the design of the complex coefficient filter is shown to be an extension of the design of the real coefficient filter several design examples including the constant group delay filters and digital phase all pass filters are presented comparisons to existing methods are made

the quantum reverse shannon theorem based on one shot information theory the quantum reverse shannon theorem states that any quantum channel can be simulated by an unlimited amount of shared entanglement and an amount of classical communication equal to the channel s entanglement assisted classical capacity in this paper we provide a new proof of this theorem which has previously been proved by bennett devetak harrow shor and winter our proof has a clear structure being based on two recent information theoretic results one shot quantum state merging and the post selection technique for quantum channels

simultaneous design in both magnitude and group delay of iir and fir filters based on multiple criterion optimization this work considers the simultaneous design in both magnitude and group delay of digital transfer functions on the basis of multiple criterion optimization both causal iir filters and nonlinear phase fir filters are studied examples of the optimal tradeoff filters both fir filters and iir filters are presented and their characteristics are analyzed

squashed entanglement an additive entanglement measure in this paper we present a new entanglement monotone for bipartite quantum states its definition is inspired by the so called intrinsic information of classical cryptography and is given by the halved minimum quantum conditional mutual information over all tripartite state extensions we derive certain properties of the new measure which we call squashed entanglement it is a lower bound on entanglement of formation and an upper bound on distillable entanglement furthermore it is convex additive on tensor products and superadditive in general continuity in the state is the only property of our entanglement measure which we cannot provide a proof for we present some evidence however that our quantity has this property the strongest indication being a conjectured fannes type inequality for the conditional von neumann entropy this inequality is proved in the classical case

minimax phase error design of iir digital filters with prescribed magnitude and phase responses infinite impulse response iir digital filters with prescribed magnitude and phase responses have been used in many applications to approximate the prescribed magnitude and phase responses we propose a new approach to the design of general iir filters by minimizing the maximum phase error subject to a prescribed or simultaneously minimized maximum magnitude error where the phase error and magnitude error are controlled by two elliptic constraints respectively with major and minor axes along the desired frequency response the sequential constrained least squares method and levy sanathanan koerner strategy are used to convert the nonconvex constraints into convex ones resulting in a series of convex optimization subproblems design examples and comparisons with recent methods demonstrate the flexibility and effectiveness of the proposed methods

design of iir eigenfilters in the frequency domain the eigenfilter approach is an appealing way of designing digital filters mainly because of the simplicity of its implementation in this correspondence a new method of applying the eigenfilter approach to the design of infinite impulse response iir filters is described the procedure works in the frequency domain and yields the coefficients of a causal rational transfer function having an arbitrary number of poles and zeros some examples of filter design are given to show the effectiveness of the method presented

a technique for multiple criterion approximation of fir filters in magnitude and group delay in spite of the attention received by nonlinear phase nlp fir filter design the best way to solve this problem is still open to debate the formulation of nonlinear phase fir filter design in terms of simultaneous magnitude and group delay approximation addresses the two parameters of ultimate interest for applications the simultaneous minimization of these two functions one of which the group delay rational is approached on the basis of an original extension of the differential correction algorithm the proposed design tool enjoys interesting theoretical properties and works very effectively the filters obtained according to the multiple criterion optimization mco formulation are compared against filters that are optimal in the complex chebychev norm then the flexibility characteristic of mco formulations of trading off between magnitude and group delay performance is exemplified

one shot decoupling if a quantum system a which is initially correlated to another system e undergoes an evolution separated from e then the correlation to e generally decreases here we study the conditions under which the correlation disappears almost completely resulting in a decoupling of a from e we give a criterion for decoupling in terms of two smooth entropies one quantifying the amount of initial correlation between a and e and the other characterizing the mapping that describes the evolution of a the criterion applies to arbitrary such mappings in the general one shot setting furthermore the criterion is tight for mappings that satisfy certain natural conditions one shot decoupling has a number of applications both in physics and information theory e g as a building block for quantum information processing protocols as an example we give a one shot state merging protocol and show that it is essentially optimal in terms of its entanglement consumption production

operational interpretation of renyi information measures via composite hypothesis testing against product and markov distributions we revisit the problem of asymmetric binary hypothesis testing against a composite alternative hypothesis we introduce a general framework to treat such problems when the alternative hypothesis adheres to certain axioms in this case we find the threshold rate the optimal error and strong converse exponents at large deviations from the threshold and the second order asymptotics at small deviations from the threshold we apply our results to find the operational interpretations of various renyi information measures in case the alternative hypothesis is comprised of bipartite product distributions we find that the optimal error and strong converse exponents are determined by the variations of renyi mutual information in case the alternative hypothesis consists of tripartite distributions satisfying the markov property we find that the optimal exponents are determined by the variations of renyi conditional mutual information in either case the relevant notion of renyi mutual information depends on the precise choice of the alternative hypothesis as such this paper also strengthens the view that different definitions of renyi mutual information conditional entropy and conditional mutual information are adequate depending on the context in which the measures are used

a new approach to the realization of low sensitivity iir digital filters a new implementation of an iir digital filter transfer function is presented that is structurally passive and hence has extremely low pass band sensitivity the structure is based on a simple parallel interconnection of two all pass sections with each section implemented in a structurally lossless manner the structure shares a number of properties in common with wave lattice digital filters computer simulation results verifying the low sensitivity feature are included along with results on roundoff noise dynamic range interaction a large number of alternatives is available for the implementation of the all pass sections giving rise to the well known wave lattice digital filters as a specific instance of the implementation

multiplicity of the second schrodinger eigenvalue on closed surfaces we improve roughly by a factor 2 the known bound on the multiplicity of the second eigenvalue of schrodinger operators i e laplace plus potential on closed surfaces this gives four new topological types of surfaces for which colin de verdiere s conjecture relating the maximal multiplicity to the chromatic number of the surface is verified the proof goes by defining a space cal p of nodal splittings of the surface equipped with a double covering to which a borsuk ulam type theorem is applied

the design of approximate hilbert transform pairs of wavelet bases several authors have demonstrated that significant improvements can be obtained in wavelet based signal processing by utilizing a pair of wavelet transforms where the wavelets form a hilbert transform pair this paper describes design procedures based on spectral factorization for the design of pairs of dyadic wavelet bases where the two wavelets form an approximate hilbert transform pair both orthogonal and biorthogonal fir solutions are presented as well as iir solutions in each case the solution depends on an allpass filter having a flat delay response the design procedure allows for an arbitrary number of vanishing wavelet moments to be specified a matlab program for the procedure is given and examples are also given to illustrate the results