blind deconvolution of symmetric noncausal impulse responses using two sided linear prediction considers the problem of estimating the time symmetric noncausal impulse response of a linear time invariant system from measurements of the response of the system to an unknown input signal which is assumed to be a realization of a white random process the symmetric impulse response is modeled by a two sided ar or arma system model the two sided ar coefficients are estimated using a two step procedure first an estimate of an unconstrained parameter vector is computed by solving a close to toeplitz plus hankel system of equations using previously developed fast algorithms then the polynomial square root of the result is obtained by solving a constrained least squares problem which has a simple solution unlike previous methods this approach requires no iterative procedure however it may lead to an unstable model in some extreme cases simulation results illustrate the performance of the proposed methods

efficient solution of a toeplitz plus hankel coefficient matrix system of equations there are well known fast algorithms such as the levinson recursion for solving linear equations with a toeplitz or hankel coefficient matrix this paper extends the saving obtained by the levinson recursion for inversion of a toeplitz matrix to problems involving the inversion of matrices which are the sum of toeplitz and hankel matrices

relaxation of quasiconvex functional in bv ω ℝp for integrands f x u u in this paper it is shown that if p x u is a quasiconvex function with linear growth then the relaxed functional in bv p of u to int limits omega f x u x nabla u x dx with respect to the l1 topology has an integral representation of the form begin gathered mathfrak f u int limits omega f x u x nabla u x dx int limits sigma u k x u x u x v x dh n 1 x hfill int limits omega f infty x u x dc u hfill end gathered where du u dx u u v dhn 1l u c u the proof relies on a blow up argument introduced by fonseca muller in the case where u w1 1 and on a recent result by alberti showing that the cantor part c u is rank one valued

hecke clifford algebras and spin hecke algebras iii the trigonometric type abstract the notions of trigonometric spin double affine hecke algebras tsdaha and trigonometric double affine hecke clifford algebras tdahca associated to classical weyl groups are introduced the pbw basis property is established an algebra isomorphism relating tdahca to tsdaha is obtained

lower semicontinuity of surface energies using the theory of indicator measures a lower semicontinuity result for quasiconvex functions in w 1 1 and assuming only l 1 convergence is obtained

fast algorithms for close to toeplitz plus hankel systems and two sided linear prediction the low displacement rank definition of close to toeplitz ct matrices is extended to close to toeplitz plus hankel ctph matrices fast algorithms for solving ctph systems of equations are presented a matrix is defined as ctph if the sum of a ct matrix and a second ct matrix postmultiplied by an exchange matrix an equivalent definition in terms of uv rank is also given this definition is motivated by the application of the algorithms to two sided linear prediction tsp autocorrelation and covariance forms of tsp analogous to those for one sided linear prediction osp are defined the covariance form of tsp is solved using the ctph fast algorithms just as the covariance form of osp is solved using ct fast algorithms numerical examples show that tsp produces smaller residuals than osp and resolves sharp spectral peaks better than osp and that covariance tsp produces smaller residuals than autocorrelation tsp

two sided filters for frame based prediction a linear prediction model based on a two sided predictor which predicts on the basis of past and future samples within a frame is presented the linear prediction model may be applied wherever frame based prediction is used a stable synthesis procedure is derived by casting the prediction equation as a cyclic convolution in the time domain when the filter order is the maximum possible the synthesis filter is shown to have a frequency response proportional to the squared magnitude of the dft of the frame a symmetric two sided predictor which has only half the number of coefficients to be coded as compared to a one sided predictor of the same order is described two sided prediction showed at least 5 db improvement in prediction gain over one sided prediction in simulations on speech data

lectures on affine hecke algebras and macdonald s conjectures this paper gives a review of cherednik s results on the representation theoretic approach to macdonald polynomials and related special functions macdonald polynomials are a remarkable 2 parameter family of polynomials which can be associated to every root system as special cases they include the schur functions the q jacobi polynomials and certain spherical functions on real and p adic symmetric spaces they have a number of elegant combinatorial properties which however are extremely difficult to prove in this paper we show that a natural setup for studying these polynomials is provided by the representation theory of hecke algebras and show how this can be used to prove some of the combinatorial identities for macdonald polynomials

twisted affine lie superalgebra of type q and quantization of its enveloping superalgebra we introduce a new quantum group which is a quantization of the enveloping superalgebra of a twisted affine lie superalgebra of type q we study generators and relations for superalgebras in the finite and twisted affine cases and also universal central extensions afterwards we apply the frt formalism to a certain solution of the quantum yang baxter equation to define that new quantum group and we study some of its properties we construct a functor of schur weyl type which connects it to affine hecke clifford algebras and prove that it provides an equivalence between two categories of modules

new analogs of split algorithms for arbitrary toeplitz plus hankel matrices fast algorithms for solving arbitrary toeplitz plus hankel systems of equations are presented the algorithms are analogs of the split levinson and schur algorithms although the more general toeplitz plus hankel structure requires that the algorithms be based on a four term recurrence relations with the previous split algorithms are considered the algorithms require roughly half as many multiplications as previous fast algorithms for toeplitz plus hankel systems

modeling and identification of symmetric noncausal impulse responces spectrally equivalent causal sec models for single input single output noncausal systems are derived with the objective of estimating the noncausal impulse response attention is restricted to symmetric noncausal impulse responses and the measurements of the system output are assumed to be noisy it is shown that by using structured sec models either state space or arma plus noise consistent estimates of the noncausal impulse response can be obtained by exploiting only the second order statistics of the measurements a new version of the correlation technique particularly suited to structured models is presented and analyzed computer simulation results are also presented to illustrate the performance of the proposed approach

elliptic quantum many body problem and double affine knizhnik zamolodchikov equation the elliptic matrix quantum olshanetsky perelomov problem is introduced for arbitrary root systems by means of an elliptic version of the dunkl operators its equivalence with the double affine generalization of the knizhnik zamolodchikov equation in the induced representations is established

subspace based parameter estimation of symmetric noncausal autoregressive signals from noisy measurements symmetric noncausal auto regressive signals snars arise in several mostly spatial signal processing applications we introduce a subspace fitting approach for parameter estimation of snars from noise corrupted measurements we show that the subspaces associated with a hankel matrix built from the data covariances contain enough information to determine the signal parameters in a consistent manner based on this result we propose a multiple signal classification music like methodology for parameter estimation of snars compared with the methods previously proposed for snars parameter estimation our snars music approach is expected to possess a better tradeoff between computational and statistical performances

on the relaxation in bv ω rm of quasi convex integrals abstract given a quasi convex function f with linear growth we find the integral representation in bv r m of the functional f arising from the relaxation of f u f u dx u c 1 r m in the l loc 1 r m topology

fast algorithms for linear prediction and system identification filters with linear phase a general finite impulse response fir filter can be used as a linear prediction filter if given only an input sample sequence or as a system identification model if given the input and output sequences from an unknown system with known correlation the coefficients of the fir filter that minimize the mean square error in both applications are found by solution of a set of normal equations with toeplitz structure using only data samples the coefficients that yield the least squared error in both applications are found by solution of a set of normal equations with near to toeplitz structure computationally efficient fast algorithms have been published to solve for the coefficients from both types of normal equation structures if the fir filter is constrained to have a linear phase then the impulse response must be symmetric this then leads to normal equations with toeplitz plus hankel or near to toeplitz plus hankel structure fast algorithms for solving these normal equations for the filter coefficients are developed in this paper they have computational complexity proportional to m2and parameter storage proportional to m where m is the filter order an application of one of these algorithms for spectral estimation concludes the paper

semicontinuity problems in the calculus of variations soit f r 3 r une fonction deux fois continument differentiable et pour u w 1 1 a b f u a b a b f x u x u x dx si f r n r m r nm r satisfait 1 f est mesurable en x continue en cs et 2 0 f x s a x c s p p ou p 1 a est une fonction localement sommable non negative et c une constante non negative alors la fonctionnelle f u a b est sequentiellement faiblement semi continue inferieurement sur w 1 p r m si et seulement si f x s est quasi convexe pour chaque s et presque chaque x

rank one convexity does not imply quasiconvexity we consider variational integrals defined for sufficiently regular functions u r m here is a bounded open subset of r n du x denotes the gradient matrix of u at x and f is a continuous function on the space of all real m n matrices m m n one of the important problems in the calculus of variations is to characterise the functions f for which the integral i is lower semicontinuous in this connection the following notions were introduced see 3 9 10