vector sampling expansion the vector sampling expansion vse is an extension of papoulis 1977 generalized sampling expansion gse to the vector case in vse n bandlimited signals all with the same bandwidth b are passed through a multi input multi output mimo linear time invariant system that generates m m spl ges n output signals the goal is to reconstruct the input signals from the samples of the output signals at a total sampling rate of n times the nyquist rate where the nyquist rate is b spl pi samples per second we find necessary and sufficient conditions for this reconstruction a surprising necessary condition for the case where all output signals are uniformly sampled at the same rate n m times the nyquist rate is that the expansion factor m n must be an integer this condition is no longer necessary when each output signal is sampled at a different rate or sampled nonuniformly this work also includes a noise sensitivity analysis of vse systems we define the noise amplification factor which allows a quantitative comparison between vse systems and determine the optimal vse systems

lipschitz factorization through subsets of hilbert space abstract the euclidean distortion of a metric space a measure of how well the metric space can be embedded into a hilbert space is currently an active interdisciplinary research topic we study the corresponding notion for mappings instead of spaces which is that of lipschitz factorization through subsets of hilbert space the main theorems are two characterizations of when a mapping admits such a factorization both of them inspired by results dealing with linear factorizations through hilbert space the first is a nonlinear version of a classical theorem of kwapien in terms of dominated sequences of vectors whereas the second is a duality result by means of a tensor product approach

mimo biorthogonal partners and applications multiple input multiple output mimo biorthogonal partners arise in many different contexts one of them being multiwavelet theory they also play a central role in the theory of mimo channel equalization especially with fractionally spaced equalizers in this paper we first derive some theoretical properties of mimo biorthogonal partners we develop conditions for the existence of mimo biorthogonal partners and conditions under which fir solutions are possible in the process of constructing fir mimo biorthogonal partners we exploit the nonuniqueness of the solution this will lead to the design of flexible fractionally spaced mimo zero forcing equalizers the additional flexibility in design makes these equalizers more robust to channel noise finally other situations where mimo biorthogonal partners occur are also considered such as prefiltering in multiwavelet theory and deriving the vector version of the least squares signal projection problem

adaptive blind source separation and equalization for multiple input multiple output systems in this paper we investigate adaptive blind source separation and equalization for multiple input multiple output mimo systems we first analyze the convergence of the constant modulus algorithm cma used in mimo systems mimo cma our analysis reveals that the mimo cma equalizer is able to recover one of the input signals remove the intersymbol interference isi and suppress the other input signals furthermore for the mimo finite impulse response fir systems satisfying certain conditions the mimo cma fir equalizers are able to perfectly recover one of the system inputs regardless of the initial settings we then propose a novel algorithm for blind source separation and equalization for mimo systems our theoretical analysis proves that the new blind algorithm is able to recover all system inputs simultaneously regardless of the initial settings finally computer simulation examples are presented to confirm our analysis and illustrate the effectiveness of blind source separation and equalization for mimo systems

efficient reconstruction of band limited sequences from nonuniformly decimated versions by use of polyphase filter banks an efficient polyphase structure for the reconstruction of a band limited sequence from a nonuniformly decimated version is developed theoretically the reconstruction involves the implementation of a bank of multilevel filters and it is shown that how all these reconstruction filters can be obtained at the cost of one mth band low pass filter and a constant matrix multiplier the resulting structure is therefore more general than previous schemes in addition the method offers a direct means of controlling the overall reconstruction distortion t z by appropriate design of a low pass prototype filter p z extension of these results to multiband band limited signals and to the case of nonconsecutive nonuniform subsampling are also summarized along with generalizations to the multidimensional case design examples are included to demonstrate the theory and the complexity of the new method is seen to be much lower than earlier ones

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

filter design for mimo sampling and reconstruction we address the problem of finite impulse response fir filter design for uniform multiple input multiple output mimo sampling this scheme encompasses papoulis generalized sampling and several nonuniform sampling schemes as special cases the input signals are modeled as either continuous time or discrete time multiband input signals with different band structures we present conditions on the channel and the sampling rate that allow perfect inversion of the channel additionally we provide a stronger set of conditions under which the reconstruction filters can be chosen to have frequency responses that are continuous we also provide conditions for the existence of fir perfect reconstruction filters and when such do not exist we address the optimal approximation of the ideal filters using fir filters and a minmax l sub 2 end to end distortion criterion the design problem is then reduced to a standard semi infinite linear program an example design of fir reconstruction filters is given

complex manifolds in q convex boundaries we consider a c infty boundary b omega subset mathbb c n which is q convex in the sense that its levi form has positive trace on every complex q plane we prove that b omega is tangent of infinite order to the complexification of each of its submanifolds which is complex tangential and of finite bracket type this generalizes diederich and fornaess ann math 107 371 384 1978 from pseudoconvex to q convex domains we also readily prove that the rows of the levi form are frac 1 2 subelliptic multipliers for the bar partial neumann problem on q forms cf ho in math ann 290 3 18 1991 this allows to run the kohn algorithm of acta math 142 79 122 1979 in the chain of ideals of subelliptic multipliers for q forms if b omega is real analytic and the algorithm gets stuck on q forms then it produces a variety of holomorphic dimension q and in fact by our result above a complex q manifold which is not only tangent but indeed contained in b omega altogether the absence of complex q manifolds in b omega produces a subelliptic estimate on q forms

suppression of adjacent channel cochannel and intersymbol interference by equalizers and linear combiners we describe the ability of a linear equalizer combiner or decision feedback equalizer to suppress all received adjacent channel intersymbol and cochannel interference the emphasis is on values among transmitter bandwidth receiver bandwidth carrier spacing and antenna diversity which provide the best opportunities for interference suppression through analyses of the number of degrees of freedom and constraints in generalized zero forcing equalizers and partial comparisons to calculations of equalizer minimum mean square performance four results are obtained first with one antenna and a linear equalizer arbitrarily large receiver bandwidths allow for marginal improvements in spectral efficiency through decreased carrier spacing because the carrier spacing cannot be reduced to a value below the symbol rate without incurring unsuppressible interference second large receiver bandwidths assist multiple antennas in improving the spectral efficiency in that carrier spacing values may go below the symbol rate even in the presence of cochannel interference third the use of equalizers and linear combiners together with large receiver bandwidths allows large transmitter bandwidths to be used fourth for cochannel interference and intersymbol interference the number of interferers that may be suppressible by a generalized zero forcing linear equalizer combiner increases linearly with the product of the number of antennas and the truncated integer ratio of the total bandwidth to the symbol rate

the coarse baum connes conjecture for spaces which admit a uniform embedding into hilbert space corollary 1 2 let be a finitely generated group if as a metric space with a word length metric admits a uniform embedding into hilbert space and its classifying space b has the homotopy type of a finite cw complex then the strong novikov conjecture holds for i e the index map from k b to k c r is injective corollary 1 2 follows from theorem 1 1 and the descent principle 23 by index theory the strong novikov conjecture implies the novikov conjecture on the homotopy invariance of higher signatures cf 8 for an excellent

new precoding for intersymbol interference cancellation using nonmaximally decimated multirate filterbanks with ideal fir equalizers in this paper we propose a new precoding method for intersymbol interference isi cancellation by using non maximally decimated multirate filterbanks unlike the existing preceding methods such as the th and trellis precodings the new preceding i may be independent of the isi channel ii is linear and does not have to implement any modulo operation iii gives the ideal fir equalization at the receiver for any fir isi channel including spectral null channels iv expands the transmission bandwidth in a minimum amount the precoding is built on non maximally decimated multirate filterbanks based on multirate filterbank theory we present a necessary and sufficient condition on an fir isi transfer function in terms of its zero set such that there is a linear fir n spl times m precoder so that an ideal fir equalizer exists where the integers k and n are arbitrarily fixed the condition is easy to check as a consequence of the condition for any given fir isi transfer function not identically 0 there always exist such linear fir precoders moreover for almost all given fir isi transfer functions there exist linear fir precoders with size n spl times n 1 i e the bandwidth is expanded by 1 n in addition to the conditions on the isi transfer functions a method for the design of the linear fir precoders and the ideal fir equalizers is also given numerical examples are presented to illustrate the theory

sampling expansions for multiband signals the class b i of finite energy signals bandlimited to a set i is considered where i denotes a finite union of disjoint open intervals bands on the real frequency axis if such a signal is sampled uniformly constant intersample spacing t it is shown that the following five propositions are equivalent 1 any signal in b i is uniquely determined from its uniform samples taken at the rate 1 t samples s 2 the set of complex exponentials e in omegat min infin max infin is complete on the set i 3 the translated sets omega k sigma omega epsiloni with 2 t do not intersect i for any k neq 0 4 each signal in b i possesses a mean square convergent sampling expansion in terms of its samples at rate 1 t samples s 5 a generalized parseval relation holds for each pair of signals in b i

sampling theorems for uniform and periodic nonuniform mimo sampling of multiband signals we examine a multiple input multiple output mimo sampling scheme for a linear time invariant continuous time mimo channel the input signals are modeled as multiband signals with different spectral supports and the channel outputs are sampled on either uniform or periodic nonuniform sampling sets with possibly different but commensurate intervals on the different outputs this scheme encompasses papoulis generalized sampling and several nonuniform sampling schemes as special cases we derive necessary and sufficient conditions on the channel and the sampling rate that allow stable perfect reconstruction of the inputs or equivalently perfect inversion of the channel from an implementation viewpoint we note that it is desirable that the reconstruction filters have continuous frequency responses we derive necessary and sufficient conditions that guarantee this continuity property the frequency responses of the reconstruction filters are specified as solutions to a system of linear equations finally we demonstrate that perfect reconstruction may be possible even when the channel outputs are sampled at an average rate that does not allow the reconstruction of any output from its samples alone in certain instances this average rate can achieve the recently presented fundamental bounds on mimo sampling density

multiple input multiple output sampling necessary density conditions we consider the problem of multiple input multiple output mimo sampling of multiband signals in this problem a set of input signals is passed through a mimo channel modeled as a known linear time invariant system the inputs are modeled as multiband signals whose spectral supports are sets of finite measure and the channel outputs are sampled on nonuniform sampling sets the aim is to reconstruct the inputs from the output samples this sampling scheme is quite general and it encompasses various others including papoulis generalized sampling and nonuniform sampling as special cases we introduce notions of joint upper and lower densities for collections of sampling sets and then derive necessary conditions on these densities for stable sampling and consistent reconstruction of the channel inputs from the sampled outputs these results generalize classical density results for stable sampling and interpolation due to landau

on explicit solutions to the bezout equation explicit constructions are given for the solution of the bezout equation for matrices whose coefficients are multivariate polynomials or entire functions of paley wiener type this procedure also provides the 1 inverse when the bezout equation has no solutions

multidimensional filter bank signal reconstruction from multichannel acquisition we study the theory and algorithms of an optimal use of multidimensional signal reconstruction from multichannel acquisition by using a filter bank setup suppose that we have an channel convolution system referred to as analysis filters in dimensions instead of taking all the data and applying multichannel deconvolution we first reduce the collected data set by an integer uniform sampling matrix and then search for a synthesis polyphase matrix which could perfectly reconstruct any input discrete signal first we determine the existence of perfect reconstruction pr systems for a given set of finite impulse response fir analysis filters second we present an efficient algorithm to find a sampling matrix with maximum sampling rate and to find a fir pr synthesis polyphase matrix for a given set of fir analysis filters finally once a particular fir pr synthesis polyphase matrix is found we can characterize all fir pr synthesis matrices and then find an optimal one according to design criteria including robust reconstruction in the presence of noise

duality for lipschitz p summing operators abstract building upon the ideas of r arens and j eells 1956 1 we introduce the concept of spaces of banach space valued molecules whose duals can be naturally identified with spaces of operators between a metric space and a banach space on these spaces we define analogues of the tensor norms of chevet 1969 3 and saphar 1970 14 whose duals are spaces of lipschitz p summing operators in particular we identify the dual of the space of lipschitz p summing operators from a finite metric space to a banach space answering a question of j farmer and w b johnson 2009 6 and use it to give a new characterization of the non linear concept of lipschitz p summing operator between metric spaces in terms of linear operators between certain banach spaces more generally we define analogues of the norms of j t lapreste 1976 11 whose duals are analogues of a pietsch s p r s summing operators a pietsch 1980 12 as a special case we get a lipschitz version of q p dominated operators

compactness of the neumann problem on convex domains the neumann operator on 0 q forms 1 q n on a bounded convex domain in cnis compact if and only if the boundary of contains no complex analytic equivalently affine variety of dimension greater than or equal toq

spatio temporal coding for wireless communication multipath signal propagation has long been viewed as an impairment to reliable communication in wireless channels this paper shows that the presence of multipath greatly improves achievable data rate if the appropriate communication structure is employed a compact model is developed for the multiple input multiple output mimo dispersive spatially selective wireless communication channel the multivariate information capacity is analyzed for high signal to noise ratio snr conditions the mimo channel can exhibit a capacity slope in bits per decibel of power increase that is proportional to the minimum of the number multipath components the number of input antennas or the number of output antennas this desirable result is contrasted with the lower capacity slope of the well studied case with multiple antennas at only one side of the radio link a spatio temporal vector coding stvc communication structure is suggested as a means for achieving mimo channel capacity the complexity of stvc motivates a more practical reduced complexity discrete matrix multitone dmmt space frequency coding approach both of these structures are shown to be asymptotically optimum an adaptive lattice trellis coding technique is suggested as a method for coding across the space and frequency dimensions that exist in the dmmt channel experimental examples that support the theoretical results are presented

on noncompactness of the neumann problem on pseudoconvex domains in c3 abstract we prove that a smooth bounded pseudoconvex domain c 3 with a one dimensional complex manifold m in its boundary has a noncompact neumann operator on 0 1 forms under the additional assumption that b has finite regular d angelo 2 type at a point of m

exact image deconvolution from multiple fir blurs we address the problem of restoring an image from its noisy convolutions with two or more blur functions channels deconvolution from multiple blurs is in general better conditioned than from a single blur and can be performed without regularization for moderate noise levels we characterize the problem of missing data at the image boundaries and show that perfect reconstruction is impossible even in the no noise case almost surely unless there are at least three channels conversely when there are at least three channels we show that perfect reconstruction is not only possible almost surely in the absence of noise but also that it can be accomplished by finite impulse response fir filtering such fir reconstruction is vastly more efficient computationally than the least squares solution and is suitable for low noise levels even in the high noise case the estimates obtained by fir filtering provide useful starting points for iterative least squares algorithms we present results on the minimum possible sizes of such deconvolver filters we derive expressions for the mean square errors in the fir reconstructions and show that performance comparable to that of the least squares reconstruction may be obtained with relatively small deconvolver filters finally we demonstrate the fir reconstruction on synthetic and real data

minimum mean squared error reconstruction for generalized undersampling of cyclostationary processes the generalized sampling problem is considered using a filter bank model with a stochastic process framework a signal reconstruction solution minimizing the time averaged mean squared error is found using a filter bank optimization technique for cyclostationary signals the use of a stochastic model approach to find a minimized error solution rather than a perfect reconstruction solution allows consideration of sampling problems that deterministic approaches cannot solve for instance a particular sampling density is not required allowing reconstruction optimization in cases of undersampling an extension is also presented for optimal reconstruction in the presence of additive noise and interference the result is a generalized sampling model which can be used for an extensive variety of scenarios combining aspects of undersampling multiple input multiple output mimo sampling and periodic nonuniform sampling

perfect reconstruction formulas and bounds on aliasing error in sub nyquist nonuniform sampling of multiband signals we examine the problem of periodic nonuniform sampling of a multiband signal and its reconstruction from the samples this sampling scheme which has been studied previously has an interesting optimality property that uniform sampling lacks one can sample and reconstruct the class spl bscr spl fscr of multiband signals with spectral support spl fscr at rates arbitrarily close to the landau 1969 minimum rate equal to the lebesgue measure of spl fscr even when spl fscr does not tile r under translation using the conditions for exact reconstruction we derive an explicit reconstruction formula we compute bounds on the peak value and the energy of the aliasing error in the event that the input signal is band limited to the span of spl fscr the smallest interval containing spl fscr which is a bigger class than the valid signals spl bscr spl fscr band limited to spl fscr we also examine the performance of the reconstruction system when the input contains additive sample noise

optimal sub nyquist nonuniform sampling and reconstruction for multiband signals we study the problem of optimal sub nyquist sampling for perfect reconstruction of multiband signals the signals are assumed to have a known spectral support spl fscr that does not tile under translation such signals admit perfect reconstruction from periodic nonuniform sampling at rates approaching landau s 1967 lower bound equal to the measure of spl fscr for signals with sparse spl fscr this rate can be much smaller than the nyquist rate unfortunately the reduced sampling rates afforded by this scheme can be accompanied by increased error sensitivity in a previous study we derived bounds on the error due to mismodeling and sample additive noise adopting these bounds as performance measures we consider the problems of optimizing the reconstruction sections of the system choosing the optimal base sampling rate and designing the nonuniform sampling pattern we find that optimizing these parameters can improve system performance significantly furthermore uniform sampling is optimal for signals with spl fscr that tiles under translation for signals with nontiling spl fscr which are not amenable to efficient uniform sampling the results reveal increased error sensitivities with sub nyquist sampling however these can be controlled by optimal design demonstrating the potential for practical multifold reductions in sampling rate

analytic discs attached to conormal bundles of cr manifolds abstract letmbe a cr submanifold ofx c n t m xthe conormal bundle tominx zo resp po a point ofm resp t m x def t m x 0 with po zo aa small analytic disc c1up to the boundary attached tomthroughzo a aliftofatot xthroughpoattachedt m x if the levi form ofmhas a constant number of negative eigenvalues in a neighborhood ofp0then we show that in factais contained inmanda int m x whenmis a hypersurface and it is pseudoconvex i e the number of its negative levi eigenvalues is identically 0 then the inclusiona mis classical and follows from the hopf lemma applied to a plurisubharmonic exhaustion function as in d f note that in this case the existence of a lifta t m xis automatic according to b f 1980 math subject classification 1985 revision 32 f

perfect blind restoration of images blurred by multiple filters theory and efficient algorithms we address the problem of restoring an image from its noisy convolutions with two or more unknown finite impulse response fir filters we develop theoretical results about the existence and uniqueness of solutions and show that under some generically true assumptions both the filters and the image can be determined exactly in the absence of noise and stably estimated in its presence we present efficient algorithms to estimate the blur functions and their sizes these algorithms are of two types subspace based and likelihood based and are extensions of techniques proposed for the solution of the multichannel blind deconvolution problem in one dimension we present memory and computation efficient techniques to handle the very large matrices arising in the two dimensional 2 d case once the blur functions are determined they are used in a multichannel deconvolution step to reconstruct the unknown image the theoretical and practical implications of edge effects and weakly exciting images are examined finally the algorithms are demonstrated on synthetic and real data

linear periodic systems and multirate filter design we present a systematic procedure for the design of filters intended for multirate systems this procedure is motivated by viewing the equiripple design of filters in linear time invariant systems as a process of obtaining optimum minimax filters for a class of bounded energy input signals the philosophy of designing optimum minimax filters for classes of input signals is extended to multirate systems which are not time invariant we develop a generalized fourier analysis appropriate for linear periodic systems and use it to derive new error criteria for multirate filter design using such criteria yields optimum minimax multirate filters for the input signal class the utility of our method is demonstrated by using it to analyze several multirate systems we give numerical results on the design of a multirate implementation of a narrowband filter and compare our work to previous work on multirate filter design our numerical analysis is based upon a new formulation of the design as a semi infinite linear programming problem

blind identification of multichannel fir blurs and perfect image restoration despite its practical importance in image processing and computer vision blind blur identification and blind image restoration have so far been addressed under restrictive assumptions such as all pole stationary image models blurred by zero or minimum phase point spread functions relying upon diversity availability of a sufficient number of multiple blurred images we develop blind fir blur identification and order determination schemes apart from a minimal persistence of the excitation condition also present with nonblind setups the inaccessible input image is allowed to be deterministic or random and of unknown color of distribution with the blurs satisfying a certain co primeness condition in addition we establish existence and uniqueness results which guarantee that single input multiple output fir blurred images can be restored blindly though perfectly in the absence of noise using linear fir filters results of simulations employing the blind order determination blind blur identification and blind image restoration algorithms are presented when the snr is high direct image restoration is found to yield better results than indirect image restoration which employs the estimated blurs in low snr indirect image restoration performs well while the direct restoration results vary with the delay but improve with larger equalizer orders

a property of the functions and distributions annihilated by a locally integrable system of complex vector fields page introduction 387 1 basic notation and ingredients 389 2 approximation and constancy on the fibers of the classical solutions of the homogeneous equations 393 3 first consequences and interpretation of the fundamental theorem 398 4 distribution solutions of the homogeneous equations 402 5 regularity of the solutions of the homogeneous equations 409 6 example of a system that is analytic hypo elliptic but not co hypo elliptic 413 references 420

analytic discs plurisubharmonic hulls and non compactness of the neumann operator we show that a complex manifold m in the boundary of a smooth bounded pseudoconvex domain in open image in new window is an obstruction to compactness of the open image in new window neumann operator on provided that at some point of m the levi form of b has the maximal possible rank n 1 dim m i e the boundary is strictly pseudoconvex in the directions transverse to m in particular an analytic disc is an obstruction provided that at some point of the disc the levi form has only one zero eigenvalue i e the eigenvalue zero has multiplicity one we also show that a boundary point where the levi form has only one zero eigenvalue can be picked up by the plurisubharmonic hull of a set only via an analytic disc in the boundary

minimum rate sampling and reconstruction of signals with arbitrary frequency support we examine the question of reconstruction of signals from periodic nonuniform samples this involves discarding samples from a uniformly sampled signal in some periodic fashion we give a characterization of the signals that can be reconstructed at exactly the minimum rate once a nonuniform sampling pattern has been fixed we give an implicit characterization of the reconstruction system and a design method by which the ideal reconstruction filters may be approximated we demonstrate that for certain spectral supports the minimum rate can be approached or achieved using reconstruction schemes of much lower complexity than those arrived at by using spectral slicing as in earlier work previous work on multiband signals have typically been those for which restrictive assumptions on the sizes and positions of the bands have been made or where the minimum rate was approached asymptotically we show that the class of multiband signals which can be reconstructed exactly is shown to be far larger than previously considered when approaching the minimum rate this freedom allows us in certain cases to have a far less complex reconstruction system