bit error rate of binary and quaternary dpsk signals with multiple differential feedback detection a differentially coherent detection scheme with improved bit error rate ber performance is presented for differentially encoded binary and quaternary phase shift keying psk modulation the improvement is based on using l symbol detectors with delays of 1 2 l symbol periods and on feeding back detected psk symbols exact formulas for the bit error probability are derived for the case that correct symbols are fed back the effect of symbol errors in the feedback path on the ber is determined by computer simulations

enhanced multiple bit differential detection of doqpsk in this paper we consider multiple bit differential detection mbdd of differential offset quadrature phase shift keying doqpsk with conventional bit wise differential encoding de we propose two novel mbdd schemes that outperform simon s mbdd and approach the performance of coherent detection cd as the observation window size n increases the first scheme uses the full available detection window spanning n 1 bit intervals and is referred to as f mbdd a careful bit error rate ber analysis shows that a significant performance improvement can be realized by reducing the detection window size to n 3 bit intervals the resulting improved mbdd i mbdd of doqpsk with bit wise de achieves a similar performance as phoel s mbdd of doqpsk with more complex symbol wise de for both f mbdd and i mbdd tight upper bounds and accurate ber approximations are derived in addition since the complexity per bit decision of brute force decoding of mbdd of doqpsk grows exponentially with n we develop optimum and suboptimum fast decoding algorithms with complexities per bit decision of orders log n 1 and n respectively

high resolution exponential analysis via regularized numerical inversion of laplace transforms the paper describes a new robust method for the exponential analysis problem solving in discrete case the regularizing operators of the inverse laplace transformation are used for transformation of experimental data into a form that is more suitable for determination of decay rates and amplitudes in the case of a continuous distribution a spectral function is obtained by regularized inverse laplace transformation of the transient the proposed method has advantages over known methods and is tolerant to the baseline offset the results of numerical testing show that the proposed method can be used in high resolution analysis for determination of spectral functions decay rates and amplitudes from experimentally measured transients

numerical determination of hitting time distributions from their laplace transforms simple cases abstract an important problem in probabilistic modeling consists of the determination of the distribution function of a positive random variable in particular a hitting time from its laplace transform in this note we use two versions of the method of maximum entropy to invert the laplace transform using a few of its values on the real line or equivalently a few fractional moments of the exponential of the variable to compare the performance of the methods we consider some simple one dimensional examples in which the laplace transform can be computed by solving a differential equation exactly and comparisons can be made

on the recovery and resolution of exponential relaxation rates from experimental data iii the effect of sampling and truncation of data on the laplace transform inversion the method of singular function expansions which in previous papers in this series was used for the inversion of the laplace transform for the cases respectively of continuous data and continuous solution and discrete data and discrete solution is extended to cover the case of discrete data and continuous solution two discrete data points distributions are considered uniform and geometric for both we prove that the singular values and the singular functions in the solution space of the problem with discrete data and continuous solution converge to the singular values and singular functions of the problem with continuous data and continuous solution when the number of points tends to infinity and the distance between adjacents points tends to zero furthermore we show by means of numerical computations that for geometrically sampled data it is possible to obtain even better approximations of the greatest singular values than in the discrete to discrete case using a similar number of data points excellent approximations of the continuous to continuous case singular functions are also obtained implementation of the inversion procedure gives continuous solutions with high computational efficiency

multiple symbol differential detection with diversity reception in this letter we first consider the maximum likelihood sequence estimator for multiple symbol differential detection msdd over the slow fading diversity channel since this optimum decision metric results in a complex receiver implementation whose average bit error probability bep performance is difficult if not impossible to obtain analytically we then focus our attention on evaluating the average bep for msdd with diversity reception in the form of postdetection equal gain combining egc giving emphasis to its ability to bridge the gap between egc of conventional differentially detected m psk and maximal ratio combining of coherently detected m psk with differential encoding

multiple bit differential detection of offset qpsk analogous to multiple symbol differential detection of quadrature phase shift keying qpsk a multiple bit differential detection scheme is described for offset qpsk that also exhibits continuous improvement in performance with increasing observation interval being derived from maximum likelihood considerations together with the representation of differentially encoded offset qpsk as a continuous phase modulation the proposed scheme is purported to be the most power efficient scheme for such a modulation and detection method

on the recovery and resolution of exponential relaxation rates from experimental data a singular value analysis of the laplace transform inversion in the presence of noise the problem of numerical inversion of the laplace transform is considered when the inverse function is of bounded strictly positive support the recent eigenvalue analysis of mcwhirter and pike for infinite support has been generalized by numerical calculations of singular values a priori knowledge of the support is shown to lead to increased resolution in the inversion and the number of exponentials that can be recovered in given levels of noise is calculated

maximum likelihood block detection of noncoherent continuous phase modulation the authors examine maximum likelihood block detection of uncoded full response continuous phase modulation cpm over an additive white gaussian noise awgn channel both the maximum likelihood metrics and the bit error probability performances of the associated detection algorithms are considered the special and popular case of minimum shift keying msk corresponding to h 0 5 and constant amplitude frequency pulse is treated separately the many new receiver structures that result from this investigation can be compared to the traditional ones that have been used in the past both from the standpoint of simplicity of implementation and optimality of performance

on quasi class a contractions abstract let qa denote the class of bounded linear hilbert space operators t which satisfy the operator inequality t t 2 t t t 2 t it is proved that if t qa is a contraction then either t has a nontrivial invariant subspace or t is a proper contraction and the nonnegative operator d t t 2 t 2 t is strongly stable it is shown that if t qa is a contraction with hilbert schmidt defect operator such that t 1 0 t 1 0 then t is completely non normal if and only if t c 10 and a commutativity theorem is proved for contractions t qa let t u and t c denote the unitary part and the cnu part of a contraction t respectively we prove that if a a u a c and b b u b c are qa contractions such that a c then a and b are quasi similar if and only a u and b u are unitarily equivalent and a c and b c are quasi similar

symbol timing recovery for cpm with correlated data symbols we consider symbol timing recovery for continuous phase modulations cpms with correlated data symbols a popular example of such a scheme is shaped offset quadrature phase shift keying soqpsk we propose an extension to an existing non data aided blind timing error detector ted to make it compatible with such modulation schemes the merits of the modified ted are demonstrated by comparing its performance with and without taking the data correlation into account as a further modification we show that a quantization scheme can be used to yield an extremely low complexity version of the system with only negligible performance losses the s curve of the proposed quantized ted is given which rules out the existence of false lock points the proposed scheme shows great promise in a wide range of applications due to its low complexity its lack of false lock points and its blind nature such applications include timing recovery for noncoherent detection schemes and false lock detectors

selection of observations in signal reconstruction in some signal reconstruction problems the observation equations can be used as a priori information for selecting the best combination of observations before acquiring them in the present correspondence the authors define a selection criterion and propose efficient methods for optimizing the criterion with respect to the combination of observations the examples illustrate the value of optimized sampling using the proposed methods

sparse bayesian learning for the laplace transform inversion in dynamic light scattering a new method is described using the sparse bayesian learning sbl algorithm of tipping to obtain an optimal and reliable solution to the laplace transform inversion in dynamic light scattering dls the linear inverse problem in dls has numerical solutions that depend on their domains and dimensions for a given domain and dimension a sparse solution in an sbl framework is the most probable solution and can be used for classifying a system of objects by a few relevant values recently we have shown that the sbl algorithm of tipping is suitable for studying cataract in ocular lenses by describing the opacity of a lens with a few dominant sizes of crystallin proteins in the lens however since the sparseness of sbl solutions cannot reflect a true system we need to develop a method by using the sbl algorithm to give a true description and at the same time a useful classification of the opacity of lenses we generate a set of sparse solutions of different domains but of the same dimension and then superimpose them to give a general solution with its dimension treated as a regularization parameter an optimal solution which provides a reliable description of a particle system is determined by the l curve criterion for selecting the suitable value of the regularization parameter the performance of our method is evaluated by analyzing simulated data generated from unimodal and bimodal distributions from the reconstructed distributions we see that our method gives high resolution comparable to the sophisticated bryan s maximum entropy algorithm which gives better resolution than contin our method is then applied to experimental dls data of the ocular lenses of a fetal calf and a rhesus monkey to obtain optimal particle size distributions of crystallins and the crystallin aggregates in the lenses we conclude by discussing possible improvements on our method for analyzing dls data and for solving any linear inverse problem by an sbl algorithm

approximation with the output of linear control systems abstract in this paper we give a new proof that for controllable and observable linear systems every l 2 0 t function can be approximated in the l 2 0 t sense with an output function generated by an l 2 0 t input function we also give a new characterization of how continuous functions on 0 t are uniformly approximated by an output generated by a continuous input function the relative degree of the transfer function of the system determines those functions that can be approximated we further show that if the initial data is allowed to vary then every continuous function is uniformly approximated by outputs generated by continuous functions

multiple bit differential detection of shaped offset qpsk we consider multiple bit differential detection mbdd of differentially encoded shaped offset quadrature phase shift keying soqpsk a highly bandwidth efficient and popular constant envelope modulation we propose two mbdd schemes that are based on a recent continuous phase modulation interpretation of soqpsk we show that the performance of these mbdd schemes approaches that of coherent detection cd as the multiple bit observation n window increases the first scheme uses a detection window that spans the full bit observation window f mbdd and is shown to require very large values of n to approach the performance of cd this presents a practical problem since the complexity of mbdd grows exponentially with n the second scheme is an improved version i mbdd with a detection window that is shortened to n 2 bit intervals although the complexity of i mbdd also increases exponentially with n it represents a significant improvement since only modest values of n are needed for high performance these performance characteristics are identified via a detailed performance analysis which provides asymptotic formulas for the bit error probability that are confirmed with computer simulations the analysis is also used to find the symmetric frequency pulse shapes with the best and worst error performance finally we develop a simplified and practical decision feedback differential detection algorithm that achieves near optimal performance with complexity that grows only linearly with n

an inverse problem of a linear dynamic system with noise in this paper we consider an inverse problem for a linear time invariant dynamic system with noise it is shown that after adjusting the system by shifting the eigenvalues of the system matrix the disturbance of the system noise can be reduced and the input signal of certain types of the system can be recovered from the discrete observations of the system output

laplace deconvolution on the basis of time domain data and its application to dynamic contrast enhanced imaging in the present paper we consider the problem of laplace deconvolution with noisy discrete non equally spaced observations on a finite time interval which appears in many different contexts we propose a new method for laplace deconvolution which is based on expansions of the convolution kernel the unknown function and the observed signal over laguerre functions basis which acts as a surrogate eigenfunction basis using regression setting the expansion results in a small system of linear equations with the matrix of the system being triangular and toeplitz the number m of the terms in the expansion of the estimator is controlled via complexity penalty the advantage of this methodology is that it leads to very fast computations produces no boundary effects due to extension at zero and cut off at t and provides an estimator with the risk within a logarithmic factor of m of the oracle risk under no assumptions on the model and within a constant factor of the oracle risk under mild assumptions we emphasize that in the present paper we consider the true observational model with possibly non equispaced observations which are available on a finite interval of length t and account for the bias associated with this model the study is motivated by perfusion imaging using a short injection of contrast agent a procedure which is widely applied for medical assessment of blood flows within tissues such as cancerous tumors presence of a tuning parameter a allows to choose the most advantageous time units so that both the kernel and the unknown right hand side of the equation are well represented for the further deconvolution in addition absence of boundary effects allows for an accurate estimator of the tissue blood flow parameter which is of great interest to medical doctors the methodology is illustrated by an extensive simulation study and a real data example which confirms that the proposed technique is fast efficient accurate usable from a practical point of view and competitive

multiple symbol differential detection of mpsk a differential detection technique for mpsk multiple phase shift keying which uses a multiple symbol observation interval is presented and its performance is analyzed and simulated the technique makes use of maximum likelihood sequence estimation of the transmitted phases rather than symbol by symbol detection as in the conventional differential detection thus the performance of this multiple symbol detection scheme fills the gap between conventional two symbol observation differentially coherent detection of mpsk and ideal coherent of mpsk with differential encoding the amount of improvement gained over conventional differential detection depends on the number of phases m and the number of additional symbol intervals added to the observation what is particularly interesting is that substantial performance improvement can be obtained for only one or two additional symbol intervals of observation the analysis and simulation results presented are for uncoded mpsk

decision feedback detectors for soqpsk we consider highly simplified decision feedback detectors for shaped offset quadrature phase shift keying soqpsk a highly bandwidth efficient and popular constant envelope modulation in particular we show that the state complexity can be reduced to a minimal level two states with asymptotically optimum performance as demonstrated by performance analysis and confirmed by computer simulations the complexity reduction is achieved by a novel manipulation of the differential encoder and the soqpsk precoder which are both part of the transmission model for soqpsk we give two possible architectures for achieving this complexity reduction the pulse amplitude modulation pam technique and the pulse truncation pt technique we also formulate these detectors for coherent and noncoherent detection the resulting family of detectors makes use of recent advances in soqpsk technology based on a continuous phase modulation cpm interpretation of soqpsk the proposed simplifications are significant because they minimize the complexity of trellis based soqpsk detectors which have become available only in recent years because trellis based soqpsk detectors are 1 2 db superior to the widely deployed family of symbol by symbol soqpsk detectors the proposed two state detectors offer the simplest means of achieving these performance gains thus these simple detection schemes are applicable in settings where high performance and low complexity are needed to meet restrictions on power consumption and cost

input recovery from noisy output data using regularized inversion of the laplace transform in a dynamical system the input is to be recovered from finitely many measurements blurred by random error of the output of the system as usual the differential equation describing the system is reduced to multiplication with a polynomial after applying the laplace transform it appears that there exists a natural unbiased estimator for the laplace transform of the output from which an estimator of the input can be obtained by multiplication with the polynomial and subsequent application of a regularized inverse of the laplace transform it is possible moreover to balance the effect of this inverse so that ill posedness remains restricted to its actual source differentiation the rate of convergence of the integrated mean square error is a positive power of the number of data the order of the differential equation has an adverse effect on the rate which on the other hand increases with the smoothness of the input as usual

a review of the parameter estimation problem of fitting positive exponential sums to empirical data exponential sum models are used frequently in heat diffusion diffusion of chemical compounds time series in medicine economics physical sciences and technology thus it is important to find good methods for the estimation of parameters in exponential sums in this paper we review and discuss results from the last forty years of research there are many different ways of estimating parameters in exponential sums and model a fit criterion which gives a valid result from the fit we find that a good choice is a weighted two norm objective function with weights based on the maximum likelihood ml criterion if the number of exponential terms is unknown statistical methods based on an information criterion or cross validation can be used to determine the optimal number it is suitable to use hybrid gauss newton gn and quasi newton algorithms to find the unknown parameters in the constrained weighted nonlinear least squares nlls problem formulated using an maximal likelihood ml objective function the problem is highly ill conditioned and it is crucial to find good starting values for the parameters to find the initial parameter values a modified prony method or a method based upon rewriting partial sums as geometrical sums is proposed

the jordan form of a bitriangular operator abstract a jordan operator is a infinite direct sum of a norm bounded sequence of finite dimensional jordan blocks an operator t is quasisimilar to a jordan operator if and only if both t and t are triangularizable whence bitriangular the canonical jordan model of such an operator is determined just by the numerical data dim ker t i n 1 ker t i n an analysis of hyperinvariant subspaces similarity orbits and other aspects of these operators are analyzed using this model

pulse shaping for differential offset qpsk pulse shaping is examined as a means to improve the performance of a differential offset quadrature phase shift keying system in a bandwidth constrained environment through optimization with respect to a composite nyquist criterion the derived pulse shapes have comparable performance to a pi 4 differential quadrature phase shift keying in an additive white gaussian noise awgn channel and better performance in a hard limited awgn channel

exponential interpolation theory and numerical algorithms we consider the problem of exponential interpolation and show that in some cases it can be solved with effective numerical procedures we show that the problem is closely related to gaussian quadrature and to the problem of partial realization in linear control theory

linear regularizing algorithms for positive solutions of linear inverse problems linear regularization methods provide a simple technique for determining stable approximate solutions of linear ill posed problems such as fredholm equations of the first kind cauchy problems for elliptic equations and backward solution of forward parabolic equations in most of these problems the solution must be positive to satisfy physical plausibility in this paper we consider ill posed first kind convolution equations and related problems such as numerical differentiation radon transform and laplace transform inversion we investigate several linear regularization algorithms which provide positive approximate solutions for these problems at least in the absence of errors on the data for noisy data the solution is not necessarily positive because the appearance of negative values can then only be an effect of the noise the negative part of the solution should be negligible with a suitable choice of the regularization parameter a price to pay for ensuring positivity is always however a reduction in resolution

hyponormal operators quasisimilar to an isometry an expression for the multiplicity of an arbitrary contraction is pre sented it is in terms of the isometries which can be densely intertwined to the given contraction this is then used to obtain a generalization of a result of sz nagy and foias concerning the existence of a c 0 contraction which is a quasiaffine transform of a contraction we then consider the problem when a hyponormal operator is quasisimilar to an isometry or more generally when two hyponormal contractions are quasisimilar to each other our main results in this respect generalize previous ones obtained by hastings and the author for quasinormal and certain subnormal operators quasisimilarity or similarity to an isometry may even imply unitary equivalence 1 introduction let f and f2 be bounded linear operators on the complex separable hilbert spaces 77 and h2 respectively we say that f is densely d intertwined to t2 tx 0 resp t x 0 for all x t is of class c resp cx if t x 0 resp t x 0 for all x 0 caj3 ca n c p for a b 0 1 a contraction f can be decomposed as us ffi ua ffi t where us and ua axe singular and absolutely continuous unitary operators and t is completely nonunitary c n u us ua and t are called the unitary part and c ai w part of f respectively following alexander 1 we say that the contraction f is of analytic type if it has no singular unitary direct summand for such a

on the analytical and numerical properties of the truncated laplace transform i the laplace transform is frequently encountered in mathematics physics engineering and other fields however the spectral properties of the laplace transform tend to complicate its numerical treatment therefore the closely related truncated laplace transforms are often used in applications we have constructed efficient algorithms for the evaluation of the singular value decomposition of truncated laplace transforms in the current paper we introduce algorithms for the evaluation of the right singular functions and singular values of truncated laplace transforms algorithms for the computation of the left singular functions will be introduced separately in an upcoming paper the resulting algorithms are applicable to all environments likely to be encountered in applications including the evaluation of singular functions corresponding to extremely small singular values e g 10 1000

on the estimation of quadratic functionals we discuss the difficulties of estimating quadratic functionals based on observations y t from the white noise model y t int t 0 f u du sigma w t quad t in lbrack 0 1 rbrack where w t is a standard wiener process on lbrack 0 1 rbrack the optimal rates of convergence as sigma rightarrow 0 for estimating quadratic functionals under certain geometric constraints are found specifically the optimal rates of estimating int 1 0 lbrack f k x rbrack 2 dx under hyperrectangular constraints sum f x j f leq cj alpha and weighted l p body constraints sum p f sum infty 1 j r x j f p leq c are computed explicitly where x j f is the j th fourier bessel coefficient of the unknown function f we develop lower bounds based on testing two highly composite hypercubes and address their advantages the attainable lower bounds are found by applying the hardest one dimensional approach as well as the hypercube method we demonstrate that for estimating regular quadratic functionals i e the functionals which can be estimated at rate o sigma 2 the difficulties of the estimation are captured by the hardest one dimensional subproblems and for estimating nonregular quadratic functionals i e no o sigma 2 consistent estimator exists the difficulties are captured at certain finite dimensional the dimension goes to infinity as sigma rightarrow 0 hypercube subproblems

on the recovery and resolution of exponential relaxation rates from experimental data ii the optimum choice of experimental sampling points for laplace transform inversion in a previous paper bertero boccacci pike proc r soc lond a 383 15 1982 we investigated the benefits of a priori knowledge of finite support of the solution in the inversion of the laplace transform and determined the number of exponential components that could be recovered from given data in the presence of quantified amounts of noise the support of the data was assumed to be unrestricted in the present paper these calculations are extended to cover the case of a necessarily finite number of experimental data points we consider two cases uniform distribution and geometric distribution of data points in both cases the condition number of singular value inversions is minimized with respect to the placing of the data points for fixed numbers of data samples the results allow optimum placing of the experimental data points as a function of the ratio of given upper and lower bounds of the support of the solution the number of exponentials recoverable is less than in the unrestricted case but for 8 we find that with 32 linearly spaced data points optimally placed this reduction is rather small geometrical sampling of experimental data reduces further the number of sample points required for inversion for 8 we show that with 5 geometrically spaced data points points optimally placed the ill conditioning in the restoration of 2 to 4 exponential components is smaller than with 32 linearly spaced data samples this has important implications for the design of a number of scientific experiments and instruments