generalizing the hough transform to detect arbitrary shapes abstract the hough transform is a method for detecting curves by exploiting the duality between points on a curve and parameters of that curve the initial work showed how to detect both analytic curves 1 2 and non analytic curves 3 but these methods were restricted to binary edge images this work was generalized to the detection of some analytic curves in grey level images specifically lines 4 circles 5 and parabolas 6 the line detection case is the best known of these and has been ingeniously exploited in several applications 7 8 9 we show how the boundaries of an arbitrary non analytic shape can be used to construct a mapping between image space and hough transform space such a mapping can be exploited to detect instances of that particular shape in an image furthermore variations in the shape such as rotations scale changes or figure ground reversals correspond to straightforward transformations of this mapping however the most remarkable property is that such mappings can be composed to build mappings for complex shapes from the mappings of simpler component shapes this makes the generalized hough transform a kind of universal transform which can be used to find arbitrarily complex shapes

comments on the cramer rao lower bounds for signals with constant amplitude and polynomial phase for original paper see ieee trans signal processing vol 39 p 749 52 march 1991 different expressions for the cramer rao lower bounds crlbs of constant amplitude polynomial phase signals embedded in white gaussian noise appear in the literature the present paper revisits the derivation of the bounds reported by peleg and porat 1991 and indicates that the resulting expressions depend on the interval over which the signal is defined the proper choice of the interval is the one that centers the signal around zero and results in the minimum lower bounds

parameter estimation for locally linear fm signals using a time frequency hough transform an estimator for the phase parameters of mono and multicomponent fm signals with both good numerical properties and statistical performance is proposed the proposed approach is based on the hough transform of the pseudo wigner ville time frequency distribution pwvd it is shown that the numerical properties of the estimator can be improved by varying the pwvd window length the effect of the window time extent on the statistical performance of the estimator is delineated experimental data is used for validation of the statistical properties

a 3 slope theorem for the infinite relaxation in the plane in this paper we consider the infinite relaxation of the corner polyhedron with 2 rows for the 1 row case gomory and johnson proved in their seminal paper a sufficient condition for a minimal function to be extreme the celebrated 2 slope theorem despite increased interest in understanding the multiple row setting no generalization of this theorem was known for this case we present an extension of the 2 slope theorem for the case of 2 rows by showing that minimal 3 slope functions satisfying an additional regularity condition are facets and hence extreme moreover we show that this regularity condition is necessary unveiling a structure which is only present in the multi row setting

parameterized centroid frequency chirp rate distribution for lfm signal analysis and mechanisms of constant delay introduction this paper presents an extension of the integrated time chirp rate analysis technique known as the parameterized centroid frequency chirp rate distribution pcfcrd for noisy multicomponent linear frequency modulated signals analysis the pcfcrd is based on a newly defined correlation function and its auto term accumulation is two dimensionally coherent the principle cross term characteristic implementation properties parameter selection criterion antinoise performance and estimation accuracy are analyzed for the pcfcrd in this paper comparisons with the coherently integrated cubic phase function maximum likelihood method and lv s distribution are performed with mathematic analyses and numerical simulations we demonstrate that the pcfcrd outperforms these three representative counterparts further by combining with analyses of the pcfcrd several unclear mechanisms of the constant delay introduction are mathematically interpreted especially quantitative influences on the chirp rate resolution and theoretical antinoise performance

facets of two dimensional infinite group problems in this paper we lay the foundation for the study of the two dimensional mixed integer infinite group problem 2dmiigp we introduce tools to determine if a given continuous and piecewise linear function over the two dimensional infinite group is subadditive and to determine whether it defines a facet of 2dmiigp we then present two different constructions that yield the first known families of facet defining inequalities for 2dmiigp the first construction uses valid inequalities of the one dimensional integer infinite group problem 1diigp as building blocks for creating inequalities for the two dimensional integer infinite group problem 2diigp we prove that this construction yields all continuous piecewise linear facets of the two dimensional group problem that have exactly two gradients the second construction we present has three gradients and yields facet defining inequalities of 2dmiigp whose continuous coefficients are not dominated by those of facets of the one dimensional mixed integer infinite group problem 1dmiigp

estimation and classification of polynomial phase signals the measurement of the parameters of complex signals with constant amplitude and polynomial phase measured in additive noise is considered a novel new integral transform that is adapted for signals of this type is introduced this transform is used to derive estimation and classification algorithms that are simple to implement and that exhibit good performance the algorithms are extended to constant amplitude and continuous nonpolynomial phase signals

equivariant perturbation in gomory and johnson s infinite group problem iii foundations for the k dimensional case with applications to k 2 k 2 we develop foundational tools for classifying the extreme valid functions for the k dimensional infinite group problem in particular we present the general regular solution to cauchy s additive functional equation on restricted lower dimensional convex domains this provides a k dimensional generalization of the so called interval lemma allowing us to deduce affine properties of the function from certain additivity relations next we study the discrete geometry of additivity domains of piecewise linear functions providing a framework for finite tests of minimality and extremality we then give a theory of non extremality certificates in the form of perturbation functions we apply these tools in the context of minimal valid functions for the two dimensional infinite group problem that are piecewise linear on a standard triangulation of the plane under a regularity condition called diagonal constrainedness we show that the extremality of a minimal valid function is equivalent to the extremality of its restriction to a certain finite two dimensional group problem this gives an algorithm for testing the extremality of a given minimal valid function

adaptive time varying cancellation of wideband interferences in spread spectrum communications based on time frequency distributions the paper proposes an adaptive method for suppressing wideband interferences in spread spectrum ss communications the proposed method is based on the time frequency representation of the received signal from which the parameters of an adaptive time varying interference excision filter are estimated the approach is based on the generalized wigner hough transform as an effective way to estimate the instantaneous frequency of parametric signals embedded in noise the performance of the proposed approach is evaluated in the presence of linear and sinusoidal fm interferences plus white gaussian noise in terms of the snr improvement factor and bit error rate ber

kernel design for time frequency signal analysis using the radon transform the authors present a kernel design technique based on using the radon transform of the modulus of the ambiguity function of the signal for determination of angles and distances of radially distributed contents of the autoterms in the ambiguity domain the proposed kernel effectively reduces the cross terms and noise for linear fm signals the result is a tool for high resolution time frequency representation of nonstationary primarily linear fm signals

an improved design of high resolution quadratic time frequency distributions for the analysis of nonstationary multicomponent signals using directional compact kernels this paper presents a new advanced methodology for designing high resolution time frequency distributions tfds of multicomponent nonstationary signals that can be approximated using piece wise linear frequency modulated pw lfm signals most previous kernel design methods assumed that signals auto terms are mostly centered around the origin of the nu tau ambiguity domain while signal cross terms are mostly away from the origin this study uses a multicomponent test signal for which each component is modeled as a pw lfm signal it finds that the above assumption is a very rough approximation of the location of the auto terms energy and cross terms energy in the ambiguity domain and it is only valid for signals that are well separated in the t f domain a refined investigation led to improved specifications for separating cross terms from auto terms in the nu tau ambiguity domain the resulting approach first represents the signal in the ambiguity domain and then applies a multidirectional signal dependent compact kernel that accounts for the direction of the auto terms energy the resulting multidirectional distribution mdd approach proves to be more effective than classical methods like extended modified b distribution s method or compact kernel distribution in terms of auto terms resolution and cross terms suppression results on simulated and real data validate the improved performance of the mdd showing up to 8 gain as compared to more standard state of the art tfds

statistical analysis of the product high order ambiguity function the high order ambiguity function haf was introduced for the estimation of polynomial phase signals pps embedded in noise since the haf is a nonlinear operator it suffers from noise masking effects and from the appearance of undesired cross terms and possibly spurious harmonics in the presence of multicomponent mc signals the product haf phaf was then proposed as a way to improve the performance of the haf in the presence of noise and to solve the ambiguity problem in this correspondence we derive a statistical analysis of the phaf in the presence of additive white gaussian noise awgn valid for high signal to noise ratio snr and a finite number of data samples the analysis is carried out in detail for single component pps but the multicomponent case is also discussed error propagation phenomena implicit in the recursive structure of the phaf based estimator are explicitly taken into account the analysis is validated by simulation results for both single and multicomponent ppss

statistical am fm models extended kalman filter demodulation cramer rao bounds and speech analysis a stochastic dynamical system model for describing time signals that are jointly amplitude am and frequency fm modulated is presented the signal is assumed to be bandpass perhaps originating from a filter bank applied to a broadband signal and includes the constraint that the magnitude of the complex baseband signal is positive motivated by speech processing and the desire for narrowband modulating signals time is divided into frames and the modulating signals are smoothly interpolated across each frame the model allows a detailed characterization of the bandwidth of the modulating signals and the statistical character of the measurement noise an adaptive estimation algorithm based on extended kalman filtering ideas for extracting the modulating signals from the measured signal is described and demonstrated on both voiced and unvoiced speech signals the cramer rao bound on the performance of any estimator is computed

fast computation of the ambiguity function and the wigner distribution on arbitrary line segments by using the fractional fourier transformation of the time domain signals closed form expressions for the projections of their auto or cross ambiguity functions are derived based on a similar formulation for the projections of the auto and cross wigner distributions and the well known two dimensional 2 d fourier transformation relationship between the ambiguity and wigner domains closed form expressions are obtained for the slices of both the wigner distribution and the ambiguity function by using discretization of the obtained analytical expressions efficient algorithms are proposed to compute uniformly spaced samples of the wigner distribution and the ambiguity function located on arbitrary line segments with repeated use of the proposed algorithms samples in the wigner or ambiguity domains can be computed on non cartesian sampling grids such as polar grids

minimal cut generating functions are nearly extreme we study continuous strongly minimal cut generating functions for the model where all variables are integer we consider both the original gomory johnson setting as well as a recent extension by yildiz and cornuejols math oper res 41 1381 1403 2016 we show that for any continuous minimal or strongly minimal cut generating function there exists an extreme cut generating function that approximates the strongly minimal function as closely as desired in other words the extreme functions are dense in the set of continuous strongly minimal functions

virtues and vices of quartic time frequency distributions we present results concerning three different types of quartic fourth order time frequency distributions tfds first we present new results on the previously introduced local ambiguity function and show that it provides more reliable estimates of instantaneous chirp rate than the wigner distribution second we introduce the class of quartic shift covariant time frequency distributions and investigate distributions that localize quadratic chirps finally we present a shift covariant distribution of time and chirp rate

t space and cutting planes in this paper we show how knowledge about t space translates directly into cutting planes for general integer programming problems after providing background on corner polyhedra and on t space this paper examines t space in some detail it gives a variety of constructions for t space facets all of which translate into cutting planes and introduces continuous families of facets in view of the great variety of possible facets no one of which can be dominated either by any other or by any combination of the others a measure of merit is introduced to provide guidance on their usefulness t spaces based on higher dimensional groups are discussed briefly as is the idea of going beyond cutting planes to iterated approximations of corner polyhedra

the cramer rao lower bound for signals with constant amplitude and polynomial phase the authors derive the cramer rao lower bound crlb for complex signals with constant amplitude and polynomial phase measured in additive gaussian white noise the exact bound requires numerical inversion of an ill conditioned matrix while its o n sup 1 approximation is free of matrix inversion the approximation is tested for several typical parameter values and is found to be excellent in most cases the formulas derived are of practical value in several radar applications such as electronic intelligence systems elint for special pulse compression radars and motion estimation from doppler measurements consequently it is of interest to analyze the best possible performance of potential estimators of the phase coefficients as a function of signal parameters the signal to noise ratio the sampling rate and the number of measurements this analysis is carried out

relations between facets of low and high dimensional group problems one dimensional infinite group problems have been extensively studied and have yielded strong cutting planes for mixed integer programs although numerical and theoretical studies suggest that group cuts can be significantly improved by considering higher dimensional groups there are no known facets for infinite group problems whose dimension is larger than two in this paper we introduce an operation that we call sequential merge we prove that the sequential merge operator creates a very large family of facet defining inequalities for high dimensional infinite group problems using facet defining inequalities of lower dimensional group problems further they exhibit two properties that reflect the benefits of using facets of high dimensional group problems they have continuous variables coefficients that are not dominated by those of the constituent low dimensional cuts and they can produce cutting planes that do not belong to the first split closure of mips further we introduce a general scheme for generating valid inequalities for lower dimensional group problems using valid inequalities of higher dimensional group problems we present conditions under which this construction generates facet defining inequalities when applied to sequential merge inequalities we show that this procedure yields some two step mir inequalities of dash and gunluk

chva tal closures for mixed integer programming problems chvatal introduced the idea of viewing cutting planes as a system for proving that every integral solution of a given set of linear inequalities satisfies another given linear inequality this viewpoint has proven to be very useful in many studies of combinatorial and integer programming problems the basic ingredient in these cutting plane proofs is that for a polyhedronp and integral vectorw if max wx x p wx integer t thenwx t is valid for all integral vectors inp we consider the variant of this step where the requirement thatwx be integer may be replaced by the requirement that bar wx be integer for some other integral vector bar w the cutting plane proofs thus obtained may be seen either as an abstraction of gomory s mixed integer cutting plane technique or as a proof version of a simple class of the disjunctive cutting planes studied by balas and jeroslow our main result is that for a given polyhedronp the set of vectors that satisfy every cutting plane forp with respect to a specified subset of integer variables is again a polyhedron this allows us to obtain a finite recursive procedure for generating the mixed integer hull of a polyhedron analogous to the process of repeatedly taking chvatal closures in the integer programming case these results are illustrated with a number of examples from combinatorial optimization our work can be seen as a continuation of that of nemhauser and wolsey on mixed integer cutting planes

equivariant perturbation in gomory and johnson s infinite group problem i the one dimensional case we give an algorithm for testing the extremality of minimal valid functions for gomory and johnson s infinite group problem that are piecewise linear possibly discontinuous with rational breakpoints this is the first set of necessary and sufficient conditions that can be tested algorithmically for deciding extremality in this important class of minimal valid functions we also present an extreme function that is a piecewise linear function with some irrational breakpoints whose extremality follows from a new principle

free vibration analysis of multiple stepped beams by the differential quadrature element method the differential quadrature element method dqem is proposed for obtaining highly accurate natural frequencies of multiple stepped beams with an aligned neutral axis to increase the computational efficiency and accuracy explicit formulas are provided for computing the weighting coefficients various examples with existing solutions are analyzed to show the accuracy and efficiency of the dqem results are compared to analytical as well as numerical solutions by using finite element method fem with very fine meshes it is seen that the rate of convergence of the dqem is very high and the dqem can yield very accurate results with much less computational effort as compared to existing numerical methods the results obtained by the dqem can be exactly the same as the existing analytical solutions to five places of decimals with a small number of grid points the proposed method is simple and efficient and can be used to analyze beams with any step changes in cross section conveniently

analysis of multicomponent lfm signals by a combined wigner hough transform the aim of the paper is the performance evaluation of a method for the analysis of mono or multicomponent linear frequency modulation lfm signals based on the hough transform of the wigner ville distribution of the signals a closed form expression is found for the signal to noise ratio and the parameter estimation accuracy the overall method as any nonlinear method exhibits a threshold effect nevertheless it is shown to be asymptotically efficient and offers a good rejection capability of the cross terms

the worst case analysis of strong knapsack facets in this paper we identify strong facet defining inequalities for the master knapsack polytope our computational experiments for small master knapsack problems show that 1 k facets for small values of k k le 4 k 4 are strong facets for the knapsack polytope we show that this finding is robust by proving that the removal of these facets from the master knapsack polytope significantly weakens the resulting relaxation in the worst case we show that the 1 k facets for k 1 k 1 are the strongest in that their removal from the master knapsack polytope weakens the relaxation by a factor of 3 2 in the worst case we then show that the 1 k facets with k 3 k 3 or 4 are the next strongest we also show that the strength of the 1 k facets weakens as k grows and that the 1 k facets with k even are stronger than the 1 k facets with k odd

linear frequency modulated signal detection using radon ambiguity transform a novel time frequency technique for linear frequency modulated lfm signal detection is proposed the design of the proposed detectors is based on the radon transform of the modulus square or the envelope amplitude of the ambiguity function af of the signal a practical assumption is made that the chirp rate is the only parameter of interest since the af of lfm signals will pass through the origin of the ambiguity plane the line integral of the radon transform is performed over all lines passing through the origin of the ambiguity plane the proposed detectors yield maxima over chirp rates of the lfm signals this reduces the two dimensional 2 d problem of the conventional wigner ville distribution wvd based detection or the radon wigner transform rwt based detector to a one dimensional 1 d problem and consequently reduces the computation load and keeps the feature of built in filtering related issues such as the finite length effect the resolution and the effect of noise are studied the result is a tool for lfm detection as well as the time varying filtering and adaptive kernel design for multicomponent lfm signals

two row mixed integer cuts via lifting recently andersen et al 1 borozan and cornuejols 6 and cornuejols and margot 9 have characterized the extreme valid inequalities of a mixed integer set consisting of two equations with two free integer variables and non negative continuous variables these inequalities are either split cuts or intersection cuts derived using maximal lattice free convex sets in order to use these inequalities to obtain cuts from two rows of a general simplex tableau one approach is to extend the system to include all possible non negative integer variables giving the two row mixed integer infinite group problem and to develop lifting functions giving the coefficients of the integer variables in the corresponding inequalities in this paper we study the characteristics of these lifting functions we show that there exists a unique lifting function that yields extreme inequalities when starting from a maximal lattice free triangle with multiple integer points in the relative interior of one of its sides or a maximal lattice free triangle with integral vertices and one integer point in the relative interior of each side in the other cases maximal lattice free triangles with one integer point in the relative interior of each side and non integral vertices and maximal lattice free quadrilaterals non unique lifting functions may yield distinct extreme inequalities for the latter family of triangles we present sufficient conditions to yield an extreme inequality for the two row mixed integer infinite group problem

extending the performance of the cubic phase function algorithm this paper details an algorithm for estimating the parameters of cubic phase signals embedded in additive white gaussian noise the new algorithm is an extension of the cubic phase cp function algorithm with the extension enabling performance at lower signal to noise ratios snrs this improvement in the snr performance is achieved by coherently integrating the cp function over a compact interval in the two dimensional cp function space the computation of the new algorithm is quite moderate especially when compared to the maximum likelihood ml technique above threshold the algorithm s parameter estimates are asymptotically efficient a threshold analysis of the algorithm is presented and is supported by simulation results a method for extending the capability of this algorithm to process higher degree phase signals is also presented furthermore the algorithm is applied to a real data signal

online bayesian inference in some time frequency representations of non stationary processes the use of bayesian inference in the inference of time frequency representations has thus far been limited to offline analysis of signals using a smoothing spline based model of the time frequency plane in this paper we introduce a new framework that allows the routine use of bayesian inference for online estimation of the time varying spectral density of a locally stationary gaussian process the core of our approach is the use of a likelihood inspired by a local whittle approximation this choice along with the use of a recursive algorithm for non parametric estimation of the local spectral density permits the use of a particle filter for estimating the time varying spectral density online we provide demonstrations of the algorithm through tracking chirps and the analysis of musical data

a geometric approach to cut generating functions the cutting plane approach to integer programming was initiated more than 40 years ago gomory introduced the corner polyhedron as a relaxation of a mixed integer set in tableau form and balas introduced intersection cuts for the corner polyhedron this line of research was left dormant for several decades until relatively recently when a paper of andersen louveaux weismantel and wolsey generated renewed interest in the corner polyhedron and intersection cuts recent developments rely on tools drawn from convex analysis geometry and number theory and constitute an elegant bridge between these areas and integer programming we survey these results and highlight recent breakthroughs in this area

estimation of multicomponent polynomial phase signals impinging on a multisensor array using state space modeling this contribution addresses the problem of estimating the parameters of multicomponent polynomial phase signals when impinging on a multisensor array an original approach is proposed based on a state space modelization of the signal and the application of an extended kalman filter for the state estimation the use of a multisensor array allows the exploitation of a spatial information and leads to the consideration of multiple filters with different observation equations computer simulations are used to demonstrate the effectiveness of the proposed algorithm

theoretical challenges towards cutting plane selection while many classes of cutting planes are at the disposal of integer programming solvers our scientific understanding is far from complete with regards to cutting plane selection i e the task of selecting a portfolio of cutting planes to be added to the lp relaxation at a given node of the branch and bound tree in this paper we review the different classes of cutting planes available known theoretical results about their relative strength important issues pertaining to cut selection and discuss some possible new directions to be pursued in order to accomplish cutting plane selection in a more principled manner finally we review some lines of work that we undertook to provide a preliminary theoretical underpinning for some of the issues related to cut selection