performance bounds for polynomial phase parameter estimation with nonuniform and random sampling schemes estimating the parameters of a cisoid with an unknown amplitude and polynomial phase using uniformly spaced samples can result in ambiguous estimates due to nyquist sampling limitations it has been shown previously that nonuniform sampling has the advantage of unambiguous estimates beyond the nyquist frequency however the effect of sampling on the cramer rao bounds is not well known this paper first derives the maximum likelihood estimators and cramer rao bounds for the parameters with known arbitrary sampling times it then outlines two methods for incorporating random sampling times into the lower variance bounds describing one in detail it is then shown that for a signal with additive white gaussian noise the bounds for the estimation with nonuniform sampling tend toward those of uniform sampling thus nonuniform sampling overcomes the ambiguity problems of uniform sampling without incurring the penalty of an increased variance in parameter estimation

estimation and statistical analysis of exponential polynomial signals we derive and analyze a suboptimal algorithm for estimating the unknown parameters of an exponential polynomial signal eps model the eps model represents a signal as an exponent raised to a complex polynomial of time that is the phase and the logarithm of the amplitude are approximated as finite order polynomials of time

analysis of polynomial phase signals by the integrated generalized ambiguity function the aim of this work is the performance analysis of a method for the detection and parameter estimation of mono or multicomponent polynomial phase signals pps embedded in white gaussian noise and based on a generalized ambiguity function the proposed method is shown to be asymptotically efficient for second order pps and nearly asymptotically efficient for third order ppss the method presents some advantages with respect to similar techniques like the polynomial phase transform for example in terms of i a closer approach to the cramer rao lower bounds ii a lower snr threshold iii a better capability of discriminating multicomponent signals

multichannel interpolation of nonuniform samples with application to image recovery abstract the multichannel trigonometric reconstruction from uniform samples was proposed recently it not only makes use of multichannel information about the signal but is also capable to generate various kinds of interpolation formulas according to the types and amounts of the collected samples the paper presents the theory of multichannel interpolation from nonuniform samples two distinct models of nonuniform sampling patterns are considered namely recurrent and generic nonuniform sampling each model involves two types of samples nonuniform samples of the observed signal and its derivatives numerical examples and quantitative error analysis are provided to demonstrate the effectiveness of the proposed algorithms additionally the proposed algorithms for recovering highly corrupted images are also investigated in comparison with the median filter and the shepard interpolation the proposed algorithms produce superior results with lower errors

time delay estimation from low rate samples a union of subspaces approach time delay estimation arises in many applications in which a multipath medium has to be identified from pulses transmitted through the channel previous methods for time delay recovery either operate on the analog received signal or require sampling at the nyquist rate of the transmitted pulse in this paper we develop a unified approach to time delay estimation from low rate samples this problem can be formulated in the broader context of sampling over an infinite union of subspaces although sampling over unions of subspaces has been receiving growing interest previous results either focus on unions of finite dimensional subspaces or finite unions the framework we develop here leads to perfect recovery of the multipath delays from samples of the channel output at the lowest possible rate even in the presence of overlapping transmitted pulses and allows for a variety of different sampling methods the sampling rate depends only on the number of multipath components and the transmission rate but not on the bandwidth of the probing signal this result can be viewed as a sampling theorem over an infinite union of infinite dimensional subspaces by properly manipulating the low rate samples we show that the time delays can be recovered using the well known esprit algorithm combining results from sampling theory with those obtained in the context of direction of arrival estimation we develop sufficient conditions on the transmitted pulse and the sampling functions in order to ensure perfect recovery of the channel parameters at the minimal possible rate

new smoothed time frequency rate representations for suppressing cross terms in this paper to suppress the cross terms in a time frequency rate representation tfrr we propose four kinds of smoothed tfrrs stfrrs based on high resolution tfrr hr tfrr and cubic phase function we first define two types of ambiguity functions of tfrr af tfrr and give a relationship between af tfrrs and tfrrs then a mask is devised to extract the auto terms and suppress the cross terms in af tfrr domain finally four stfrrs are obtained based on the masked af tfrrs stfrrs are suitable for a signal composed of multiple linear frequency modulated components or cubic phase components with small third order parameters to analyze a signal composed of multiple cubic phase components with large third order parameters we propose smoothed time chirp rate representations stcrrs in the same way as stfrrs numerical examples demonstrate that stfrrs and stcrrs can suppress the cross terms effectively

estimating parameters of multiple wideband polynomial phase sources in sensor arrays we consider the problem of estimating the parameters of multiple wideband polynomial phase signal pps sources in sensor arrays a new maximum likelihood ml direction of arrival doa estimator is introduced and the exact cramer rao bound crb is derived for the general case of multiple constant amplitude polynomial phase sources since the proposed exact ml estimator is computationally intensive an approximate solution is proposed originating from the analysis of the log likelihood ll function in the single chirp signal case as a result a new form of spatio temporal matched filter referred to as the chirp beamformer is derived which is applicable to well separated sources that have distinct time frequency or and spatial signatures this beamforming approach requires solving a three dimensional 3 d optimization problem and therefore enjoys essentially simpler implementation than that entailed by the exact ml simulation results are presented illustrating the performance of the estimators and validating our theoretical crb analysis

the fractional fourier transform and time frequency representations the functional fourier transform frft which is a generalization of the classical fourier transform was introduced a number of years ago in the mathematics literature but appears to have remained largely unknown to the signal processing community to which it may however be potentially useful the frft depends on a parameter spl alpha and can be interpreted as a rotation by an angle spl alpha in the time frequency plane an frft with spl alpha spl pi 2 corresponds to the classical fourier transform and an frft with spl alpha 0 corresponds to the identity operator on the other hand the angles of successively performed frfts simply add up as do the angles of successive rotations the frft of a signal can also be interpreted as a decomposition of the signal in terms of chirps the authors briefly introduce the frft and a number of its properties and then present some new results the interpretation as a rotation in the time frequency plane and the frft s relationships with time frequency representations such as the wigner distribution the ambiguity function the short time fourier transform and the spectrogram these relationships have a very simple and natural form and support the frft s interpretation as a rotation operator examples of frfts of some simple signals are given an example of the application of the frft is also given

product high order ambiguity function for multicomponent polynomial phase signal modeling parameter estimation and performance analysis issues are studied for multicomponent polynomial phase signals ppss embedded in white gaussian noise identifiability issues arising with existing approaches are described first when dealing with multicomponent pps having the same highest order phase coefficients this situation is encountered in applications such as synthetic aperture radar imaging or propagation of polynomial phase signals through channels affected by multipath and is thus worthy of a careful analysis a new approach is proposed based on a transformation called product high order ambiguity function phaf the use of the phaf offers a number of advantages with respect to the high order ambiguity function haf more specifically it removes the identifiability problem and improves noise rejection capabilities performance analysis is carried out using the perturbation method and verified by simulation results

higher order boundary value problems on time scales in this paper we study the existence of solutions for lidstone boundary value problems on time scale firstly by using schauder fixed point theorem in a cone we obtain the existence of solutions to a lidstone boundary value problem lbvp secondly existence result for this problem is also given by the monotone method finally by using krasnosel skii fixed point theorem it is proved that the lbvp has a positive solution

dynamic range of the detectable parameters for polynomial phase signals using multiple lag diversities in high order ambiguity functions two lag diversities in the high order ambiguity functions for single component polynomial phase signals pps was explored by zhou and wang see ieee signal processing lett vol 4 p 240 42 1997 and signal processing vol 65 no 2 p 1452 55 1998 the lag diversity enlarges the dynamic range of the detectable parameters for pps in this paper we first find a connection between the above multiple lag diversity problem and the multiple undersampling problem in the frequency detection using discrete fourier transform dft using the connection and some results on the multiple undersampling problem we recently obtained we prove that the dynamic range obtained by zhou and wang is already the maximal one for the detectable parameters for single component pps furthermore the dynamic range for the detectable parameters for multicomponent pps is given when multiple lag diversities are used we show that the maximal dynamic range is reached when the number of the lags in the high order ambiguity function haf is at least twice of the number of the single components in a multicomponent pps more lags than twice the number of single components do not increase the dynamic range

positive solutions for second order semipositone problems on time scales we are concerned with the existence of positive solutions for second order superlinear semipositone sturm liouville boundary value problems on general time scales in particular we unify and generalize semipositone results of this type in the continuous and discrete cases to quantum and arbitrary time scales and then introduce a related second order multi point semipositone problem that is new on all time scales

nonparametric estimation of instantaneous frequency the local polynomial approximation of time varying phase is used in order to estimate the instantaneous frequency and its derivatives for a complex valued harmonic signal given by discrete time observations with a noise the considered estimators are high order nonparametric generalizations of the short time fourier transform and the wigner ville distribution the asymptotic variance and bias of the estimates are obtained

bootstrap modeling of a class of nonstationary signals the problem of modeling polynomial phase signals is considered techniques based on the bootstrap and multiple hypotheses tests for optimal model selection of constant amplitude polynomial phase signals embedded in stationary noise are developed phase parameter estimators based on both the least squares method and the polynomial phase transform are used the proposed techniques are compared with existing ones including akaike s 1978 1974 information criterion and rissanen s 1978 minimum description length criterion and are shown to outperform these procedures for the considered small sample sizes

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

estimation of chirp radar signals in compound gaussian clutter a cyclostationary approach signal detection of known within a complex scaling rank one waveforms in non gaussian distributed clutter has received considerable attention we expand on published solutions to consider the case of rank one waveforms that have some unknown parameters i e signal amplitude initial phase doppler shift and doppler rate of change the contribution of this paper is the derivation and performance analysis of two joint estimators of doppler shift and doppler rate the chirp embedded in correlated compound gaussian clutter one solution is based on the maximum likelihood ml principle and the other one on target signal second order cyclostationarity the hybrid cramer rao lower bounds hcrlbs and a large sample closed form expression for the mean square estimation error only for the doppler shift are also derived numerical examples are provided to show the behavior of the proposed estimator under different non gaussian clutter scenarios

a method for time frequency analysis a method for time frequency signal analysis is presented the proposed method belongs to the general class of smoothed pseudo wigner distributions it is derived from the analysis of the wigner distribution defined in the frequency domain this method provides some substantial advantages over the wigner distribution the well known cross term effects are reduced or completely removed the oversampling of signal is not necessary in addition the computation time can be significantly shorter the results are demonstrated on two numerical examples with frequency modulated signals

polynomial wigner ville distributions and their relationship to time varying higher order spectra the wigner ville distribution wvd has optimal energy concentration for linear frequency modulated fm signals this paper presents a generalization of the wvd in order to effectively process nonlinear polynomial fm signals a class of polynomial wvd s pwvd s that give optimal concentration in the time frequency plane for fm signals with a modulation law of arbitrary polynomial form are defined a class of polynomial time frequency distributions ptfd s are also defined based on the class of pwvd s the optimal energy concentration of the pwvd enables it to be used for estimation of the instantaneous frequency if of polynomial fm signals finally a link between pwvd s and time varying higher order spectra tvhos is established just as the expected value of the wvd of a nonstationary random signal is the time varying power spectrum the expected values of the pwvd s have interpretations as reduced tvhos

viterbi detection for compressively sampled fhss gfsk signals this paper proposes a sequence detector designed to retrieve data bits from compressively sampled frequency hopping spread spectrum fhss gaussian frequency shift keying gfsk signals the received signal waveform is not reconstructed from the compressive measurements nor are received bits detected on a symbol by symbol basis rather the entire sequence of transmitted symbols is detected from the entire sequence of compressive measurements another novel aspect of the work is that a non cooperative scenario is assumed specifically the receiver is assumed to have no prior knowledge of the specific spread spectrum hopping sequence used by the transmitter the most significant contribution of the work is the design of adaptive sampling kernels that exploit the structure of an fhss gfsk signal to obtain significant performance improvements over random kernel sampling the resulting system can automatically choose an appropriate compression ratio as a function of the signal to noise ratio snr without explicit knowledge of the snr additionally the noise folding problem present in random kernel sampling is greatly alleviated by use of the adaptive sampling kernels compared with nyquist sampling adaptive compressive sampling offers compression ratios ranging from 20 to 32 depending on the snr while suffering less than 1 db loss in the resulting bit error rate

analysis and synthesis of multicomponent signals using positive time frequency distributions a new approach to the analysis and reconstruction of multicomponent nonstationary signals from their time frequency distribution tfd is presented specifically we consider a tfd based on the recently introduced minimum cross entropy principle mce this positive tfd is cross terms free and hence has an advantage over the family of bilinear distributions based on the mce tfd a new algorithm for reconstructing the phase and amplitude parameters of each component of the signal is developed to evaluate the accuracy of the algorithm monte carlo simulations are presented and compared with the corresponding cramer rao bound it is shown that the new algorithm is superior to presently available methods in both efficiency and performance it is concluded that together with the mce tfd representation the proposed approach provides a powerful tool for analysis of nonstationary multicomponent signals embedded in additive gaussian noise

a fast algorithm for estimating the parameters of a quadratic fm signal this paper describes a fast algorithm that can be used for estimating the parameters of a quadratic frequency modulated fm signal the proposed algorithm is fast in that it requires only one dimensional 1 d maximizations the optimal maximum likelihood method by contrast requires a three dimensional 3 d maximization which can only be realized with an exhaustive 3 d grid search asymptotic statistical results are derived for all the estimated parameters the amplitude estimate is seen to be optimal whereas the phase parameters are in general suboptimal of the four phase parameter estimates two approach optimality as the signal to noise ratio snr tends to infinity the other two have mean square errors that are within 50 of the theoretical lower bounds for high snr simulations are provided to support the theoretical results extensions to multiple components and higher order fm signals are also discussed

channel estimation in wireless ofdm systems with irregular pilot distribution this paper addresses pilot assisted channel estimation for wireless orthogonal frequency division multiplexing ofdm systems with irregular pilot arrangements using nonuniform sampling techniques we propose a novel channel estimator that is based on conjugate gradient iterations and features very low computational complexity we investigate the impact of the pilot arrangement on the channel estimation mean square error and we provide a heuristic stopping criterion for early termination of the conjugate gradient iterations one dimensional and two dimensional channel estimator implementations and applications of our method to multiple antenna and multiuser ofdm systems are discussed extensive numerical simulations corroborate that the proposed method performs similarly to computationally much more expensive minimum mean square error estimators

functionally weighted lagrange interpolation of band limited signals from nonuniform samples a modification of the conventional lagrange interpolator is proposed in this paper that allows one to approximate a band limited signal from its own nonuniform samples with high accuracy the modification consists in applying the lagrange method to the signal but pre multiplied by a fixed function and then solving for the desired signal value its efficiency lies in the fact that the fixed function is independent of the sampling instants it is shown in this paper that the function can be selected so that the interpolation error decreases exponentially with the number of samples for the case in which the sampling instants have a maximum deviation from a uniform grid this paper includes a low complexity recursive implementation of the method its accuracy is validated in the numerical examples by comparison with several interpolators in the literature and by deriving upper and lower bounds for its maximum error

incomplete sampling series and the recovery of missing samples from oversampled band limited signals it is well known that a band limited oversampled signal is completely determined even if an arbitrary finite number of samples is lost it is shown that an alternative simple proof of this fact carries over to generalized sampling expansions more precisely it is shown that any finite number of missing samples can be recovered from the remaining ones in the case of generalized kramer sampling expansions if an appropriate oversampling constraint is satisfied the recovery can be accomplished either iteratively or noniteratively

efficient estimation of a narrow band polynomial phase signal impinging on a sensor array the parameters of interest of a polynomial phase signal observed by a sensor array include the direction of arrival and the polynomial coefficients the direct maximum likelihood estimation of these parameters requires a nonlinear multidimensional search in this paper we present a two step estimation approach the estimation requires only a one dimensional search in the direction of arrival space and involves a simple least squares solution for the polynomial coefficients the efficiency of the estimates is corroborated by monte carlo simulations

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

global analysis for strong solutions to the equations of a ferrofluid flow model national science foundation of china 10531020 national natural science foundation of china nsaf 10976026

unique solvability for the density dependent navier stokes equations abstract in this paper we consider the incompressible navier stokes equations with a density dependent viscosity in a bounded domain of r n n 2 3 we prove the local existence of unique strong solutions for all initial data satisfying a natural compatibility condition this condition is also necessary for a very general initial data moreover we provide a blow up criterion for the regularity of the strong solution for these results the initial density need not be strictly positive it may vanish in an open subset of

a high resolution time frequency rate representation and the cross term suppression in this paper we propose a high resolution time frequency rate representation hr tfrr and derive its analytical formula this formula implies that the hr tfrr has a narrower frequency rate support than the cubic phase function cpf therefore the hr tfrr has a higher frequency rate fr resolution than the cpf and can distinguish closer components in the time frequency rate domain due to the bilinear transform the hr tfrr suffers the cross term when the instantaneous frequency functions of the components are cross or very close in order to suppress the cross term we further propose a smoothed hr tfrr shr tfrr by introducing an fr window to the hr tfrr which is expressed in the convolution form finally numerical examples demonstrate that the hr tfrr and the shr tfrr outperform their counterparts in frequency rate resolution and cross term suppression respectively in addition satisfactory performance of the proposed methods in phase parameter estimation and real world signal analysis is given

polynomial phase signal analysis based on the polynomial derivatives decompositions an exact decomposition of the derivatives of any order of a polynomial spl phi t is proposed in terms of spl phi t t sub 0 spl phi t t sub n this result allows us to introduce generalized time frequency distributions for studying signals having a polynomial phase and a constant amplitude in order to determine the degree and the coefficients of the corresponding phase the relationships between these distributions and the already known polynomial distributions i e the polynomial phase transform and the polynomial wigner ville distribution are discussed illustrations by example are proposed

parameter estimation of phase modulated signals using bayesian unwrapping parametric estimation of phase modulated signals pms in additive white gaussian noise is considered the prohibitive computational expense of maximum likelihood estimation for this problem has led to the development of many suboptimal estimators which are relatively inaccurate and cannot operate at low signal to noise ratios snrs in this paper a novel technique based on a probabilistic unwrapping of the phase of the observations is developed the method is capable of more accurate estimation and operates effectively at much lower snrs than existing algorithms this is demonstrated in monte carlo simulations

performance of instantaneous frequency rate estimation using high order phase function the high order phase function hpf is a useful tool to estimate the instantaneous frequency rate ifr of a signal with a polynomial phase in this paper the asymptotic bias and variance of the ifr estimate using the hpf are derived in closed forms for the polynomial phase signal with an arbitrary order the cramer rao bounds crbs for ifr estimation in both exact and asymptotic forms are obtained and compared with the asymptotic mean square error mse of the hpf based ifr estimator simulations are provided to verify our theoretical results

subspace based error and erasure correction with dft codes for wireless channels this paper deals with the decoding of lowpass discrete fourier transform dft codes in the presence of both errors and erasures we propose a subspace based approach for the error localization that is similar to the subspace approaches followed in the array signal processing for direction of arrival doa estimation the basic idea is to divide a vector space into two orthogonal subspaces of which one is spanned by the error locator vectors the locations of the errors are estimated from the spanning eigenvectors of the complement subspace however unlike the subspace approach in doa estimation which is similar to estimating the subspaces from the syndrome covariance matrix after a projection in the proposed approach the subspaces are estimated from the modified syndrome covariance matrix after a whitening transform simulation results with a gauss markov source reveal that the proposed algorithm is more efficient than the coding theoretic approach on impulsive channels as well as the subspace approach with projection on lossy channels

strong solutions to the equations of a ferrofluid flow model abstract we study the differential system introduced by m i shliomis to describe the motion of a ferrofluid driven by an external magnetic field the system is a combination of the navier stokes equations the magnetization equation and the magnetostatic equations no regularizing term is added to the magnetization equation we prove the local in time existence of strong solutions to the system

discrete chirp fourier transform and its application to chirp rate estimation the discrete fourier transform dft has found tremendous applications in almost all fields mainly because it can be used to match the multiple frequencies of a stationary signal with multiple harmonics in many applications wideband and nonstationary signals however often occur one of the typical examples of such signals is chirp type signals that are usually encountered in radar signal processing such as synthetic aperture radar sar and inverse sar imaging due to the motion of a target the radar return signals are usually chirps and their chirp rates include the information about the target such as the location and the velocity in this paper we study discrete chirp fourier transform dcft which is analogous to the dft besides the multiple frequency matching similar to the dft the dcft can be used to match the multiple chirp rates in a chirp type signal with multiple chirp components we show that when the signal length n is prime the magnitudes of all the sidelobes of the dcft of a quadratic chirp signal are 1 whereas the magnitude of the mainlobe of the dcft is spl radic n with this result an upper bound for the number of the detectable chirp components using the dcft is provided in terms of signal length and signal and noise powers we also show that the n point dcft performs optimally when n is a prime

identifiability and aliasing in polynomial phase signals polynomial phase signals have numerous applications including radar sonar geophysics and radio communication many techniques for estimating the parameters of polynomial phase signals have been described in the literature despite the significant interest aliasing of polynomial phase parameters has not been fully clarified we address the problem of identifiability and aliasing in polynomial phase signals we fully describe the region in which aliasing does not occur for polynomial phase signals of any order we call this the identifiable region we find that this region is the voronoi region of a lattice generated by the coefficients of a set of polynomials known as the integer valued polynomials we show how aliasing can be resolved by solving the nearest lattice point problem we discuss some of the consequences of these results on a popular estimator for polynomial phase signals that is based on the discrete polynomial phase transform dppt it is shown that the range of parameters suitable for the dppt estimator is very small compared to the identifiable region

instantaneous frequency estimation of quadratic and cubic fm signals using the cross polynomial wigner ville distribution the cross polynomial wigner ville distribution x pwvd is applied to instantaneous frequency if estimation of polynomial fm signals the x pwvd is used in a simple iterative algorithm similar to the one proposed by boashash and o shea see ibid vol 41 no 3 p 1439 1993 for the cross wigner ville distribution x wvd the advantage of the x pwvd over the polynomial wigner ville distribution is that the former is linear with respect to the observed signal and as a result it attains the cramer rao bound at lower signal to noise ratios snrs

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

on the existence of positive solutions for semilinear elliptic equations in the annulus abstract we study the existence of positive radial solutions of u g x u 0 in annuli with dirichlet dirichlet neumann boundary conditions we prove that the problems have positive radial solutions on any annulus if is sublinear at 0 and

joint model order selection and parameter estimation of chirps with harmonic components we consider the problem of jointly determining the number of harmonic components of a fundamental linear chirp and estimating its parameters i e its initial frequency and frequency rate given time samples of the observed signal common model order criteria select the number of harmonics based on the maximum likelihood estimator we develop exact and approximated maximum likelihood estimators of these parameters to avoid an exhaustive search in the initial frequency frequency rate space involved by those estimators we propose an alternative low complexity two step estimation method the first step separates the signal to its harmonic components then in the second step the parameters of interest are estimated using least squares method given the phases of the harmonic components the method is compared to the exact and approximated maximum likelihood estimators and to the well known high order ambiguity function based method numerical simulations and real data examples demonstrate that the proposed low complexity method can successfully replace the maximum likelihood estimator in the model order criteria at moderate to high signal to noise ratio since the estimates obtained by the proposed method achieve the cramer rao lower bound at these signal to noise ratios

block based methods for the reconstruction of finite length signals from nonuniform samples two novel block based algorithms are presented for the reconstruction of uniform samples given the nonuniform samples the first algorithm uses a sinc interpolator whereas the second one uses a dft based interpolator it is shown that the proposed algorithms are stable and the error due to noise and sampling jitter is bounded by the corresponding error norms of noise and jitter respectively we show that both of the block based algorithms provide nearly perfect reconstruction for a class of practically time and bandlimited signals boundary effects are considered and single and multiblock processing is discussed a modified block based algorithm is developed by using the windowing technique in order to improve the mean squared error mse performance for nonbandlimited signals it is shown that this algorithm performs better than a group of alternative algorithms including yen s third algorithm for a variety of signal noise and sampling grids

a low complexity blind estimator of narrowband polynomial phase signals consider the problem of estimating the parameters of multiple polynomial phase signals observed by a sensor array in practice it is difficult to maintain a precisely calibrated array the array manifold is then assumed to be unknown and the estimation is referred to as blind estimation to date only an approximated maximum likelihood estimator amle was suggested for blindly estimating the polynomial coefficients of each signal however this estimator requires a multidimensional search over the entire coefficient space instead we propose an estimation approach which is based on two steps first the signals are separated using a blind source separation technique which exploits the constant modulus property of the signals then the coefficients of each polynomial are estimated using a least squares method applied to the unwrapped phase of the estimated signal this estimator does not involve any search in the coefficient spaces the computational complexity of the proposed estimator increases linearly with respect to the polynomial order whereas that of the amle increases exponentially simulation results show that the proposed estimator achieves the cramer rao lower bound at moderate or high signal to noise ratio

design of barycentric interpolators for uniform and nonuniform sampling grids this paper proposes a method to convert a fixed instant interpolator for band limited signals into a variable instant one which has the form of a barycentric interpolator this interpolator makes it possible to approximate the signal and its derivatives with minimal complexity in a range that surrounds the initial instant and is applicable to uniform and nonuniform sampling grids the barycentric form of the interpolator is derived using two different procedures first by the repeated use of bernstein s inequality and taylor s theorem and second by truncating a lagrange type series these procedures show that the proposed method can be applied to existing fixed instant interpolators and that it can be accurate in long time intervals finally an evaluation procedure for barycentric interpolators and their derivatives is presented that minimizes the number of divisions solving at the same time the numerical problems associated with small denominators this paper includes several numerical examples

ordinary differential equations transport theory and sobolev spaces we obtain some new existence uniqueness and stability results for ordinary differential equations with coefficients in sobolev spaces these results are deduced from corresponding results on linear transport equations which are analyzed by the method of renormalized solutions

the discrete polynomial phase transform the discrete polynomial phase transform dpt is a new tool for analyzing constant amplitude polynomial phase signals the main properties of the dpt are its ability to identify the degree of the phase polynomial and to estimate its coefficients the transform is robust to deviations from the ideal signal model such as slowly varying amplitude additive noise and nonpolynomial phase the authors define the dpt derive its basic properties and use it to develop computationally efficient estimation and detection algorithms a statistical accuracy analysis of the estimated parameters is also presented

difference equation representation of chirp signals and instantaneous frequency amplitude estimation we present a time varying coefficient difference equation representation for sinusoidal signals with time varying amplitudes and frequencies we first obtain a recursive equation for a single chirp signal then using this result we obtain time varying coefficient difference equation representations for signals composed of multiple chirp signals we analyze these equations using the skew shift operators we show that the phases of the poles of the difference equations produce instantaneous frequencies if and the magnitudes are proportional to the ratio of successive values of the instantaneous amplitudes ia then algorithms are presented for the estimation of instantaneous frequencies and instantaneous amplitudes for multicomponent signals composed of chirps using the difference equation representation the first algorithm we propose is based on the skew shift operators next we derive the conditions under which we can use the so called frozen time approach we propose an algorithm for if and ia estimation based on the frozen time approach then we propose an automatic signal separation method finally we apply the proposed algorithms to single and multicomponent signals and compare the results with some existing methods

estimating signal parameters using the nonlinear instantaneous least squares approach a novel method for signal parameter estimation is presented termed the nonlinear instantaneous least squares nils estimator the basic idea is to use the observations in a sliding window to compute an instantaneous short term estimate of the amplitude used in the separated nonlinear least squares nlls criterion the effect is a significant improvement of the numerical properties in the criterion function which becomes well suited for a signal parameter search for small sized sliding windows the global minimum in the nlis criterion function is wide and becomes easy to find for maximum size windows the nils is equivalent to the nlls estimator which implies statistical efficiency for gaussian noise a blind signal parameter search algorithm that does not use any a priori information is proposed the nils estimator can be interpreted as a signal subspace projection based algorithm moreover the nils estimator can be interpreted as an estimator based on the prediction error of a structured linear predictor hereby a link is established between nlls signal subspace fitting and linear prediction based estimation approaches the nils approach is primarily applicable to deterministic signal models specifically polynomial phase signals are studied and the nils approach is evaluated and compared with other approaches simulations show that the signal to noise ratio snr threshold is significantly lower than that of the other methods and it is confirmed that the estimates are statistically efficient just as the nlls approach the nils estimator can be applied to nonuniformly sampled data

filterbank reconstruction of bandlimited signals from nonuniform and generalized samples this paper introduces a filterbank interpretation of various sampling strategies which leads to efficient interpolation and reconstruction methods an identity which is referred to as the interpolation identity is developed and is used to obtain particularly efficient discrete time systems for interpolation of generalized samples as well as a class of nonuniform samples to uniform nyquist samples either for further processing in that form or for conversion to continuous time the interpolation identity also leads to new sampling strategies including an extension of papoulis 1977 generalized sampling expansion

higher order three point boundary value problem on time scales in this paper we consider a higher order three point boundary value problem on time scales we study the existence of solutions of a non eigenvalue problem and of at least one positive solution of an eigenvalue problem later we establish the criteria for the existence of at least two positive solutions of a non eigenvalue problem examples are also included to illustrate our results

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

interpolation and the discrete papoulis gerchberg algorithm analyze the performance of an iterative algorithm similar to the discrete papoulis gerchberg algorithm and which can be used to recover missing samples in finite length records of band limited data no assumptions are made regarding the distribution of the missing samples in contrast with the often studied extrapolation problem in which the known samples are grouped together indeed it is possible to regard the observed signal as a sampled version of the original one and to interpret the reconstruction result studied as a sampling result the authors show that the iterative algorithm converges if the density of the sampling set exceeds a certain minimum value which naturally increases with the bandwidth of the data they give upper and lower bounds for the error as a function of the number of iterations together with the signals for which the bounds are attained also they analyze the effect of a relaxation constant present in the algorithm on the spectral radius of the iteration matrix from this analysis they infer the optimum value of the relaxation constant they also point out among all sampling sets with the same density those for which the convergence rate of the recovery algorithm is maximum or minimum for low pass signals it turns out that the best convergence rates result when the distances among the missing samples are a multiple of a certain integer the worst convergence rates generally occur when the missing samples are contiguous

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

fft interpolation from nonuniform samples lying in a regular grid this paper presents a method to interpolate a periodic band limited signal from its samples lying at nonuniform positions in a regular grid which is based on the fft and has the same complexity order as this last algorithm this kind of interpolation is usually termed the missing samples problem in the literature and there exists a wide variety of iterative and direct methods for its solution the one presented in this paper is a direct method that exploits the properties of the so called erasure polynomial and provides a significant improvement on the most efficient method in the literature which seems to be the burst error recovery ber technique of marvasti s the paper includes numerical assessments of the method s stability and complexity

on green s functions and positive solutions for boundary value problems on time scales in this paper we offer a form of self adjoint differential equations on time scales so that the associated green s function is found symmetric in the usual sense for this purpose together with the delta derivative we employ the nabla derivative as well we introduce the concepts of lebesgue delta and nabla integrals on time scales next sign properties of the green s function are investigated and existence results for positive solutions of nonlinear boundary value problems are established upper and lower bounds for these positive solutions also are given

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

positive solutions of semipositone higher order differential equations on time scales abstract in this paper we are concerned with the following 2 n th order differential equations on time scales 1 n y 2 n t g t f t y t t a b y 2 i a i 1 y 2 i 1 a i 1 y 2 i i 1 y 2 i y 2 i b 0 i n 1 where a b n 1 i 0 1 i b a i a i 0 i b i i 1 a i b i 1 2 n the functions g a b 0 and f a b 0 are continuous or g is singular at t a and or t b we obtain some properties and sharp estimates of the corresponding green s function and investigate the existence of positive solutions of the semipositone problems for 2 n order differential equations by the use of the property of green s function variable transformation and the fixed point index theorem

efficient algorithms for burst error recovery using fft and other transform kernels we show that the problem of signal reconstruction from missing samples can be handled by using reconstruction algorithms similar to the reed solomon rs decoding techniques usually the rs algorithm is used for error detection and correction of samples in finite fields for the case of missing samples of a speech signal we work with samples in the field of real or complex numbers and we can use fft or some new transforms in the reconstruction algorithm dsp implementation and simulation results show that the proposed methods are better than the ones previously published in terms of the quality of recovered speech signal for a given complexity the burst error recovery method using the fft kernel is sensitive to quantization and additive noise like the other techniques however other proposed transform kernels are very robust in correcting bursts of errors with the presence of quantization and additive noise

distributed source channel coding based on real field bch codes we use real number codes to compress statistically dependent sources and establish a new framework for distributed lossy source coding in which we compress sources before rather than after quantization this change in the order of binning and quantization blocks makes it possible to model the correlation between continuous valued sources more realistically and compensate for the quantization error partially we then focus on the asymmetric case i e lossy source coding with side information at the decoder the encoding and decoding procedures are described in detail for a class of real number codes called discrete fourier transform dft codes both for the syndrome and parity based approaches we leverage subspace based decoding to improve the decoding and by extending it we are able to perform distributed source coding in a rate adaptive fashion to further improve the decoding performance when the statistical dependency between sources is unknown we also extend the parity based approach to the case where the transmission channel is noisy and thus we perform distributed joint source channel coding in this context the proposed system is well suited for low delay communications as the mean squared reconstruction error mse is shown to be reasonably low for very short block length

a hybrid cpf haf estimation of polynomial phase signals detailed statistical analysis in this paper we consider parameter estimation of high order polynomial phase signals ppss we propose an approach that combines the cubic phase function cpf and the high order ambiguity function haf and is referred to as the hybrid cpf haf method in the proposed method the phase differentiation is first applied on the observed pps to produce a cubic phase signal whose parameters are in turn estimated by the cpf the performance analysis carried out in the paper considers up to the tenth order ppss and is supported by numerical examples revealing that the proposed approach outperforms the haf in terms of the accuracy and signal to noise ratio threshold extensions to multicomponent and multidimensional ppss are also considered all supported by numerical examples specifically when multicomponent ppss are considered the product version of the cpf haf outperforms the product haf phaf that fails to estimate parameters of components whose pps order exceeds three

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

on polynomial phase signals with time varying amplitudes we address the parameter estimation problem for a class of nonstationary signals modeled as polynomial phase signals with time varying amplitudes exponentially damped polynomial phase signals are treated as a special case and are analyzed in detail high order instantaneous moments provide the basic analytical tool but links are shown to exist with either the usually employed fft based technique or the high resolution kumaresan tufts 1982 music and matrix pencil methods asymptotic properties of the relevant estimators are established cramer rao lower bounds on the amplitude and phase parameter estimates are derived and computer simulations are carried out to evaluate the performance of various schemes we focus on parametric modeling of am fm signals mainly because parametric techniques offer parsimony and allow for theoretically unlimited resolution

generalized high order phase function for parameter estimation of polynomial phase signal the high order phase function hpf has been introduced recently to estimate the parameters of a polynomial phase signal pps in this correspondence we generalize the standard hpf by introducing multiple time instants thus the standard hpf can be treated as a special example of the generalized hpf with identical time instants we propose a procedure for finding time instants minimizing the mean square error mse the proposed method achieves better performances than the high order ambiguity function haf and polynomial wigner ville distribution pwvd the theoretical analysis as well as the monte carlo simulations verify the advantages such as lower mse and lower snr threshold for the pps

multicomponent polynomial phase signal analysis using a tracking algorithm we describe an efficient technique analyzing signals that comprise a number of polynomial phase components the technique is based on a previously proposed multiple frequency tracker which is an algorithm for recursive estimation of parameters of multiple sine waves in noise it has a relatively low snr threshold and moderate computational complexity

compressed sensing off the grid this paper investigates the problem of estimating the frequency components of a mixture of s complex sinusoids from a random subset of n regularly spaced samples unlike previous work in compressed sensing the frequencies are not assumed to lie on a grid but can assume any values in the normalized frequency domain 0 1 an atomic norm minimization approach is proposed to exactly recover the unobserved samples and identify the unknown frequencies which is then reformulated as an exact semidefinite program even with this continuous dictionary it is shown that o slog s log n random samples are sufficient to guarantee exact frequency localization with high probability provided the frequencies are well separated extensive numerical experiments are performed to illustrate the effectiveness of the proposed method

existence of n solutions and or positive solutions to a semipositone elastic beam equation abstract the existence of n solutions and or positive solutions is established for a nonlinear fourth order two point boundary value problem where n is an arbitrary natural number and the nonlinear term has a nonpositive lower bound in mechanics the problem describes deformation of the elastic beam whose two ends are simply supported the main results show that the problem has at least n solutions and or positive solutions provided that the heights of the nonlinear term are appropriate on some bounded sets

improving polynomial phase parameter estimation by using nonuniformly spaced signal sample methods this paper investigates the computationally efficient parameter estimation of polynomial phase signals embedded in noise many authors have previously proposed multilinear analysis methods which operate on uniformly spaced samples of the signal such methods include the higher order ambiguity functions hafs the polynomial wigner ville distributions pwvds and the higher order phase hp functions this paper investigates the use of multilinear methods which operate on nonuniformly spaced signal samples it is seen that the relaxation of the requirement to use uniformly spaced samples in the analysis can lead to significant performance improvements a theoretical analysis and simulations are presented in support of these claims

hybrid fm polynomial phase signal modeling parameter estimation and cramer rao bounds parameter estimation for a class of nonstationary signal models is addressed the class contains combination of a polynomial phase signal pps and a frequency modulated fm component of the sinusoidal or hyperbolic type such signals appear in radar and sonar applications involving moving targets with vibrating or rotating components a novel approach is proposed that allows us to decouple estimation of the fm parameters from those of the pps relying on properties of the multilag high order ambiguity function ml haf the accuracy achievable by any unbiased estimator of the hybrid fm pps parameters is investigated by means of the cramer rao lower bounds crlbs both exact and large sample approximate expressions of the bounds are derived and compared with the performance of the proposed methods based on monte carlo simulations

a high resolution quadratic time frequency distribution for multicomponent signals analysis the paper introduces a new kernel for the design of a high resolution time frequency distribution tfd we show that this distribution can solve problems that the wigner ville distribution wvd or the spectrogram cannot in particular the proposed distribution can resolve two close signals in the time frequency domain that the two other distributions cannot moreover we show that the proposed distribution is more accurate than the wvd and the spectrogram in the estimation of the instantaneous frequency of a stepped fm signal embedded in additive gaussian noise synthetic and real data collected from real world applications are shown to validate the proposed distribution

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

a new class of multilinear functions for polynomial phase signal analysis this paper introduces a new class of multilinear functions which can be used for analyzing a signal with time varying frequency the new class subsumes a number of existing functions including the higher order ambiguity functions hafs the polynomial wigner ville distributions pwvds and the higher order phase hp functions as well as establishing a link between these existing functions the new class provides a formalism which allows for the creation of useful new multilinear functions a number of new functions are derived from the class

multiple positive solutions of singular dirichlet problems on time scales via variational methods abstract this paper is devoted to using variational techniques and critical point theory to derive some sufficient conditions for the existence of multiple positive solutions to a singular second order dynamic equation with homogeneous dirichlet boundary conditions

stability and uniqueness of magnetic fluid motions we examine the uniqueness and asymptotic stability of the equilibrium and arbitrary flows for a general class of the governing equations for magnetic fluids stability bounds for equilibrium base flows in mechanically isolated domains are obtained and it is shown that in general these are asymptotically stable for general non trivial flows we obtain stability bounds and establish uniqueness theorems for the initial boundary value problems of magnetic fluids