on tests for normality the problem of deciding whether a sample of a random field was generated by a gaussian distribution is considered based on extensions of large deviation estimates due to m d donsker and s r s varadhan 1985 a test that is optimal in a generalized neyman pearson sense is proposed this test turns out to depend on properties of the entropy of gaussian processes and does not depend on cumulant computations

time domain procedures for testing that a stationary time series is gaussian a class of time domain procedures for testing that a stationary time series is gaussian is presented and analyzed these tests are based on the deviations of the sample value of finite memory nonlinear transformations of the process from their ensemble averaged counterparts asymptotic distributions of these tests are derived under the null hypothesis of gaussianity and under a class of local and fixed alternatives specific tests are then developed based respectively on higher order moments and on the characteristic functions practical construction of the test statistics is discussed with a special emphasis on the estimation of the covariance of the sample statistics which appears to play a key role in the performance of the tests when dealing with small samples

on the three coefficient window family the definition of the three coefficient window family is extended to the form w t b 0 5 1 b 0 5 cos 2 pi t t 0 5b cos 4 pi t t mod t mod

a fast sinc function gridding algorithm for fourier inversion in computer tomography the fourier inversion method for reconstruction of images in computerized tomography has not been widely used owing to the perceived difficulty of interpolating from polar or other measurement grids to the cartesian grid required for fast numerical fourier inversion although the fourier inversion method is recognized as being computationally faster than the back projection method for parallel ray projection data the artifacts resulting from inaccurate interpolation have generally limited application of the method this paper presents a computationally efficient gridding algorithm which can be used with direct fourier transformation to achieve arbitrarily small artifact levels the method has potential for application to other measurement geometries such as fan beam projections and diffraction tomography and nmr imaging

analysis of the short time unbiased spectrum estimation algorithm the short time unbiased spectrum estimation stuse algorithm is analyzed and expressions for the mean and variance of the spectrum estimates are derived the stuse algorithm deliberately adds biased spectrum estimates in order to yield unbiased estimates and at the same time have excellent spectral leakage suppression capabilities computer simulations are presented verifying the theoretical results and also comparing the stuse algorithm with the conventional weighted overlapped segment averaging wosa method

fast estimators of time delay and doppler stretch based on discrete time methods estimation of the time delay and the doppler stretch of a signal is required in several signal processing applications this paper is focused on the joint fine estimation of these two parameters by a fast interpolation of the estimated ambiguity function four discrete time methods viz multirate piecewise scaling linear scaling and indirect estimators based on an orthogonal model are introduced their mean square error is mathematically derived for random signals corrupted by additive random noises the obtained expressions have been evaluated for some typical parameter sets in the reference case of gaussian signals and noises the numerical results compared with the accuracy of a continuous time estimator show the near efficiency of the multirate estimator for a wide range of snrs in fact the adjustable multirate estimator can operate under near optimal conditions unlike the approximate i e piecewise and linear scaling and the indirect methods based on constant sampling rates

effects of the poisson ratio and negative thrust on the dynamic stability of a free plate subjected to a follower force abstract the macroscopic poisson ratio of a large plate like truss structure may vary due to the geometry of the truss studied are the effects of the poisson ratio and negative thrust on the dynamic stability of a flexible rectangular plate which has four free edges one of the four edges is subjected to a tangential follower thrust the model is simplified to a continuous isotropic plate and is investigated by means of modal analysis a change in poisson ratio sometimes reduces the flutter load drastically the drastic reduction comes from the existence of a weak flutter instability it is also shown that there may exist both flutter and divergence even for negative thrust and that the tensile divergence load is smaller than the compressive one

sigma delta modulation with leaky integration and constant input exact descriptions of the behavior of quantization noise for single loop multistage cascade and multiloop sigma delta modulators for a variety of input signals have been found during recent years under the assumption of ideal integration the techniques used to solve the ideal integrator case do not easily extend to the more realistic model of a leaky integrator sigma delta in this paper a dynamical system representation for the leaky integrator sigma delta with a constant input is developed several properties of the resulting piecewise monotone and piecewise linear transformation t on the interval

the jackknife and the bootstrap for general stationary observations we extend the jackknife and the bootstrap method of estimating standard errors to the case where the observations form a general stationary sequence we do not attempt a reduction to i i d values the jackknife calculates the sample variance of replicates of the statistic obtained by omitting each block of l consecutive data once in the case of the arithmetic mean this is shown to be equivalent to a weighted covariance estimate of the spectral density of the observations at zero under appropriate conditions consistency is obtained if l l n rightarrow infty and l n n rightarrow 0 general statistics are approximated by an arithmetic mean in regular cases this approximation determines the asymptotic behavior bootstrap replicates are constructed by selecting blocks of length l randomly with replacement among the blocks of observations the procedures are illustrated by using the sunspot numbers and some simulated data

fast computation of exact confidence limits for the common odds ratio in a series of 2 2 tables abstract the odds ratio is widely used as a measure of association in epidemiologic studies and clinical trials we consider calculation of exact confidence limits for the common odds ratio in a series of independent 2 2 tables and propose three modifications of the network algorithm of mehta patel and gray 1 formulating and dealing with the problem in algebraic instead of graph theoretic terms 2 performing convolutions on the natural scale instead of the logarithmic scale and 3 using the secant method instead of binary search to compute roots of polynomial equations enhancement of computational efficiency exceeding an order of magnitude afforded by these modifications is empirically demonstrated we also compare the modified method with one based on the fast fourier transform fft further we show that the fft method can also result in considerable loss of numerical accuracy the modifications proposed in this article yield an algorithm that is not only fast and accurate but that combine

dynamic stability of shallow shells subjected to follower forces dynamic stability of cylindrically curved shallow shells subjected to follower forces is presented the shell analysis uses a two field variable variational principle with the transverse displacement and airy stress function as field variables starting from the variational equation of the problem the euler lagrange equations governing the problem and the boundary conditions on the transverse displacement and the airy stress function are obtained a finite element formulation that preserves c 1 continuity is used for the solution of the problem numerical results are given and the results obtained are discussed it is shown that the use of the two field variable variational principle permits through static condensation a reduction in the effort needed for the solution of the stability problem to that of flat plate similarity between the response of a flexible structure to a follower force and the aerodynamic supersonic panel flutter is discussed practical applications of the problem are large space structures such as solar power stations which can undergo flutter or divergence instabilities due to their low rigidity when thrusted by follower forces

fine estimators of two dimensional parameters and application to spatial shift estimation this paper presents a fast technique for fine estimation of two dimensional 2 d parameters based on a parabolic interpolation of the same ambiguity function samples and aimed at block oriented estimation of the spatial shift between pairs of images in video sequences expressions for the bias and variance of the position error and the prediction error are derived the method is tested using a synthetically generated autocorrelation function varying the directionality and the eccentricity factor in order to compare the performance of the proposed 2 d estimator to the case of two separate one dimensional 1 d estimators the method has also been applied in vision systems evidencing encouraging results for estimating the parameters of sophisticated global motion models from real images

divergence and flutter instability of elastic specially orthotropic plates subject to follower forces abstract divergence and flutter instabilities of a rectangular specially orthotropic plate simply supported on a pair of opposite sides subject to follower forces are computationally analyzed the effects of the tangential follower parameter aspect ratio boundary condition on the side opposite the loaded edge and material orthotropy on the magnitude of the critical load and the mode divergence or flutter of instability are detailed for the three boundary conditions considered built in simply supported and free free for the side opposite the loaded edge and given material orthotropy the plane is divided into regions corresponding to different governing instabilities both the number and size of these regions depend strongly upon the boundary condition considered as does the governing instability for a given boundary condition the configuration of the stability regions is independent of material orthotropy material orthotropy affects only the buckling loads corresponding to the instabilities and the size of the regions

redundant logarithmic arithmetic a number system that offers advantages in some situations over conventional floating point and sign logarithmic number systems is described redundant logarithmic arithmetic like conventional logarithmic arithmetic relies on table lookups to make the arithmetic unit simpler than an equivalent floating point unit the cost of 32 bit subtraction in a redundant logarithmic number system is lower than previously published logarithmic subtraction methods the total memory requirement for a 29 bit redundant logarithmic unit is 16 k words compared to 22 k words by the best previously published conventional sign logarithm unit assuming similar addition techniques are employed a redundant logarithmic number system can be implemented with online arithmetic which would be impractical for a conventional sign logarithm number system the disadvantages of redundant arithmetic are typical of redundant number systems first the redundancy doubles the storage requirements for data values second the representation can become ill conditioned especially as a result of iterated multiplications third division and square root operations are more difficult to implement in redundant logarithmic arithmetic

spectral leakage suppression properties of linear and quadratic windowing it is shown that the leakage suppression properties of segment averaging spectrum estimation methods using linear windows and equivalent quadratic windows are asymptotically the same under the assumption that segments relatively far apart are uncorrelated thus for large data lengths one can effectively replace linear windowing by its equivalent quadratic windowing and hope to get similar leakage suppression at a substantially reduced computational cost a simulation example that supports this conclusion is presented

analytical derivation of nonlinear spectral effects and 1 f scaling artifact in signal processing of real world data in estimating the frequency spectrum of real world time series data we must violate the assumption of infinite length orthogonal components in the fourier basis while it is widely known that care must be taken with discretely sampled data to avoid aliasing of high frequencies less attention is given to the influence of low frequencies with period below the sampling time window here we derive an analytic expression for the side lobe attenuation of signal components in the frequency domain representation this expression allows us to detail the influence of individual frequency components throughout the spectrum the first consequence is that the presence of low frequency components introduces a 1 f formula see text component across the power spectrum with a scaling exponent of formula see text this scaling artifact could be composed of diffuse low frequency components which can render it difficult to detect a priori further treatment of the signal with standard digital signal processing techniques cannot easily remove this scaling component while several theoretical models have been introduced to explain the ubiquitous 1 f formula see text scaling component in neuroscientific data we conjecture here that some experimental observations could be the result of such data analysis procedures

some windows with very good sidelobe behavior some of the windows presented by harris 1 are not correct in terms of their reported peak sidelobes and optimal behavior we present corrected plots of harris windows and also derive additional windows with very good sidelobes and optimal behavior under several different constraints the temporal weightings are characterized as a sum of weighted cosines over a finite duration the plots enable the reader to select a window to suit his requirements in terms of bias due to nearby sidelobes and bias due to distant sidelobes

beyond floating point un systeme numerique est propose pour l arithmetique d ordinateur basee sur des fonctions exponentielles iterees l avantage principal est d extirper le sous passement et le depassement de capacite mais il y a quelques autres avantages et ceux ci sont decrits et discutes

variable parameter window families for digital spectral analysis two different window function families namely the first order bessel i sub 1 cosh family and raised cosine family which have variable parameters and hence make them flexible in digital spectrum analysis applications are considered closed form expressions are obtained which facilitate the tradeoffs between record length spectral resolution leakage suppression bandwidth etc simple expressions relating to mainlobe width and maximum sidelobe level are given for the two families considered the results are compared to those obtained by j f kaiser and r w schafer 1980 in the case of zeroth order bessel i sub 0 sinh family

on some fourier methods for inference abstract common statistical procedures such as maximum likelihood and m estimation admit generalized representations in the fourier domain the fourier domain provides fertile ground for approaching a number of difficult problems in inference in particular the empirical characteristic function and its extension for stationary time series are shown to be fundamental tools which support numerically simple inference procedures having arbitrarily high asymptotic efficiency and certain robustness features as well a numerical illustration involving the symmetric stable laws is given

fourier based reconstruction for fully 3 d pet optimization of interpolation parameters fourier based approaches for three dimensional 3 d reconstruction are based on the relationship between the 3 d fourier transform ft of the volume and the two dimensional 2 d ft of a parallel ray projection of the volume the critical step in the fourier based methods is the estimation of the samples of the 3 d transform of the image from the samples of the 2 d transforms of the projections on the planes through the origin of fourier space and vice versa for forward projection reprojection the fourier based approaches have the potential for very fast reconstruction but their straightforward implementation might lead to unsatisfactory results if careful attention is not paid to interpolation and weighting functions in our previous work we have investigated optimal interpolation parameters for the fourier based forward and back projectors for iterative image reconstruction the optimized interpolation kernels were shown to provide excellent quality comparable to the ideal sinc interpolator this work presents an optimization of interpolation parameters of the 3 d direct fourier method with fourier reprojection 3d frp for fully 3 d positron emission tomography pet data with incomplete oblique projections the reprojection step is needed for the estimation from an initial image of the missing portions of the oblique data in the 3d frp implementation we use the gridding interpolation strategy combined with proper weighting approaches in the transform and image domains we have found that while the 3 d reprojection step requires similar optimal interpolation parameters as found in our previous studies on fourier based iterative approaches the optimal interpolation parameters for the main 3d frp reconstruction stage are quite different our experimental results confirm that for the optimal interpolation parameters a very good image accuracy can be achieved even without any extra spectral oversampling which is a common practice to decrease errors caused by interpolation in fourier reconstruction

a hybrid number system processor with geometric and complex arithmetic capabilities the architecture design and performance of a hybrid number system processor are described the processor performs multiplication division square root and square in the logarithmic number system lns domain however the input output addition and subtraction are all executed in the 32 b ieee standard floating point number system with the lns multiplier and pipelined architecture the processor is able to perform the geometric and complex arithmetic very effectively the processor is also shown to compare well to an existing 32 b floating point dsp digital signal processor chip for the same level of cmos technology the performance ratios between the hybrid number system and the floating point processor are shown to be 6 4 1 and 8 1 for division and square root respectively for the complex fft fast fourier transform algorithm the ratio is around 2 1

a new optimal window signal processing an optimal window that can provide the best tradeoff between the peak sidelobe level and the total sidelobe level is presented necessary and sufficient conditions are established for the optimal window a design algorithm is presented and examples are discussed the examples demonstrate that the window is capable of much better performance than previously available windows such as the hamming window relationships between the maximum error and the mean squared error are explored for the window optimization problem it is concluded that the minimax and least squares approximations are both fundamentally inefficient this conclusion is supported by experimental evidence and mathematical analyses

optimum binary windows for discrete fourier transforms a class of windows called binary windows for the frequency domain implementation of the discrete fourier transform is proposed while the conventional time domain windowing requires n 2 stored values of the data window and n multiplications the binary windows do not require multiplications or stored constants rather they are replaced by shift and add operations typical hardware structures are presented for efficient implementation of the binary windows

fir filters with sigma delta modulation encoding two methods are presented for building fir finite impulse response digital filters where either the impulse response or the input signal is encoded using sigma delta modulation for each method both single loop and two stage sigma delta modulation are used for encoding these systems are operated at a sampling rate higher than the nyquist rate of the signal and their performance depends on the oversampling ratio except in the decoding circuit these filters require no multiplication and hence can be built using simple hardware an analysis of the systems is provided and examples for filters realized using these approaches are given

approximate synthesis of nonseparable design responses for rectangular arrays a method is presented for the approximation of any real symmetrical nonseparable array design response polynomial of order m 1 by n 1 for rectangular arrays with m by n uniformly spaced elements m geq n previously a sampling method has been used to exactly synthesize response functions of a single variable by n element line arrays 1 and nonseparable functions of two variables by n times n square arrays the sampling method is extended herein to apply to rectangular arrays by deriving the element weights for an m by n rectangular array that exactly yield the values of any desired real symmetrical array response function on an m by n grid of the interelement phase shifts this would yield the designed array response exactly everywhere if the design equation were of order m 1 with respect to one dimension and of order n 1 with respect to the other dimension to approximate this condition the original design function of order n 1 in both dimensions is modified to make it of order m 1 in one dimension and of order n 1 along a single grid line in the other dimension a second function is derived with these roles reversed the resulting function has the form of the original design function exactly equaling it along the n grid lines of m points each and along the single perpendicular chosen grid line of n points and closely approximating it throughout the entire range of the variables this technique is illustrated for chebyshev response functions for which the two approximating functions are derived and evaluated for several combinations of m and n the responses are shown to have generally uniform sidelobe regions with all but a small percentage of the sidelobes within 1 db of the designed sidelobe value

a cost minimization approach for optimal window design in spectral analysis of sampled signals the problem of digital window design is formulated in terms of cost minimization this cost quantizes the leakage from one frequency to another the choice of the penalty function appearing in the cost expression may be adapted to a specific spectral analysis problem and allows the designer to control undesirable leakages the approach is applied in one particular optimization problem the minimization of the second order moment extension to the case of sampled signal spectra this example leads to a correct justification of the papoulis 1977 window in the case of digital signals applications show examples of window design and the interest in the papoulis window in some problems of spectral parameters estimation pisarenko 1973 frequency estimation and autoregressive modelization

improved addition for the logarithmic number system the logarithmic number system lns which offers a wide dynamic range with an independently choosable signal to noise ratio is discussed to realize addition voluminous lookup tables are needed a method is proposed to reduce the storage requirements of these tables by means of chebyshev approximation with unequally spaced partition points

a pulsed beam summation formulation for short pulse radiation based on windowed radon transform wrt frames a new time domain td representation for radiation from apertures wherein the field is expanded in a discrete lattice of shifted tilted and retarded pulsed beam pb propagators is proposed the pb representation provides a uniformly accurate systematic framework for ray based tracking of ultrawide band transient fields in complex configurations e g slowly or abruptly varying inhomogeneous media the excitation coefficients of the pbs are extracted from the aperture source distribution via a new discretized local slant stack transform the formulation is structured upon a new class of frames termed windowed radon transform frames the sets of expansion and analysis functions are shown to be dual frames thus facilitating representation of arbitrary bandlimited source fields explicit expressions for the processing windows the analysis frame set and for the pb propagators the expansion set are provided for the class of isodiffracting pbs accuracy of the pb expansion technique is demonstrated for a focusing aperture case that tends to fail the conventional ray shooting schemes

two stage sigma delta modulation an exact analysis of the nonlinear difference equation describing a discrete time two stage sigma delta quantizer with dc and sinusoidal inputs is presented it is shown that for dc inputs the binary quantizer error of the second quantizer which appears at the output of the modulator as a second order difference is asymptotically white uniformly distributed and uncorrelated with the input for sinusoidal inputs this result holds with one exception the autocorrelation which is a sum of weighted bessel functions does not correspond to that of a white noise process at large oversampling ratios the autocorrelation is approximately white and hence the white additive noise model is a good approximation for evaluating the first and second order moments it is found that for both a sinc sup 3 decoder filter and an ideal low pass filter decoder the average quantization noise power is inversely proportional to the fifth power of the oversampling ratio r for both types of inputs this represents an improvement over the single loop sigma delta quantizer by a factor of r sup 2 simulation results that agree with the theoretical analysis are presented

fpga designs with optimized logarithmic arithmetic using a general polynomial approximation approach we present an arithmetic library generator for the logarithmic number system lns the generator produces optimized lns arithmetic libraries that improve significantly over previous lns designs on area and latency we also provide area cost estimation and bit accurate simulation tools that facilitate comparison between lns and floating point designs

a system level model reduction technique for the efficient simulation of flexible multibody systems flexible multibody systems are governed by sets of non linear differential algebraic equations dae the number of degrees of freedom dofs required for accurate body flexibility modeling as well as the presence of the algebraic constraint equations limit the simulation speed body level model reduction and general purpose system level model reduction techniques do not result in optimal model dimension reduction and do not necessarily transform the dae set into a cheaper to solve set of ordinary differential equations as opposed to model reduction techniques such as global modal parameterization gmp which are based on describing the system motion by the contribution of its dominant configuration dependent system level modal patterns their use as a simulation tool has not been thoroughly investigated this paper investigates the influence of the modal content of the configuration dependent mode set on the simulation accuracy through numerical experiments by including the dynamically excited eigenmodes and static deformation patterns for dofs in which the system is externally loaded the system can be accurately represented by a very limited number of dofs phenomena such as mode veering and mode crossing in which the modal content of eigenmodes rapidly varies can be expected to be problematic for such a description which is confirmed with numerical experiments copyright 2010 john wiley sons ltd

dynamic stability of a rectangular plate with four free edges subjected to a follower force one of the four free edges of the plate is subjected to a tangential follower force the flutter load and divergence load are obtained for various slenderness ratios of the rectangular plate by means of modal analysis in the calculation many weak instabilities were found

on efficient implementations of 2 d digital filters using logarithmic number systems the implementation of 2 d digital filters using logarithmic number systems lns s is discussed in detail the properties of such systems are derived with reference to an iterative rounding scheme which allows increasing the accuracy of the filter coefficient representation by using more than one power of the base a the optimization of the base is proposed as an efficient tool for the design of accurate 2 d filters different design strategies are considered together with a discussion of the degree of precision required for the circuits which determine the base of the lns the efficiency and versatility of this approach are demonstrated with several design examples in 2 d

correlation and spectral methods for determining uncertainty in propagating discontinuities the accurate determination of the speed of a propagating disturbance is important for a number of applications a nonstationary cross spectral density phase ncsdp technique was developed to provide a statistical estimate of the propagation time of sharp discontinuities such as steps or spikes that model shock or detonation waves the uncertainty of the phase estimate is dependent on the coherence between the signals for discrete implementation of the ncsdp technique a weighted resetting unwrap of the phase angle was proposed to discard values of the coherence below a threshold value that is only the unwrapped phase angle above the threshold was accepted in addition an envelop function was used which improved the technique the technique was found to be unsuitable for step disturbances but was more effective in estimating the time delay with a small standard deviation if the sharp disturbance also showed a rapid decay the method was applied to shock and detonation waves

multistage sigma delta modulation a theoretical basis is provided for multistage sigma delta modulation msm which is a cascade realization of several single loop sigma delta modulators with a linear combinatorial network equations are derived describing the output and the quantization noise of msm for an arbitrary input signal and the noise shaping characteristic of msm is investigated the spectral characteristics of an m stage sigma delta modulator with both dc and sinusoidal inputs are developed for both types of inputs the binary quantizer noise of the mth m or 3 quantizer which appears at the output as an mth order difference is asymptotically white uniformly distributed and uncorrelated with the input level it is also found that for an m stage sigma delta quantizer with either an ideal low pass filter or a sinc sup m 1 filter decoder the average quantization noise of the system is inversely proportional to the 2m 1 th power of the oversampling ratio this implies that the high order systems are favourable in terms of the trade off between the quantization noise and oversampling ratio simulation results are presented to support the theoretical analysis

kernel design for reduced interference distributions the authors present a class of time frequency signal representations tfrs called the reduced interference distribution rid an overview of commonly used tfrs is given and desirable distribution properties are introduced particular attention is paid to the interpretation of cohen s class of time frequency distributions of tfrs in the ambiguity temporal correlation spectral correlation and time frequency domains based on the desirable kernel requirements the rid is discussed and further defined a systematic procedure to create rid kernels or equivalently compute rids is proposed some aspects and properties of the rid are discussed the authors estimate design considerations for rids and compare various selections of the primitive window some experimental results demonstrating the performance of the rid are presented

orthogonal sets of data windows constructed from trigonometric polynomials suboptimal easily computable substitutes for the discrete prolate spheroidal windows used by d j thomson proc ieee vol 70 p 1055 1096 1982 for spectral estimation are given trigonometric coefficients and energy leakages of the window polynomials are tabulated

semi logarithmic number systems we present a new class of number systems called semi logarithmic number systems that constitute a family of various compromises between floating point and logarithmic number systems this allows trade between the speed of the arithmetic operations and the size of the required tables we give arithmetic algorithms addition subtraction multiplication division for the semi logarithmic number systems and we compare these number systems to the classical floating point or logarithmic number systems

performance of digital linear regulators which use logarithmic arithmetic this paper analyzes the performance of digital linear regulators which use finite precision logarithmic arithmetic a linear equation is derived which describes the steady state covariance matrix of such a closed loop regulator system the utility of this covariance matrix in designing regulators which use logarithmic arithmetic is illustrated through several numerical examples and the presentation of a regulator design methodology

time domain tests for gaussianity and time reversibility statistical signal processing algorithms often rely upon gaussianity and time reversibility two important notions related to the probability structure of stationary random signals and their symmetry parametric models obtained via second order statistics sos are appropriate when the available data is gaussian and time reversible on the other hand evidence of nonlinearity non gaussianity or time irreversibility favors the use of higher order statistics hos in order to validate gaussianity and time reversibility and quantify the tradeoffs between sos and hos consistent time domain chi squared statistical tests are developed exact asymptotic distributions are derived to estimate the power of the tests including a covariance expression for fourth order sample cumulants a modification of existing linearity tests in the presence of additive gaussian noise is discussed briefly the novel gaussianity statistic is computationally attractive leads to a constant false alarm rate test and is well suited for parametric modeling because it employs the minimal hos lags which uniquely characterize arma processes simulations include comparisons with an existing frequency domain approach and an application to real seismic data time reversibility tests are also derived and their performance is analyzed both theoretically and experimentally

spectrum adapted tight graph wavelet and vertex frequency frames we consider the problem of designing spectral graph filters for the construction of dictionaries of atoms that can be used to efficiently represent signals residing on weighted graphs while the filters used in previous spectral graph wavelet constructions are only adapted to the length of the spectrum the filters proposed in this paper are adapted to the distribution of graph laplacian eigenvalues and therefore lead to atoms with better discriminatory power our approach is to first characterize a family of systems of uniformly translated kernels in the graph spectral domain that give rise to tight frames of atoms generated via generalized translation on the graph we then warp the uniform translates with a function that approximates the cumulative spectral density function of the graph laplacian eigenvalues we use this approach to construct computationally efficient spectrum adapted tight vertex frequency and graph wavelet frames we give numerous examples of the resulting spectrum adapted graph filters and also present an illustrative example of vertex frequency analysis using the proposed construction

dynamic stability of a completely free plate subjected to a controlled non conservative follower force abstract the dynamic instability of a rectangular plate with four free edges is investigated one edge of the completely free plate is subjected to a uniformly distributed non conservative follower force the direction of which is controlled in proportion to the rotation angle of the loading edge the plate may have both flutter and divergence type instabilities when the force is non conservative although it may have only divergence type instabilities when the force is conservative

a two parameter class of bessel weightings for spectral analysis or array processing the ideal weighting window pairs a unified theory for array processing in 1 2 or 3 dimensions is pointed out and illustrated by a two parameter class of bessel weightings this class subsumes the i 0 sinh weighting window pair as well as the ideal space factor of van der maas in one dimension the weightings that realize the ideal space factor in 2 and 3 dimensions are generalized functions more singular than the delta function required in 1 dimension

stability of a rectangular plate under nonconservative and conservative forces abstract a study is made of the flutter and divergence instabilities of a rectangular plate with two independent loading parameters the plate is subjected to the combined action of a tangential follower force and a unidirectional axial force along one edge two opposite sides of the plate are simply supported one side being clamped and the other being a free edge where the in plane forces act depending on the relative magnitudes of the follower and axial forces the plate may lose its stability by flutter or divergence the flutter problem is solved by maximizing the flutter load over the frequency and thereby obtaining the maximum point of an eigencurve the stability boundaries are given for plates with different aspect ratios the two dimensional nature of the problem reveals some interesting results not observed in the one dimensional counterpart of the problem which is a cantilevered column under vertical and follower forces the effect of an elastic foundation on the stability boundaries are determined the influence of poisson s ratio on the flutter load and frequency is investigated it is shown that no general rule can be formulated as to the effect of poisson s ratio on the flutter load and that this effect will vary according to the aspect ratio and axial load

accumulation of coefficient roundoff error in fast fourier transforms implemented with logarithmic number system when a fast fourier transform fft is implemented on a digital computer or with special purpose hardware quantization errors will arise due to finite word lengths in the digital system this correspondence presents an analysis of error accumulation due to coefficient rounding in the fft implemented with a logarithmic number system the theoretical result of the coefficient roundoff error analysis is verified by computer simulations the results indicate that the fft implemented with the logarithmic number system provides better signal to noise performance than that implemented with a fixed point or floating point number system

low power logarithmic number system addition subtraction and their impact on digital filters this paper presents techniques for low power addition subtraction in the logarithmic number system lns and quantifies their impact on digital filter vlsi implementation the impact of partitioning the look up tables required for lns addition subtraction on complexity performance and power dissipation of the corresponding circuits is quantified two design parameters are exploited to minimize complexity namely the lns base and the organization of the lns word a roundoff noise model is used to demonstrate the impact of base and word length on the signal to noise ratio of the output of finite impulse response fir filters in addition techniques for the low power implementation of an lns multiply accumulate mac units are investigated furthermore it is shown that the proposed techniques can be extended to cotransformation based circuits that employ interpolators the results are demonstrated by evaluating the power dissipation complexity and performance of several fir filter configurations comprising one two or four mac units simulations of placed and routed vlsi lns based digital filters using a 90 nm 1 0 v cmos standard cell library reveal that significant power dissipation savings are possible by using optimized lns circuits at no performance penalty when compared to linear fixed point two s complement equivalents

testing that a stationary time series is gaussian on propose une classe de procedures pour tester les hypotheses composites selon lesquelles un processus stochastique stationnaire est gaussien

a goodness of fit test based on the empirical characteristic function when parameters must be estimated summary the goodness of fit test using the empirical characteristic function proposed by koutrouvelis 1980 is extended to the case where parameters must be estimated the proposed test statistic is shown to have an asymptotic chi squared distribution with degrees of freedom reduced by the number of parameters estimated

rapidly detecting disorder in rhythmic biological signals a spectral entropy measure to identify cardiac arrhythmias we consider the use of a running measure of power spectrum disorder to distinguish between the normal sinus rhythm of the heart and two forms of cardiac arrhythmia atrial fibrillation and atrial flutter this spectral entropy measure is motivated by characteristic differences in the power spectra of beat timings during the three rhythms we plot patient data derived from ten beat windows on a disorder map and identify rhythm defining ranges in the level and variance of spectral entropy values employing the spectral entropy within an automatic arrhythmia detection algorithm enables the classification of periods of atrial fibrillation from the time series of patients beats when the algorithm is set to identify abnormal rhythms within 6 s it agrees with 85 7 of the annotations of professional rhythm assessors for a response time of 30 s this becomes 89 5 and with 60 s it is 90 3 the algorithm provides a rapid way to detect atrial fibrillation demonstrating usable response times as low as 6 s measures of disorder in the frequency domain have practical significance in a range of biological signals the techniques described in this paper have potential application for the rapid identification of disorder in other rhythmic signals

pipelined computation of very large word length lns addition subtraction with polynomial hardware cost a novel pipelined method is proposed to compute the addition subtraction in very large word length logarithmic number system lns arithmetic digit parallel additive normalization and digit on line multiplicative normalization methods are adopted to compute the exponential and logarithmic functions respectively in lns addition subtraction these two methods can both be implemented in a pipelined and regular architecture the size of the required lookup tables is now proportional to a third order polynomial function instead of an exponential function of the word length the total size of the tables in a 32 bit lns unit is estimated to be less than 53 5 kbits and the total size of the table s in a 64 bit lns unit will be less than 471 kbits furthermore the hardware cost of the other circuits in the proposed lns unit is only proportional to the square of the word length this study also develops a simple leading zero bits prediction technique that can significantly enhance the precision in lns addition subtraction computation when compared to floating point arithmetic design our approach still suffers from large hardware cost and pipeline latency however the proposed approach has provided a theoretical advancement in the development of very large word length lns arithmetic

b spline design of maximally flat and prolate spheroidal type fir filters a digital fir filter is described that offers excellent passband and stopband characteristics for general applications design formulae include parameters that adjust the magnitude response from one having characteristics like the maximally flat designs of hermann 1971 and kaiser 1975 1979 to one having characteristics like the minimum sidelobe energy approximations of kaiser and saramaki 1989 the impulse response coefficients are more straightforward to obtain than these filter designs while offering preferable response characteristics in many instances unlike fir filters designed by window or frequency sampling methods the filter coefficients are determined from the inverse fourier transform in closed form once b splines have been used to replace sharp transition edges of the magnitude response although the filters are developed in the frequency domain a convergence window is identified in the convolution series and compared with windows of popular fir filters by means of example adjustment of the transitional parameter is shown to produce a filter response that rivals the stopband attenuation and transition width of prolate spheroidal designs the design technique is extended to create additional transitional filters from prototype window functions such as the transitional hann window filter the filters are particularly suitable for precision filtering and reconstruction of sampled physiologic and acoustic signals common to the health sciences but will also be useful in other applications requiring low passband and stopband errors

applying features of ieee 754 to sign logarithm arithmetic various features found in standard floating point arithmetic ieee 754 are examined in light of their appropriateness for sign logarithm arithmetic the emphasis is on a 32 b word size comparable to ieee 754 single precision although other word sizes are possible a multilayer sign logarithm format is considered the lowest layer similar to previous implementations would provide only normalized representations but would not provide representations for zero denormalized values infinities and nans the highest layer would provide most of the features found in ieee 754 including zeros denormalized values infinities and nans novel algorithms for implementing logarithmic denormalized arithmetic are presented simulation results show that the error characteristics of the proposed logarithmic denormalized arithmetic algorithms are similar to those of the denormalized floating point arithmetic in ieee 754

the evaluation of the conjugate function of a periodic spline on a uniform mesh abstract we present an o n log n algorithm for the simultaneous evaluation at all n points of a uniform mesh of a function conjugate to a periodic spline the algorithm is based on the attenuation factor theory and makes use of the fft it can be applied to other function classes with known attenuation factors also for the approximation by functions conjugate to splines of odd degree we state several optimality criterions and error bounds

efficient techniques for binary to multidigit multidimensional logarithmic number system conversion using range addressable look up tables the multidimensional logarithmic number system mdlns which has similar properties to the classical logarithmic number system lns provides more degrees of freedom than the lns by virtue of having two or more orthogonal bases and has the ability to use multiple mdlns components or digits unlike the lns there is no monotonic relationship between standard binary representations and mdlns representations using look up tables luts to perform the mapping function can be unrealistic for hardware implementations when large binary ranges or multiple digits are used this work proposes a novel range addressable technique for using look up tables that allows efficient conversion from binary to single or multidigit mdlns with varying accuracies depending on the selected implementation

detection of multiplicative noise in stationary random processes using second and higher order statistics this paper addresses the problem of detecting the presence of colored multiplicative noise when the information process can be modeled as a parametric arma process for the case of zero mean multiplicative noise a cumulant based suboptimal detector is studied this detector tests the nullity of a specific cumulant slice a second detector is developed when the multiplicative noise is nonzero mean this detector consists of filtering the data by an estimated ar filter cumulants of the residual data are then shown to be well suited to the detection problem theoretical expressions for the asymptotic probability of detection are given simulation derived finite sample roc curves are shown for different sets of model parameters

improving accuracy in mitchell s logarithmic multiplication using operand decomposition logarithmic number systems lns offer a viable alternative in terms of area delay and power to binary number systems for implementing multiplication and division operations for applications in signal processing the mitchell algorithm ma proposed reduces the complexity of finding the logarithms and the antilogarithms using piecewise straight line approximations of the logarithm and the antilogarithm curves the approximations however result in some loss of accuracy thus several methods have been proposed in the literature for improving the accuracy of mitchell s algorithm in this work we investigate a new method based on operand decomposition od to improve the accuracy of mitchell s algorithm when applied to logarithmic multiplication in the od technique proposed for reducing the amount of switching activity in binary multiplication the two inputs to be multiplied are together decomposed into four binary operands and the product is expressed as the sum of the products of the decomposed numbers we show that applying operand decomposition to the inputs as a preprocessing step to mitchell s multiplication algorithm significantly improves the accuracy experimental results indicate that the proposed algorithm for logarithmic multiplication reduces the error percentage of mitchell s algorithm by 44 7 percent on the average it is also shown that the od method yields further improvement when combined with the other correction methods proposed in the literature

delayed block transfer function in the frequency domain when the impulse response of a transfer system is long it is difficult for the standard cross spectrum method to obtain an accurate estimate of the transfer function by applying the fast fourier transform fft with a finite length window the bias error in the estimate is large especially around the resonant frequency of the transfer system in the paper therefore the authors propose an alternative new method to obtain an accurate estimate of the transfer function the delayed block transfer function is introduced to detect the components that are correlated to the signal in the input window but leak from the output window based on these transfer functions the total characteristics of the transfer system are estimated accurately in the latter half of the paper the authors derive the theoretical expressions for the bias errors in the transfer functions estimated by the proposed and the standard methods by thoroughly comparing the resultant expressions the superiority and the usefulness of the proposed method are theoretically confirmed finally the simulation experiments show the advantages of the proposed method

arithmetic co transformations in the real and complex logarithmic number systems the real logarithmic number system which represents a value with a sign bit and a quantized logarithm can be generalized to create the complex logarithmic number system which replaces the sign bit with a quantized angle in a log polar coordinate system although multiplication and related operations are easy in both real and complex systems addition and subtraction are hard especially when interpolation is used to implement the system both real and complex logarithmic arithmetic benefit from the use of co transformation which converts an addition or subtraction from a region where interpolation is expensive to a region where it is easier two co transformations that accomplish this goal are introduced the first is an approximation based on real analysis of the subtraction logarithm the second is based on simple algebra that applies for both real and complex values and that works for both addition and subtraction

the gridding method for image reconstruction by fourier transformation the authors explore a computational method for reconstructing an n dimensional signal f from a sampled version of its fourier transform f spl circ the method involves a window function w spl circ and proceeds in three steps first the convolution g spl circ w spl circ f spl circ is computed numerically on a cartesian grid using the available samples of f spl circ then g wf is computed via the inverse discrete fourier transform and finally f is obtained as g w due to the smoothing effect of the convolution evaluating w spl circ f spl circ is much less error prone than merely interpolating f spl circ the method was originally devised for image reconstruction in radio astronomy but is actually applicable to a broad range of reconstructive imaging methods including magnetic resonance imaging and computed tomography in particular it provides a fast and accurate alternative to the filtered backprojection the basic method has several variants with other applications such as the equidistant resampling of arbitrarily sampled signals or the fast computation of the radon hough transform

windows with rapidly decaying sidelobes and steerable sidelobe dips a window in the form of a sum of cosine terms is considered and the temporal weights are evaluated analytically so that it can have rapidly decaying sidelobes as well as steerable sidelobe dips an analytic expression is derived so that the window designer can exploit the trade off between a high sidelobe falloff rate slfor and many steerable sidelobe dips ssld the treatment is based on using the l degrees of freedom inherent in the l temporal weights of the l 1 term window in partially achieving the goals of a high slfor and many ssld in the extreme case where all degrees of freedom are used in achieving the maximum slfor a simple closed form expression is derived for the temporal weights thus formalizing and generalizing the results of nuttall 1981 the other extreme case where all degrees of freedom are used in creating many ssld has been recently treated by zhong et al see ibid vol 40 no 6 p 1452 1459 1992 combining both desired features in one unified mathematical framework is the main objective of this paper simulation results demonstrate the superior performance of a window having both features to that of a window having only one feature in extracting a weak sinusoidal signal dominated by a leakage from another stronger signal

design of windows with steerable sidelobe dips based on the frequency sampling method a novel and simple window design technique was established upon three theorems the technique produces a set of windows which have simple expressions and the steerable sidelobe dip ssld property by steering the dips in the sidelobes it is easy to reduce the edge of the mainlobe or to minimize the height of sidelobes or to create a hole in the sidelobes if its desired to reduce spectral leakage at a particular frequency it is found that windows constructed as a weighted sum of cosines over a finite support and with a 6 db oct sidelobe falloff rate can all be simulated by appropriate ssld distributions in this sense many good windows such as hamming blackman blackman harris and minimum sidelobe behaviors can be created with a minor constraint this renders design flexibility for various applications finally the new technique can be easily incorporated with other techniques to produce windows with hybrid merits

sign logarithm arithmetic for fft implementation sign logarithm arithmetic is applicable to a variety of numerical applications where wide dynamic range and small wordsize are required in this paper the basic sign logarithm arithmetic operations required for signal processing i e addition subtraction and multiplication are reviewed the computational errors are analyzed for fft realization and simulation results are presented which serve to verify the analysis it is shown that the sign logarithm approach provides improved arithmetic quantization error performance for a given word size over fft s implemented with conventional fixed or floating point arithmetic and that the sign logarithm implementation is faster and less complex than conventional approaches

a unified approach to nonparametric spectrum estimation algorithms different approaches to spectrum estimation can be broadly classified as parametric and nonparametric methods in the parametric techniques an underlying model is assumed in the formulation of the spectrum estimation problem and one estimates the parameters of the model for nonparametric methods no such model is assumed in this paper several nonparametric spectrum estimation algorithms are brought under a unified framework by the introduction of a generalized nonparametric spectrum estimation algorithm a four stage approach is employed it contains as special cases the blackman tukey algorithm the weighted overlapped segment averaging wosa method the lag reshape approach rader s algorithm and the short time unbiased spectrum estimation stuse algorithm the framework proposed in the paper is more general than the one recently proposed by nuttall and carter theoretical expressions for the spectrum estimation variance of the generalized algorithm are derived and then verified via simulation example also several nonparametric approaches for obtaining unbiased spectrum estimates are discussed and compared finally we conclude the paper with a brief discussion of the applicability and usefulness of several methods in specific situations

interleaved memory function interpolators with application to an accurate lns arithmetic unit this paper describes a new method for polynomial interpolation in hardware with advantages demonstrated by its application to an accurate logarithmic number system lns arithmetic unit the use of an interleaved memory reduces storage requirements by allowing each stored function value to be used in interpolation across several segments this strategy can be shown to always use fewer words of memory than an optimized polynomial with stored polynomial coefficients interleaved memory function interpolators are then applied to the specific goal of an accurate logarithmic number system arithmetic unit many accuracy requirements for the lns arithmetic unit are possible although a round to nearest would be desirable it cannot be easily achieved the goal suggested is to insure that the worst case lns relative error is smaller than the worst case floating point fp relative error using the interleaved memory interpolator the detailed design of an lns arithmetic unit is performed using a second order polynomial interpolator including approximately 91k bits of rom this arithmetic unit has better accuracy and less complexity than previous lns units

integrated circuit logarithmic arithmetic units this correspondence examines integrated circuit logarithmic arithmetic units which include adders subtracters multipliers and dividers the design of these arithmetic units is reviewed and an example arithmetic unit which performs multiplication followed by addition is designed in detail the design results are used to develop a size and speed comparison of integrated circuit logarithmic and fixed point arithmetic units this comparison is exercised through a video signal processing example it is concluded from this comparison that logarithmic arithmetic units are smaller than and as fast as fixed point arithmetic units with comparable capabilities in digital signal processing applications characterized by large dynamic range and moderate computational accuracy requirements further this comparison quantitatively illustrates the interaction of digital signal processing and integrated circuit issues in the design of special purpose digital signal processors

an efficient multiscale method for time domain waveform tomography this efficient multiscale method for time domain waveform tomography incorporates filters that are more efficient than hamming window filters a strategy for choosing optimal frequency bands is proposed to achieve computational efficiency in the time domain a staggered grid explicit finite difference method with fourth order accuracy in space and second order accuracy in time is used for forward modeling and the adjoint calculation the adjoint method is utilized in inverting for an efficient computation of the gradient directions in the multiscale approach multifrequency data and multiple grid sizes are used to overcome somewhat the severe local minima problem of waveform tomography the method is applied successfully to 1d and 2d heterogeneous models it can accurately recover low and high wavenumber components of the velocity models the inversion result for the 2d model demonstrates that the multiscale method is computationally efficient and converges faster than a conventional single scale method

the synchronized short time fourier transform properties and definitions for multichannel source separation this paper proposes the use of a synchronized linear transform the synchronized short time fourier transform sstft for time frequency analysis of anechoic mixtures we address the short comings of the commonly used time frequency linear transform in multichannel settings namely the classical short time fourier transform cstft we propose a series of desirable properties for the linear transform used in a multichannel source separation scenario stationary invertibility relative delay relative attenuation and finally delay invariant relative windowed disjoint orthogonality dirwdo multisensor source separation techniques which operate in the time frequency domain have an inherent error unless consideration is given to the multichannel properties proposed in this paper the sstft preserves these relationships for multichannel data the crucial innovation of the sstft is to locally synchronize the analysis to the observations as opposed to a global clock improvement in separation performance can be achieved because assumed properties of the time frequency transform are satisfied when it is appropriately synchronized numerical experiments show the sstft improves instantaneous subsample relative parameter estimation in low noise conditions and achieves good synthesis

an efficient fourier method for 3 d radon inversion in exact cone beam ct reconstruction the radial derivative of the three dimensional 3 d radon transform of an object is an important intermediate result in many analytically exact cone beam reconstruction algorithms the authors briefly review grangeat s 1991 approach for calculating radon derivative data from cone beam projections and then present a new efficient method for 3 d radon inversion i e reconstruction of the image from the radial derivative of the 3 d radon transform called direct fourier inversion dfi the method is based directly on the 3 d fourier slice theorem from the 3 d radon derivative data which is assumed to be sampled on a spherical grid the 3 d fourier transform of the object is calculated by performing fast fourier transforms ffts along radial lines in the radon space then an interpolation is performed from the spherical to a cartesian grid using a 3 d gridding step in the frequency domain finally this 3 d fourier transform is transformed back to the spatial domain via 3 d inverse fft the algorithm is computationally efficient with complexity in the order of n sup 3 log n the authors have done reconstructions of simulated 3 d radon derivative data assuming sampling conditions and image quality requirements similar to those in medical computed tomography ct

dynamic stability of a non conservative viscoelastic rectangular plate abstract based on the thin plate theory and the two dimensional 2d viscoelastic differential constitutive relation the differential equation of motion of the viscoelastic rectangular plate subjected to uniformly distributed tangential follower force in laplace domain is deduced the equation is suitable for various viscoelastic models of differential type the differential equation of motion of the viscoelastic plate constituted by the kelvin voigt model under the action of uniformly distributed tangential follower force in time domain is also derived the generalized eigenequations of non conservative viscoelastic rectangular plate with four edges simply supported two opposite edges simply supported and other two edges clamped are established by the differential quadrature method and the curves of real parts and imaginary parts of the first three order dimensionless complex frequencies vs uniformly distributed tangential follower force are obtained the factors influencing the dynamic stability of the visoelastic rectangular plate are discussed

dithering and its effects on sigma delta and multistage sigma delta modulation the spectrum of the quantization error in a dithered sigma delta modulator is derived under the constraint that the dithering signal does not cause overload the results apply to dc sinusoidal and more general quasi stationary signals it is shown in the case of a simple sigma delta modulation that no overload dithering can smooth the error spectrum and can make the quantization error asymptotically uncorrelated with the input it does not however make the quantization error white in the case of multistage sigma delta modulation with the appropriate dithering the quantization error becomes white even for a system with only two stages the signal to quantization noise ratio sqnr is derived for sigma delta and multistage sigma delta oversampled analog to digital conversion with additive dithering simulation results are presented to support the theoretical analysis

bootstrapping bispectra an application to testing for departure from gaussianity of stationary signals we propose a bootstrap version of a bispectrum based test for departure from gaussianity that achieves high power while maintaining the level of significance even for small sample sizes the proposed procedure can be also used to set confidence bands for a measure of the bicoherence of stationary random signals

a new window and comparison to standard windows a new window w t 0 62 0 48 mod t mod 0 38 cos 2 pi t mod t mod or 1 2 is introduced it is shown that the window is of a group with similar but different tradeoff properties with the bartlett the hanning and the hamming windows the proposed window is more effective than the bartlett and the hanning in the near sidelobes and more effective than the bartlett and the hamming in the far sidelobes