symmetries of the kadomtsev petviashvili equation generalized symmetries with arbitrary functions of time t for the well known 2 1 dimensional integrable model kadomtsev petviashvili kp equation are found by means of the extended mastersymmetry approach then an explicit and simple constructive formula for the symmetries of the kp equation is derived directly from the symmetry definition equation without using complicated recursion operators all the known symmetries appear as special cases of those obtained in this paper the general infinite dimensional lie algebra constituted by these symmetries is also given

reply to comment on invariants of differential equations defined by vector fields we undertook the determination of fundamental sets of invariants for differential equations defined by vector fields in a recent paper using the equivariant moving frame method a more exhaustive list for these invariants was found in a subsequent comment by francis valiquette we reply to that paper and point out some essential inconsistencies in the comment

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

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

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

infinitely many lax pairs and symmetry constraints of the kp equation starting from a known lax pair one can get some infinitely many coupled lax pairs infinitely many nonlocal symmetries and infinitely many new integrable models in some different ways in this paper taking the well known kadomtsev petviashvili kp equation as a special example we show that infinitely many nonhomogeneous linear lax pairs can be obtained by using infinitely many symmetries differentiating the spectral functions with respect to the inner parameters using a known lax pair and the darboux transformations dt infinitely many nonhomogeneous nonlinear lax pairs can also be obtained by means of the infinitely many lax pairs dt and the conformal invariance of the schwartz form of the kp equation infinitely many new nonlocal symmetries can be obtained naturally infinitely many integrable models in 1 1 dimensions 2 1 dimensions 3 1 dimensions and even in higher dimensions can be obtained by virtue of symmetry constraints of the kp equation related to the infinitely many lax pairs

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

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

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

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

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 method for the equivalence group and its infinitesimal generators we give an effective method for the systematic determination of the equivalence group for any family of differential equations and for the determination of the infinitesimal generators of this group this is achieved by viewing the equivalence group as a projected subgroup related to the full symmetry group of the equation in which the coefficients specifying the family element in the equation are also considered as dependent variables the method is extended to provide the exact number of fundamental invariants of the equation without any prior calculation of these invariants it is then applied to review a number of results obtained in the recent literature on the subject of invariant functions of differential equations the method is also applied probably for the first time to a case of nonlinear equation

on spinor vertex operator algebras and their modules abstract in this paper we first present a generator theorem and introduce an asymmetric tensor of two colored vertex operator superalgebras with the same grading and supermap then we give axioms which characterize a class of vertex operator superalgebras constructed from clifford algebras in particular we are able to give a shorter argument for the jacobi identity than the existing proofs by using elements analogous to coherent states and our generator theorem using the new tensor and the same techniques we classify twisted irreducible modules of these algebras in a constructive way

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

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

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

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

invariants of a semi direct sum of lie algebras we show that any semi direct sum l of lie algebras with levi factor s must be perfect if the representation associated with it does not possess a copy of the trivial representation as a consequence all invariant functions of l must be casimir operators when the number of invariants is given for all possible dimensions of l replacing the traditional method of solving the system of determining pdes by the equivalent problem of solving a system of total differential equations the invariants are found for all dimensions of the radical up to 5 an analysis of the results obtained is made and this leads to a theorem on invariants of lie algebras depending only on the elements of certain subalgebras

symmetry reduction for the kadomtsev petviashvili equation using a loop algebra the kadomtsev petviashvili kp equation ut 3uux 2 1 4 uxxx x 3 uyy 4 0 allows an infinite dimensional lie group of symmetries i e a group transforming solutions amongst each other the lie algebra of this symmetry group depends on three arbitrary functions of time t and is shown to be related to a subalgebra of the loop algebra a 1 4 low dimensional subalgebras of the symmetry algebra are identified specifically all those of dimension n 3 and also a physically important six dimensional lie algebra containing translations dilations galilei transformations and quasirotations new solutions of the kp equation are obtained by symmetry reduction using the one dimensional subalgebras of the symmetry algebra these solutions contain up to three arbitrary functions of t

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

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

a characterization of vertex algebras associated to even lattices abstract we give a characterization of vertex algebras associated to even lattices by classifying a certain class of simple vertex algebras

comment on invariants of differential equations defined by vector fields in ndogmo 2008 j phys a math theor 41 025207 the author claims to have determined a complete list of functionally independent differential invariants up to order 2 for the equivalence group of differential equations defined by vector fields when there are two and three independent variables in this comment we show that this is not the case using the equivariant moving frame method we derive a complete set of functionally independent differential invariants of orders 1 and 2 for an arbitrary number n 2 of independent variables in the particular case n 2 we obtain six functionally independent invariants two of which were not found in ndogmo 2008 j phys a math theor 41 025207 in the case n 3 we get 21 functionally independent invariants six of which are new we also give a complete classification of the differential invariants

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

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

invariants of differential equations defined by vector fields we determine the most general group of equivalence transformations for a family of differential equations defined by an arbitrary vector field on a manifold we also find all invariants and differential invariants for this group up to the second order a result on the characterization of classes of these equations by the invariant functions is also given

differential invariant algebras of lie pseudo groups abstract the aim of this paper is to describe in as much detail as possible and constructively the structure of the algebra of differential invariants of a lie pseudo group acting on the submanifolds of an analytic manifold under the assumption of local freeness of a suitably high order prolongation of the pseudo group action we develop computational algorithms for locating a finite generating set of differential invariants a complete system of recurrence relations for the differentiated invariants and a finite system of generating differential syzygies among the generating differential invariants in particular if the pseudo group acts transitively on the base manifold then the algebra of differential invariants is shown to form a rational differential algebra with non commuting derivations the essential features of the differential invariant algebra are prescribed by a pair of commutative algebraic modules the usual symbol module associated with the infinitesimal determining system of the pseudo group and a new prolonged symbol module constructed from the symbols of the annihilators of the prolonged pseudo group generators modulo low order complications the generating differential invariants and differential syzygies are in one to one correspondence with the algebraic generators and syzygies of an invariantized version of the prolonged symbol module our algorithms and proofs are all constructive and rely on combining the moving frame approach developed in earlier papers with grobner basis algorithms from commutative algebra

on twisted representations of vertex algebras abstract in this paper we develop a formalism for working with representations of vertex and conformal algebras by generalized fields formal power series involving non integer powers of the variable the main application of our technique is the construction of a large family of representations for the vertex superalgebra v corresponding to an integer lattice for an automorphism v v coming from a finite order automorphism we find the conditions for existence of twisted modules of v we show that the category of twisted representations of v is semisimple with finitely many isomorphism classes of simple objects

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

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

maurer cartan equations for lie symmetry pseudogroups of differential equations a new method of constructing structure equations of lie symmetry pseudogroups of differential equations dispensing with explicit solutions of the infinitesimal determining systems of the pseudogroups is presented and illustrated by the examples of the kadomtsev petviashvili and korteweg de vries equations

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

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

equations of arbitrary order invariant under the kadomtsev petviashvili symmetry group by means of a simple new approach a general kadomtsev petviashvili kp family with an arbitrary function of group invariants of arbitrary order is proposed it is proved that the general kp family possesses a common infinite dimensional kac moody virasoro lie point symmetry algebra the known fourth order one can be re obtained as a special example the finite transformation group is presented in a clearer form the kac moody virasoro group invariant solutions and the kac moody group invariant solutions of the kp family are determined by the boussinesq and kdv families respectively

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

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