design of arbitrary fir log filters by weighted least squares technique an efficient method to design fir filters with arbitrary log magnitude and phase responses is proposed the method is based on an iterative weighted least squares wls approach to obtain a nearly optimal approximation to the given log magnitude function in the least squares sense the weighting function at each iteration is updated using the result of the previous iteration which leads to an equiripple approximation in the log magnitude error the method can be easily modified to approximate arbitrary log complex valued frequency response such as complex fir log filters several examples are illustrated to show the effectiveness of the present approach

some results in the theory of crosstalk free transmultiplexers the crosstalk free transmultiplexer cf tmux focuses on crosstalk cancellation cc rather than on suppressing it the authors present an analysis of the cf tmux based on the polyphase component matrices of the filter banks used in tdm to fdm and fdm to tdm conversions respectively thus a necessary and sufficient condition for complete cc is obtained it is shown that the filters for a cf tmux are the same as the filters for a 1 skewed alias free qmf bank in addition if the qmf bank satisfies the perfect reconstruction pr property then the tmux also satisfies pr the relation between cf tmux filters and alias free qmf banks is used to obtain a direct design procedure for cf tmux filters both fir and iir it is also shown that approximately crosstalk free tmux filters can be obtained from any approximately alias free qmc bank design examples and comparison tables are included

an extension of the split levinson algorithm and its relatives to the joint process estimation problem it is shown that the split levinson algorithm the split schur algorithm and the split lattice algorithm to compute the reflection coefficients of the optimal linear prediction filter for a discrete time stationary stochastic process can be extended to the more general case of the joint process estimation problem the new algorithms are essentially based on well defined recurrence relations for symmetric prediction filters and symmetric estimation filters they are more economical than the standard methods in terms of storage space and number of arithmetic operations

second order sensitivity derivatives in structural analysis haug s 1981 expressions for the calculation of static constraint function second derivatives have resulted in an order of magnitude saving over conventional methods for the calculation of such derivatives a similar but simplified procedure is presented which results in a reduction of computational cost by an additional factor of two the results are presented in a notation that is different from that of haug but more common in other work on structural synthesis and analysis

pseudo qmf banks with near equiripple performance a novel method using the parks mcclellan equiripple design procedure obtains a linear phase spectral factor of an equiripple approximate 2mth band lowpass filter this filter which is an equiripple prototype of an m channel pseudo qmf bank is modified to make it a closer approximation of a linear phase spectral factor of a 2mth band filter reducing the maximum overall reconstruction error to the order of the stopband ripple while slightly compromising equiripple performance

efficient implementation of nearly perfect reconstruction fir cosine modulated filterbanks in this paper a new fast implementation of nearly perfect reconstruction finite impulse response fir cosine modulated filterbanks is shown a new expression for the analysis bank has been developed and based on it an efficient implementation structure is obtained for specific prototype filter lengths the new computationally efficient algorithm can be applied to both the conventional cosine modulated filterbank and the koilpillai vaidyanathan pseudo quadrature mirror filterbank we also show how the implementation cost measured in multiplications and additions per input sample is reduced

performance of svd based fractionally spaced equalizers in data transmission systems an algorithm is presented for implementing a complex fractionally spaced equalizer cfse that uses the least mean square lms algorithm and singular value decomposition svd svd is used to reduce the eigenvalue spread of the autocorrelation matrix of the cfse tap inputs it is shown that svd accelerates the convergence of the cfse in proportion to the receiver oversampling factor but maintains the steady state excess mean square error mse at approximately the same level as that of the cfse that does not have an svd based receiver prefilter the authors choice of a prefilter from the autocorrelation matrix of the received signal will facilitate easier and faster tracking of the principal components in an adaptive environment

on linear prediction models constrained to have unit modulus poles and their use for sinusoidal frequency estimation linear prediction models with their poles restricted to the unit circle can be efficiently determined by using the levinson or the split levinson algorithm a simple proof of this property is presented the prime application of linear prediction models constrained to have unit modulus poles is the estimation of sinusoidal frequencies the consistency properties of the corresponding frequency estimates are analyzed it is shown that in the presence of noise the estimates are inconsistent an explicit expression for the asymptotic bias is provided

discrete all pole modeling a method for parametric modeling and spectral envelopes when only a discrete set of spectral points is given is introduced this method called discrete all pole dap modeling uses a discrete version of the itakura saito distortion measure as its error criterion one result is an autocorrelation matching condition that overcomes the limitations of linear prediction and produces better fitting spectral envelopes for spectra that are representable by a relatively small discrete set of values such as in voiced speech an iterative algorithm for dap modeling that is shown to converge to a unique global minimum is presented results of applying dap modeling to real and synthetic speech are also presented dap modeling is extended to allow frequency dependent weighting of the error measure so that spectral accuracy can be enhanced in certain frequency regions

sensitivity of human subjects to head related transfer function phase spectra head related transfer functions hrtfs for human subjects in anechoic space were modeled with modified phase spectra including minimum phase plus delay linear phase and reversed phase plus delay functions the overall wide band interaural time delay itd for the modeled hrtfs was made consistent with that of the empirical hrtfs by setting the position dependent frequency independent delay in the hrtf for the lagging ear signal analysis of the minimum phase plus delay reconstructions indicated that model hrtfs deviate from empirical hrtf measurements maximally for contralateral azimuths and low elevations subjects assessed the perceptual validity of the model hrtfs in a four interval two alternative forced choice discrimination paradigm results indicate that monaural discrimination performance of subjects was at chance for all three types of hrtf models binaural discrimination performance was at chance for the linear phase hrtfs was above chance for some locations for the minimum phase plus delay hrtfs and was above chance for all tested locations for the reversed phase plus delay hrtfs an analysis of low frequency timing information showed that all of these results are consistent with efficient use of interaural time differences in the low frequency components of the stimulus waveforms it is concluded that listeners are insensitive to hrtf phase spectra as long as the overall itd of the low frequency components does not provide a reliable cue in particular the minimum phase plus delay approximation to the hrtf phase spectrum is an adequate approximation as long as the low frequency itd is appropriate these results and conclusions are all limited to the anechoic case when the hrtfs correspond to brief impulse responses limited to a few milliseconds

new family of modal methods for calculating eigenvector derivatives a new family of modal methods for the calculation of eigenvector derivatives in non sell adjoint systems with a singular coefficient matrix is developed the family contains the modal and modified modal methods as a subset in the family the component of the mth eigenvector in the expansion of the derivative of the jth eigenvector is multiplied by various powers of the eigenvalue ratio j m thereby accelerating convergence the family of methods is applied to a sell adjoint example problem namely a cantilever beam whose root depth is used as the design variable to which the sensitivity of the first four mode shapes is sought

on the design of pole zero approximations using a logarithmic error measure for obtaining a pole zero approximation of a linear discrete time system a new method is presented which minimizes the squared difference between the log magnitude spectrum of the system and that of the approximation using an iterative procedure a locally optimal solution is found for the poles and zeros of the system approximation

a note on minimizing the prediction error when the zeros are restricted to the unit circle it is shown that the problem of minimizing the prediction error under the constraint that the zeros of the predictor polynomial be on the unit circle can be solved by using a modification of the levinson algorithm consequences of this result are discussed

dynamic response sensitivity of inelastic structures abstract a general finite element solution method for the dynamic response sensitivity of inelastic structures is developed employing a direct differentiation method the gradient equation of motion is solved without iteration and by taking advantage of the available solution of the response special attention is given to sensitivities with respect to inelastic material parameters and detailed derivations are made for the j 2 plasticity model with a linear hardening rule the method can be applied to any other inelastic material model that has an analytically defined yield function and flow rule the formulation is easily incorporated in existing finite element codes numerical examples demonstrate the accuracy and efficiency of the method

a lattice algorithm for factoring the spectrum of a moving average process triangular decomposition of the semi infinite covariance matrix of a moving average process can be used as a spectral factorization technique an efficient lattice algorithm is derived for performing the necessary computations this technique is a special case of the fast cholesky decomposition of stationary covariance matrices the algorithm can be used to factor multichannel spectra to a desired degree of accuracy

efficient design of high complexity cosine modulated filter banks using 2 m th band conditions this paper presents several new properties of biorthogonal cosine modulated filter banks cmfbs and efficient algorithms for designing cmfbs with a very large number of subbands and very long filters for a biorthogonal cmfb we find the periodicity and symmetry of its overall transfer function and aliasing transfer functions which can be efficiently computed based on a decimated uniform discrete fourier transform dft analysis filter bank by exploiting gradient information and 2m th band conditions efficient algorithms are proposed for designing both orthogonal and biorthogonal cmfbs in addition an efficient matrix inversion algorithm with o n 2 complexity is also presented several numerical examples and comparisons with many other existing methods are included to demonstrate the design performance and efficiency of the algorithms

on model reduction of discrete time systems abstract in this paper further justification of model reduction by badreddin mansour s method is presented in particular connections between polynomial root location properties coefficient properties and schur cohn coefficient properties are established lattice realizations of a discrete system and its reduced model are given which illustrate certain relationships between the original model and its reduced form these relationships give insight into the validity of the method of reduction and offer insight on the order of approximation

design of recursive group delay filters by autoregressive modeling a new method of design of recursive group delay filters is presented in this paper the method uses autoregressive modeling to derive parameters of the filter the design is based on the following line of argument the desired group delay characteristics are to be realized through a stable all pass filter the transfer function of an all pass filter is completely determined by the coefficients of either the numerator or the denominator polynomial for a stable all pass filter the denominator polynomial must be a minimum phase polynomial for a minimum phase polynomial the magnitude function and the group delay function are related through cepstral coefficients therefore from the given group delay specification the cepstral coefficients corresponding to the pole part inverse of the denominator polynomial of the desired filter are first determined the magnitude spectrum corresponding to these cepstral coefficients is approximated using autoregressive modeling a wide variety of group delay filters can be realized by the proposed method depending on the nature of approximation used and the accuracy desired the design procedure is illustrated through examples

efficient design of cosine modulated filter banks via convex optimization this paper presents efficient approaches for designing cosine modulated filter banks with linear phase prototype filter first we show that the design problem of the prototype filter being a spectral factor of 2m th band filter is a nonconvex optimization problem with low degree of nonconvexity as a result the nonconvex optimization problem can be cast into a semi definite programming sdp problem by a convex relaxation technique then the reconstruction error is further minimized by an efficient iterative algorithm in which the closed form expression is given in each iteration several examples are given to illustrate the effectiveness of the proposed method over the existing ones

design of pseudo qmf banks with rational sampling factors using several prototype filters a method is presented for designing filter banks that allow the spectrum of a signal to be split into nonuniform width subbands the filters of the banks are obtained by the cosine modulation of more than one prototype the method uses the cancellation of the main aliasing component of the reconstructed signal this imposes constraints on the prototypes that become dependent on each other the procedure can be applied to banks with both integer and rational decimation factors numerical examples are presented to show the effectiveness of the design procedure

speech enhancement using a minimum mean square error short time spectral amplitude estimator this paper focuses on the class of speech enhancement systems which capitalize on the major importance of the short time spectral amplitude stsa of the speech signal in its perception a system which utilizes a minimum mean square error mmse stsa estimator is proposed and then compared with other widely used systems which are based on wiener filtering and the spectral subtraction algorithm in this paper we derive the mmse stsa estimator based on modeling speech and noise spectral components as statistically independent gaussian random variables we analyze the performance of the proposed stsa estimator and compare it with a stsa estimator derived from the wiener estimator we also examine the mmse stsa estimator under uncertainty of signal presence in the noisy observations in constructing the enhanced signal the mmse stsa estimator is combined with the complex exponential of the noisy phase it is shown here that the latter is the mmse estimator of the complex exponential of the original phase which does not affect the stsa estimation the proposed approach results in a significant reduction of the noise and provides enhanced speech with colorless residual noise the complexity of the proposed algorithm is approximately that of other systems in the discussed class

a weighted least squares method for the design of stable 1 d and 2 d iir digital filters we present a new approach to the least squares design of stable infinite impulse response iir digital filters the design is accomplished by using an iterative scheme in which the denominator polynomial obtained from the preceding iteration is treated as a part of the weighting function and each iteration is carried out by solving a standard quadratic programming problem that yields a stable rational function when the iteration converges a stable and truly least squares solution is obtained the method is then extended to address the least squares design of stable iir two dimensional 2 d filters examples are included to illustrate the proposed design techniques

on the cocharacter sequence of 3 3 matrices abstract let m 3 f be the algebra of 3 3 matrices with involution over a field f of characteristic zero we study the polynomial identities of m 3 f where t is the transpose involution through the representation theory of the hyperoctahedral group b n after decomposing the space of multilinear polynomial identities of degree n under the b n action we determine which irreducible b n modules appear with non zero multiplicity in symbols we write the nth cocharacter n m 3 f r 0 n r h 6 n r h 3 m where and are partitions of r and n r respectively is the irreducible b n character associated to the pair and m 0 is the corresponding multiplicity we prove that for any n the multiplicities m are always non zero except the trivial case 1 6 and

a formal inverse to the cayley hamilton theorem abstract we prove that a q algebra r with formal trace can be realized as n n matrices if and only if it satisfies the cayley hamilton identity of degree n

eigenvalue eigenvector sensitivity analysis of linear time invariant singular systems this note refers to the eigenvalue eigenvector sensitivity analysis of linear time invariant multivariable singular systems procedures that can be easily programmed on a digital computer are presented for the determination of the deviation of the eigenvalues and the corresponding right and left eigenvectors which are caused by the system s parameter changes about their nominal values the method is illustrated by two examples

statistics of complex eigenvalues in friction induced vibration abstract self excited vibrations appear in many mechanical systems with sliding contacts there are several mechanisms whereby friction can cause the self excited vibration to become unstable of these mechanisms mode coupling is thought to be responsible for generating annoying high frequency noise and vibration in brakes conventionally in order to identify whether a system is stable or not complex eigenvalue analysis is performed however what has recently received much attention of researchers is the variability and uncertainty of input variables in the stability analysis of self excited vibrations for this purpose a second order perturbation method is extended and employed in the current study the moments of the output distribution along with its joint moment generating function are used for quantifying the statistics of the complex eigenvalues moreover the eigen derivatives required for the perturbation method are presented in a way that they can deal with the asymmetry of the stiffness matrix and non proportional damping since the eigen derivatives of such systems are complex valued numbers it is mathematically more informative and convenient to derive the statistics of the eigenvalues in a complex form without decomposing them into two real valued real and imaginary parts then the variance and pseudo variance of the complex eigenvalues are used for determining the statistics of the real and imaginary parts the reliability and robustness of the system in terms of stability can also be quantified by the approximated output distribution

an exact recursion for the composite nearest neighbor degeneracy for a 2 n lattice space a set theoretic argument is utilized to develop a recursion relation that yields exactly the composite nearest neighbor degeneracy for simple indistinguishable particles distributed on a 2 n lattice space the associated generating functions as well as the expectation of the resulting statistics are also treated

matrix algebras with involution and standard polynomial identities in symmetric variables abstract let m be a positive integer and m 2 m f be the algebra of 2 m 2 m matrices over an algebraically closed field of characteristic zero f endowed with the transpose or the symplectic involution in this paper we construct a basis b of m 2 m f over f such that b is a group whose elements are symmetric or skew with respect to the given involution moreover all elements of this basis commute or anti commute among themselves the construction is based on a specific irreducible representation of b an extra special 2 group as an application this basis solves the problem on finding the minimal degree of a standard polynomial identity in symmetric variables of m 2 m f s where s is the symplectic involution

solution and sensitivity analysis of a complex transcendental eigenproblem with pairs of real eigenvalues this paper considers complex transcendental eigenvalue problems where one is interested in pairs of eigenvalues that are restricted to take real values only such eigenvalue problems arise in dynamic stability analysis of non conservative physical systems flutter analysis of aeroelastic systems to name one example some available solution methods are discussed and a new method is presented two computational approaches are described for analytical evaluation of the sensitivities of these eigenvalues when they are dependent on other parameters the algorithms presented are illustrated through examples

design of linear phase iir filters from fir specifications a simple method is presented for the characterization of a stable iir filter matching a finite portion of the impulse response and autocorrelation coefficients of a given fir filter it is shown that the problem is reduced to the solution of a set of linear equations derived using the impulse response and autocorrelation data the method is characterized by its computational simplicity and is illustrated by some examples to show its superior performance when compared to the existing methods

the poles of symmetric linear prediction models lie on the unit circle symmetric linear prediction models have their poles on the unit circle a simple proof of this result is presented

sensitivity analysis for problems of dynamic stability abstract in mechanics as well as in physics the most general and important thing is to study the dependence of the characteristics of a physical process on problem parameters problems of dynamic stability for non conservative systems involve determination of eigenvalues and eigenvectors for these problems it is shown in general how the different sensitivity analyses can be performed without any new eigenvalue analyses the main question relates to the change in flutter load as a function of change in stiffness mass boundary conditions or load distribution discretized as well as non discretized examples are presented in details

model reduction of digital systems using discrete walsh series this study discusses the application of discrete walsh series expansion to reduce the order of a linear time invariant digital system described by z transfer function the approach is based on matching the discrete walsh spectra to determine both the coefficients of the denominator and numerator of the reduced model the proposed method is simple for computation can preserve the dynamic characteristic of the original model satisfactorily and guarantees to have the same zero initial response as the original system

a weighted least squares algorithm for quasi equiripple fir and iir digital filter design it has been demonstrated by several authors that if a suitable frequency response weighting function is used in the design of a finite impulse response fir filter the weighted least squares solution is equiripple the crux of the problem lies in the determination of the necessary least squares frequency response weighting function a novel iterative algorithm for deriving the least squares frequency response weighting function which will produce a quasi equiripple design is presented the algorithm converges very rapidly it typically produces a design which is only about 1 db away from the minimax optimum solution in two iterations and converges to within 0 1 db in six iterations convergence speed is independent of the order of the filter it can be used to design filters with arbitrarily prescribed phase and amplitude response

stability analysis of thermo acoustic nonlinear eigenproblems in annular combustors part i sensitivity we present an adjoint based method for the calculation of eigenvalue perturbations in nonlinear degenerate and non self adjoint eigenproblems this method is applied to a thermo acoustic annular combustor network the stability of which is governed by a nonlinear eigenproblem we calculate the first and second order sensitivities of the growth rate and frequency to geometric flow and flame parameters three different configurations are analysed the benchmark sensitivities are obtained by finite difference which involves solving the nonlinear eigenproblem at least as many times as the number of parameters by solving only one adjoint eigenproblem we obtain the sensitivities to any thermo acoustic parameter which match the finite difference solutions at much lower computational cost

iir approximation of fir filters via discrete time vector fitting we present a novel technique for approximating finite impulse response fir filters with infinite impulse response iir structures through extending the vector fitting vf algorithm used extensively for continuous time frequency domain rational approximation to its discrete time counterpart called vfz vfz directly computes the candidate filter poles and iteratively relocates them for progressively better approximation each vfz iteration consists of the solutions of an overdetermined linear equation and an eigenvalue problem with real domain arithmetic to accommodate complex poles pole flipping and maximum pole radius constraint guarantee stability and robustness against finite precision implementation comparison against existing algorithms confirms that vfz generally exhibits fast convergence and produces highly accurate iir approximants

design of arma digital filters by pole zero decomposition a new technique for design of digital filters is presented in this paper the technique exploits the spectral approximation property of autoregressive modeling to reduce ripple at the edges of the transition band in the filter response an autoregressive model approximates a given spectrum better at the peaks than at the valleys spectral information around the transition band is transformed into peaks by splitting the given squared magnitude frequency response into two component spectra this splitting is accomplished using a pole zero decomposition technique which in turn uses the properties of the derivative of phase spectrum of minimum phase filters one of the component spectra corresponds nearly to the response of an all pole filter and the other component spectrum corresponds nearly to the response of an all zero filter each of these corresponends spectra can be represented by a small number of coefficients using autoregressive modeling the resulting two sets of autoregressive coefficients determine poles and zeros of the autoregressive moving average arma digital filter ripple characteristics in the response of the arma filter can be controlled by appropriately choosing the number of poles and zeros it is shown that a wide variety of magnitude frequency response characteristics can be approximated by an arma filter of low order using this technique the technique does not work well in cases where spectral approximation by autoregressive modeling is poor such cases arise when the component spectra have very large dynamic range

infinite impulse response models of the head related transfer function head related transfer functions hrtfs measured from human subjects were approximated using infinite impulse response iir filter models models were restricted to rational transfer functions plus simple delays so that specific models are characterized by the locations of poles and zeros in the complex plane the all pole case with no nontrivial zeros is treated first using the theory of linear prediction then the general pole zero model is derived using a weighted least squares wls formulation of the modified least squares problem proposed by kalman 1958 both estimation algorithms are based on solutions of sets of linear equations and result in efficient computational schemes to find low order model hrtfs the validity of each of these two low order models was assessed in psychophysical experiments specifically a four interval two alternative forced choice paradigm was used to test the discriminability of virtual stimuli constructed from empirical and model hrtfs for corresponding locations for these experiments the stimuli were 80 ms noise tokens generated from a wideband noise generator results show that sounds synthesized through model hrtfs were indistinguishable from sounds synthesized from original hrtf measurements for the majority of positions tested the advantages of the techniques described here are the computational efficiencies achieved for low order iir models properties of the all pole and pole zero estimators are discussed in the context of low order hrtf representations and implications for basic and applied contexts are considered

embeddings for the jordan algebra of a bilinear form abstract let k be a field of characteristic zero and let j be a jordan algebra with a formal trace we prove that the algebra j can be embedded into a jordan algebra of a non degenerate symmetric bilinear form over some associative and commutative k algebra c if and only if j satisfies all trace identities of the jordan algebra of a non degenerate symmetric bilinear form over the field k this is an extension of results of procesi and berele concerning the analogous problem for the associative matrix algebras and the matrix algebras with involution as a consequence of these results we also prove that the ideal of all trace identities of the jordan algebra of a non degenerate symmetric bilinear form over k satisfies the specht property

a generalized companion matrix of a polynomial and some applications abstract a generalized companion matrix of a polynomial is introduced the concept is applied to estimates of polynomial roots and to the explicit determination of the characteristic equation of matrix

sizing design sensitivity analysis of non linear structural systems part ii numerical method a numerical method is presented to carry out sizing design sensitivity calculations outside established finite element analysis codes using postprocessing data only geometric as well as material non linearities are treated to demonstrate the accuracy of the proposed method numerical results are presented for structural systems with linear elastic material large displacements large rotations and small strains a distributed parameter approach to structural design sensitivity analysis is used to retain the continuum elasticity formulation throughout the derivation of design sensitivity results using this approach and an adjoint variable method design sensitivity computations are carried out for structural performance functionals stress and displacement are considered it is shown that computations can be performed with the same computational effort as for sizing design sensitivity analysis of linear structural systems accurate design sensitivity results are obtained for both linear and non linear structural systems without the uncertainty of numerical accuracy and high cost associated with the selection of finite difference perturbations also the method does not require differentiation of element stiffness and mass matrices in conventional finite element models

nonlinear transient response and second order sensitivity using time finite element method a procedure based on time finite element method to obtain the second order sensitivity of the transient response with respect to various system parameters is developed and applied to single and two degree of freedom structural dynamic systems the proposed method directly differentiates the algebraic equations resulting from the time finite element formulation with respect to system parameters computational algorithms are given and detailed derivations are presented the second order sensitivity analysis has been used for approximation schemes for efficient solution of design optimization problems also the results can be applied to gradient based parameter identification schemes the results are found to be in excellent agreement with those obtained using the finite difference method the main advantages of the time finite element approach are the ease of use and the numerical efficiency with which the sensitivity of the transient response can be obtained

design of iir fir filters using a frequency domain bootstrapping technique and lpc methods a technique is described for designing iir fir digital filters which are specified by the number of poles and zeros the sampling frequency and a magnitude response versus frequency the iterative technique to carry out the design bootstraps back and forth between the iir all pole section and fir all zero section updating the design each time in the frequency domain using the data from the previous iir or fir section and the desired filter response coefficient calculations at each iteration are based upon standard lpc linear prediction coefficient and inverse lpc methods an efficient computer program has been written to implement the technique using levinson and fft pruning algorithms the combination of the efficiency from lpc and pruning methods and the ease of iteration and interpretation in the frequency domain creates a straightforward and workable computer program for general digital filter design based upon spectral magnitude specifications examples of the filter design program illustrate how well the technique works as a function of the number of iterations

a recursive method for the approximation of lti systems using subband processing using the subband technique an lti system can be implemented by the composition of an analysis filterbank followed by a transfer matrix subband model and a synthesis filterbank the advantage of this approach is that it offers a good tradeoff between latency and computational complexity in this paper we propose an optimization method for approximating an lti system using the subband technique the proposed method includes optimal allocation of parameters from different fir entries of the subband model while keeping constant the total number of parameters for a better utilization of the available coefficients the optimization is done in a weighted least squares sense considering either linear or logarithmic amplitude scale simulation results demonstrate the advantages of the proposed method when compared with classical implementation approaches using pole zero transfer functions or segmented fft algorithms

convergence error and higher order sensitivity estimations differential equation with respect to the design variables the accuracies of the convergence error and higher order sensitivity estimation methods are verified using laplace euler and navier stokes equations the developed methods are used to improve the accuracy of the finite difference sensitivity calculations in iteratively solved problems aboundonthenormvalueofthe finite differencesensitivityerrorinthestatevariablesisminimizedwith respect to the finite difference step size the optimum finite difference step size is formulated as a function of the norm values of both convergenceerror andhigher order sensitivities thesensitivities calculated with the analytical and the finite difference methods are compared the performance of the proposed methods on the convergence of inverse design optimization is evaluated

reduced order iir approximation to fir digital filters an algorithm for designing an infinite impulse response iir stable filter using a finite impulse response fir given filter with the objective of reducing the delay and order is described the design is in the time domain using the least squares inverse algorithm which is briefly described in this method the numerator of the approximated filter is part of the fir filter itself and no calculations and minimization are needed to find the numerator coefficients except finding the fir roots an error analysis between the given fir and approximated iir filters is provided this error analysis enables the designer to fix a design parameter often unnoted keeping the energies of the approximated and original filters equal results and two illustrative examples are presented

asymptotics in cocharacters of simple algebras with involution abstract we compute the asymptotics of the colength and maximal multiplicity sequences of simple algebras with involution

calculation of sensitivity derivatives in thermal problems by finite differences the transient thermal analysis of large aerospace vehicles such as the space shuttle requires models with thousands of degrees of freedom the design of thermal protection systems for such vehicles requires the repetitive thermal analysis of the vehicle and the calculation of sensitivities derivatives of the transient response with respect to design parameters when the number of design parameters is large the cost of the sensitivity calculations may become prohibitive the present work is concerned with reducing the computational cost and errors in sensitivity calculations with one of the simplest available methods the finite difference approach a technique for calculating simultaneously the nominal and perturbed solutions required for the finite difference derivative is proposed an expression for the optimum value of the perturbation parameter is obtained which permits reducing the computational error an insulated cylinder is used as an example which demonstrates that significant improvements in accuracy and efficiency may be obtained

on stability and root location of linear prediction models simple algebraic proofs are given for some results pertaining to the location of the roots of linear prediction models also called all pole or autoregressive models

analytic signal generation tips and traps in this correspondence we discuss methods to produce the discrete analytic signal from a discrete real valued signal such an analytic signal is complex and contains only positive frequencies its projection onto the real axis is the same as the original signal our use stems from instantaneous frequency estimation and time frequency signal analysis problems for these problems the negative frequency component of real signals causes unwanted interference the task of designing a filter to produce an approximation to the ideal analytic signal is not as simple as its formulation might suggest our result is that the direct methods of zeroing the negative frequencies or using hilbert transform filters have undesirable defects we present an alternative which is similar to the quadrature filters used in modem designs

a conjecture of regev about the capelli polynomial abstract let x1 xn2 y1 yn2 be generic n n matrices over a field k of characteristic zero if x 1 x n is a multilinear invariant of x1 xn then s z 2 sign f x 1 y 1 x 2 y 2 y 3 y 4 x 3 y 5 y 9 x n y n 2 2n 2 y n 2 f x 1 x n y where sn2 is the symmetric group of degree n2 y is the discriminant of y1 yn2 and tf x 1 x n is a uniquely defined multilinear invariant of x1 xn thus tf defines a function from the vector space of multilinear invariants of x1 xn to itself an analysis of this function is used to prove regev s conjecture that s z 2 sign x n 1 y 1 x 2 x 3 x 4 y 2 y 3 y 4 x 5 x n 2 2 2 x n 2 y n 2 2n 2 y n 2 is nonzero in addition a variant of the above function is used to evaluate the capelli polynomial

design of iir digital filters with arbitrary log magnitude function by wls techniques the authors propose a technique for designing iir infinite impulse response digital filters to have an arbitrary log magnitude frequency response the technique is based on an iterative weighted least squares wls approach in the frequency domain a weight updating procedure is introduced to obtain a nearly optimal approximation to the given log magnitude function in the least squares sense the weighting function is updated using the results of the previous iteration in such a way that the weighted error approximates the log magnitude error filter coefficients at each iteration are efficiently computed using a fast recursive algorithm for a set of linear equations derived from the wls problem several design examples demonstrate the rapid convergence of the design algorithm the algorithm is extended to equiripple approximation by means of a minor modification of the weight updating procedure

design of multirate filter banks by spl hscr sub spl infin optimization a procedure is developed to design iir synthesis filters in a multirate filter bank the filters minimize the l sub 2 induced norm of the error system between the multirate filter bank and a desired pure time delay system this criterion is reduced to one of spl hscr sub spl infin optimization for which there is ready made software

sensitivity analysis and optimization of aeroelastic stability abstract the present paper deals with problems concerning sensitivity analysis and optimization of aeroelastic stability of distributed systems in sections 1 3 the optimization problem of aeroelastic stability of a slender wing in incompressible flow is formulated and solved the optimal control function h y to be determined represents the mass and stiffness distribution along a wing span sensitivity analysis of flutter systems is developed first the gradients of flutter and divergence critical speeds are derived and necessary optimality conditions are obtained then the solution technique is described and numerical results are presented in section 4 the problem of determining the optimal distribution of nonstructural mass along the wing span is considered the optimality conditions are established and the bang bang optimal distributions are obtained

kronecker products for compact semisimple lie groups a review is given of the application of s function techniques to the evaluation of kronecker products of irreducible representations of compact semisimple lie groups explicit formulae are derived for all irreducible representations of all such groups recent developments involving composite young diagrams are brought to fruition and the vexed problem of so2k is dealt with completely new branching rules for the classical groups are given in an appendix these are exploited in the evaluation of kronecker products by means of a technique which is applied to both classical and exceptional groups a discussion is made of various modification rules which are needed to express the final results in standard form

efficient design of oversampled npr gdft filterbanks we propose a flexible efficient design technique for the prototype filter of an oversampled near perfect reconstruction npr generalized discrete fourier transform gdft filterbank such filterbanks have several desirable properties for subband processing systems that are sensitive to aliasing such as subband adaptive filters the design criteria for the prototype filter are explicit bounds derived herein on the aliased components in the subbands and the output the distortion induced by the filterbank and the imaged subband errors in the output it is shown that the design of an optimal prototype filter can be transformed into a convex optimization problem which can be efficiently solved the proposed design technique provides an efficient and effective tool for exploring many of the inherent tradeoffs in the design of the prototype filter including the tradeoff between aliasing in the subbands and the distortion induced by the filterbank we calculate several examples of these tradeoffs and demonstrate that the proposed method can generate filters with significantly better performance than filters obtained using current design methods

sensitivity analysis of discrete structural systems methods for calculating sensitivity derivatives for discrete structural systems are surveyed primarily covering literature published during the past two decades methods are described for calculating derivatives of static displacements and stresses eigenvalues and eigenvectors transient structural response and derivatives of optimum structural designs with respect to problem parameters the survey is focused on publications developed in nonstructural fields such as electronics controls and physical chemistry which are directly applicable to structural problems most notable among the nonstructural based methods are the adjoint variable technique from control theory and the green s function and fast methods from physical chemistry

the design of uniformly and nonuniformly spaced pseudoquadrature mirror filters in the past quadrature mirror filters qmf s have been used to derive both uniformly and nonuniformly spaced filterbanks a pair of qmf s divides a signal into two equal bands which can be decimated at 2 1 and subsequently combined to reconstruct the original signal in order to derive filterbanks with more than two bands qmf s are combined in a binary tree structure pseudoquadrature mirror filters are similar to qmf s but can be designed to split a signal directly into any number of equally spaced bands thus generalizing the qmf concept in this paper the theory of pseudoquadrature mirror filters is reviewed these filters retain the desirable property that the channel signals from a uniformly spaced bank of m filters can be decimated by m 1 then interpolated and reassembled to reproduce the original signal an extension is made to the theory to allow a set of nonuniformly spaced filters to be derived from a uniformly spaced set and still retain all the desirable characteristics another extension to the theory is the derivation of a family of different sized filterbanks all derived from the same original prototype potential applications for the new filterbanks include improvements in subband coding of speech and music and analog scrambling of speech

digital filter bank design quadratic constrained formulation formulate the filter bank design problem as an quadratic constrained least squares minimization problem the solution of the minimization problem converges very quickly since the cost function as well as the constraints are quadratic functions with respect to the unknown parameters the formulations of the perfect reconstruction cosine modulated filter bank of the near perfect reconstruction pseudo qmf bank and of the two channel biorthogonal linear phase filter bank are derived using the proposed approach compared with other design methods the proposed technique yields pr filter banks with much higher stopband attenuation the proposed technique can also be extended to design multidimensional filter banks

nonuniform multirate filter banks analysis and design with an spl hscr sub spl infin performance measure a general multirate filter bank system with multiple channels and nonuniform bands is studied with the reconstruction performance measured by the worst case energy gain spl hscr sub spl infin norm of the error system between the multirate system and a pure time delay system using blocking and polyphase decomposition we associate with the multirate system an equivalent linear time invariant lti system whose transfer matrix can be computed by a simple procedure based on this lti system the optimal design problem can be reduced to one of spl hscr sub spl infin optimization which can be solved by ready made software in many cases for illustration optimal synthesis filters are designed for a two channel example and their properties are studied in detail

maximum likelihood methods for direction of arrival estimation five methods of direction of arrival doa estimation which can be derived from the maximum likelihood ml principle are considered the ml method mlm results from the application of the ml principle to the statistics of the observed raw data the standard multiple signal classification music procedure called music 1 is obtained as a brute force approximation of the mlm an improved music procedure named music 2 is obtained by applying the ml principle to the statistics of certain linear combinations of the sample noise space eigenvectors a procedure which compromises between the good performance of the mlm and the computational simplicity of music is a method of direction estimation mode 1 which is derived as a large sample realization of the mlm a fifth method called mode 2 is obtained by using the ml principle on the statistics of certain linear combinations of the sample eigenvectors mode 2 is computationally less demanding than the mlm it is of the same complexity as mode 1 and statistically more efficient a numerical comparison of these five doa estimation methods is presented it confirms the analytic results on their theoretical performance levels

integrated structural analysis and design using three dimensional finite elements a design approach that combines iterative structural analysis with a traditional iterative optimization algorithm is applied to the optimum design of the shape of a hole in a plate in tension the plate is modeled by threedimensional finite elements and an element by el ement preconditioned conjugate gradient iterative algorithm is used for solving the equations of equilibrium several parameterizations of the optimum shape are considered and it is shown that a sine series can describe the optimum shape with only three design variables whereas other series require seven variables for similar results the optimum shape compares well with an experimental optimum obtained by a j durelli an investigation is performed to determine the best way of obtaining finite difference derivatives of the stresses with respect to design variables it is shown that a method based on modifying the equations of equilibrium for the perturbed problem performs best the benefit of the integrated approach is determined by comparing convergence with different initial iterates for the displacement field it is shown that using the final iterate of the previous solution can reduce the number of analysis iterations by about 40 compared to starting with a zero initial iterate

derivatives of eigenvalues and eigenvectors of a general complex matrix a survey of methods for sensitivity analysis of the algebraic eigenvalue problem for non hermitian matrices is presented in addition a modification of one method based on a better normalizing condition is proposed methods are classified as direct or adjoint and are evaluated for efficiency operation counts are presented in terms of matrix size number of design variables and number of eigenvalues and eigenvectors of interest the effect of the sparsity of the matrix and its derivatives is also considered and typical solution times are given general guidelines are established for the selection of the most efficient method

sensitivity calculations for iteratively solved problems the calculation of sensitivity derivatives of solutions of iteratively solved systems of algebraic equations is investigated a modified finite difference procedure is presented which improves the accuracy of the calculated derivatives the procedure is demonstrated for a simple algebraic example as well as an element by element preconditioned conjugate gradient iterative solution technique applied to truss examples

minimum state unsteady aerodynamics for aeroservoelastic configuration shape optimization of flight vehicles the minimum state technique for creating linear time invariant state space models of unsteady aerodynamic loads leads to major savings in terms of the dimension of the resulting aeroservoelastic systems compared to alternative techniques the upfront effort of the generation of minimum state approximants however is large and involves an iterative double least squares function fitting process when the overall shape of a configuration varies during the repetitive analysis required for configuration design optimization the cost of creating new minimum state approximations becomes prohibitive this paper presents an efficient method for obtaining shape sensitivity analysis of minimum state approximants the resulting sensitivities are then used based on a single detailed analysis and sensitivity analysis at some reference design to generate approximate aeroelastic poles divergence speed and flutter speed results for configurations that are subject to considerable planform shape changes

a wise method for designing iir filters the problem of designing optimal digital iir filters with frequency responses approximating arbitrarily chosen complex functions is considered the real valued coefficients of the filter s transfer function are obtained by numerical minimization of carefully formulated cost which is referred here to as the weighted integral of the squared error wise criterion the wise criterion linearly combines the wls criterion that is used in the weighted least squares approach toward filter design and some time domain components the wls part of wise enforces the quality of the frequency response of the designed filter while the time domain part of the wise criterion restricts the positions of the filter s poles to the interior of an origin centred circle with arbitrary radius this allows one not only to achieve stability of the filter but also to maintain some safety margins a great advantage of the proposed approach is that it does not impose any constraints on the optimization problem and the optimal filter can be sought using off the shelf optimization procedures the power of the proposed approach is illustrated with filter design examples that compare favorably with results published in research literature

quadrature mirror filter design for an arbitrary number of equal bandwidth channels the two channel quadrature mirror filter structure of croisier and esteban may be extended to an arbitrary number of equal bandwidth channels given certain restrictions on the bandpass filters the most serious restriction is that the stopband attenuation of eacli band pass filter must be high for all frequencies outside twice the nominal 3 db bandwidth of the filter this restriction is not really a limiting factor for speech subband waveform coding since high adjacent channel attenuation is a necessity for the confinement of quantization noise a key feature of our filter structure is that the number of multiplies adds and stored coefficients required for implementation is significantly less than those needed for the conventional qmf structure given the same number of channels fortran code for a 16 channel filter structure is listed as an example of efficient implementation

on the splitting of classical algorithms in linear prediction theory the levinson algorithm has been shown recently to be redundant in complexity it can be broken down into two simpler algorithms either of these split levinson algorithms needs only to be processed in the present paper it is shown that the schur algorithm the lattice algorithm and the normalized lattice algorithm for computing reflection coefficients can be broken down in a similar manner the number of multiplications in each of the resulting split algorithms is reduced with respect to the classical version by a factor lying between 1 5 and 2