sigma delta modulation with i i d gaussian inputs the response of a single loop sigma delta modulator to an independent identically distributed i i d gaussian input signal is analyzed a continuous time stochastic model is developed and the connection of the model to the system is described a condition is given so that the difference between the behavior of the model and that of the true system can be made arbitrarily small theories from renewal and wiener processes are applied to show the convergence and mixing properties of the output sequence also derived is the power spectrum of the quantization noise compared to the spectrum when the input is dc the i i d gaussian random process smears the discrete spectrum into band structures

roundoff noise analysis of signals represented using signed power of two terms it is a well known fact that the multiplication of a number by an integer power of two is a very simple process in binary arithmetic hence digital filters whose coefficient values are integer power of two are essentially multiplierless the design of digital filters with power of two coefficient values require time consuming optimization process and may not always be possible in some applications such as in adaptive filtering since hardware circuitry for real time conversion of a binary integer into a sum of a limited number of signed power of two spt terms is available if the signal is expressed in spt terms i e in digit code the filter is also multiplierless even though the coefficient values are not spt when each signal data is rounded to a limited number of spt terms a roundoff noise representing the roundoff error is introduced in the spt space the quantization step size is nonuniform and so the roundoff noise characteristic is different from that produced when the quantization step size is uniform this paper presents an analysis for the roundoff noise of signal represented using a limited number of spt terms the result is useful for determining the number of spt terms required to represent a signal subject to a given roundoff noise

fully sigma delta modulation encoded fir filters the author suggests an fir filter structure where both the input signal and the impulse response are encoded using sigma delta modulation as a result the convolution can be obtained by summing a collection of binary or ternary numbers depending on the quantizer in the sigma delta modulator this filter structure can accept analog input signals directly and can be built using modular hardware the overall error spectrum due to the encoding decoding processes is derived and the implementation issues of this filter structure are discussed an example of its performance with different input signals is provided

quantization of filter bank frame expansions through moving horizon optimization this paper describes a novel approach to quantization in oversampled filter banks the new technique is based on moving horizon optimization does not rely on an additive white noise quantization model and allows stability to be explicitly enforced in the associated nonlinear feedback loop moreover the quantization structure proposed here includes sigmadelta and linear predictive subband quantizers as a special case and in general outperforms them

brief constrained linear state estimation a moving horizon approach this article considers moving horizon strategies for constrained linear state estimation additional information for estimating state variables from output measurements is often available in the form of inequality constraints on states noise and other variables formulating a linear state estimation problem with inequality constraints however prevents recursive solutions such as kalman filtering and consequently the estimation problem grows with time as more measurements become available to bound the problem size we explore moving horizon strategies for constrained linear state estimation in this work we discuss some practical and theoretical properties of moving horizon estimation we derive sufficient conditions for the stability of moving horizon state estimation with linear models subject to constraints on the estimate we also discuss smoothing strategies for moving horizon estimation our framework is solely deterministic

new initialization methods for discrete coefficient fir filter design with coefficient scaling and the use of scale factor in the design process the initialization of filter coefficients in discrete coefficient finite impulse response fir filter design with coefficient scaling using coefficient value assignment based optimization techniques is considered a common weakness of existing initialization measures a total square error tse measure and a maximum error me measure is described new tse and me measures that overcome the weakness are introduced as opposed to the current knowledge it is revealed that tse and me measures do not necessarily provide different initial coefficient set information and that the initial coefficient set information by the me measure is not unique in general on a parallel track the treatment of coefficient scaling in the optimization process is considered the closed form expression of the objective function normalized peak ripple magnitude nprm which was defined implicitly in the literature is given in contrast to existing methods the computation of nprm accordingly does not require a scale factor parameter independent of filter coefficients although coefficient scaling persists then tse and me measures become practically equivalent although in general they indicate different initial scale factors since an explicit scale factor parameter is no longer needed

decision feedback equalization via separating hyperplanes the design of finite length decision feedback equalization dfe forward and feedback filters under the assumption of genie aided feedback and independent and equally likely transmitted symbols is considered it is shown that the problem of determining dfe filters that minimize the probability of symbol error at high signal to noise ratio snr is equivalent to finding the hyperplane that maximally separates two given finite groups of points in a finite dimensional euclidean space the latter task can be formulated as a quadratic program which is readily solved numerically it is also shown that the problem of finding finite length dfe filters that minimize the probability of symbol error at any snr subject to a certain separation condition is a convex optimization problem the case where the transmitted data is coded using a runlength limited code is also investigated examples show that this criterion yields a performance that is better than zero forcing dfe on severely distorted channels at high snr

block decision feedback equalization a natural generalization of the conventional decision feedback equalizer dfe based on block processing and maximum a posteriori decisions is presented this block dfe is indexed by two parameters depending on the block length p and the number of decisions q

maximal normal sets of n planes inr2n abstract y c wong and k p mok have introduced the notion of normal sets of n planes inr 2 n we show that every maximal set defined by a subspace of nonsingular n n matrices is indeed a maximal isoclinic set we also resolve a conjecture of wong mok that every maximal subspace of scalar multiples of orthogonal n n matrices is also maximal as a subspace of nonsingular matrices

delayed decision feedback sequence estimation the authors delayed decision feedback sequence estimation ddfse for uncoded pam signals is considered estimates on the performance of the algorithm are given and simulation results are provided for several examples a more general form of ddfse applicable to coded modulation systems is also presented as an example detection of trellis coded qpsk quadrature phase shift keyed signals over intersymbol interference channels is discussed

semisystolic incremental realization of fir digital filters using ternary arithmetic a fully incremental realization of finite impulse response fir filters is presented in which ternary incremental representations are used for all the signals in the structure and the impulse response delta modulation dm is used for this purpose allowing a considerable simplification of the arithmetic involved in the filtering operations simulation showed that the proposed dm adder has lower mean square error mse and reduced processing delay with respect to existing dm adders while demonstrating the feasibility of the proposed modular incremental realization for fir filters

a class of high precision multiplier free fir filter realizations with periodically time varying coefficients proposes a class of high precision multiplier free realizations for fir filters these realizations use upsampling and downsampling in conjunction with a periodically time varying system to achieve time invariant multiplier free fir filter operation nonbinary encoding schemes are used for obtaining the filter coefficients which are periodically time varying ptv i e they vary in a periodic fashion each target filter coefficient is directly mapped into a set of ptv coefficients so that the realizations are easy to obtain the values of the ptv coefficients are restricted to either the ternary set

quantization noise in single loop sigma delta modulation with sinusoidal inputs an exact nonlinear difference equation is derived and solved for a simple sigma delta modulator consisting of a discrete time integrator and a binary quantizer inside a single feedback loop and an arbitrary input signal it is shown that the system can be represented as an affine operation discrete time integration of a biased input followed by a memoryless nonlinearity an extension of the transform method for the analysis of nonlinear systems is applied to obtain formulas for first and second order time average moments of the binary quantization noise including the sample mean energy and autocorrelation the results are applied to the special case of a sinusoidal input signal to evaluate these time averages and the power spectrum in the limit of large oversampling ratios the marginal moments behave as if the quantization noise had a uniform distribution the spectrum is neither white nor continuous however even in the limit of large oversampling ratios

non nested tests for competing models estimated by generalized method of moments non nested tests are proposed for competing models estimated by generalized method of moments results are presented for non nested linear regression models with het eroskedasticity and serial correlation of unknown form and differing instrument validity assumptions regression forms of the statistics are also presented this paper is concerned with providing a procedure whereby non nested models estimated by generalized method of moments gmm hansen 1982 may be com pared in particular cox type cox 1961 1962 and encompassing tests mizon and richard 1986 are proposed implicit in such tests is a degree of arbitrariness in the way the statistics are constructed as typically the assumptions underlying gmm estima tion techniques are minimal and do not fully specify the data generation process dgp underlying the observable random variables in contradistinction to the method of maximum likelihood our procedures allow the population moment conditions on which gmm estimation of the competing models is based to differ in the conditioning sets under which conditional expectation is taken such differences may reflect different a priori assumptions concerning the exogeneity status of random variables in the models these tests may be regarded as generalizations of singleton 1985 more recent work includes ghysels and hall 1990 which requires the specification of the dgp under the null hypothesis and wooldridge 1990b which proposes heteroskedasticity robust tests for non nested non linear regression models our results are specialized to provide non nested tests for competing regression models estimated by instrumental variables where we allow a degree of heteroskedastic ity and serial correlation in the process generating the disturbance terms by assuming appropriate mixing conditions white 1984 and the instrument validity assumptions to differ across the models cf godfrey 1983 1984 which assume a scalar covariance matrix for the disturbances and that the set of instruments is valid in both models thus our framework includes models which may be both simultaneous and dynamic section 2 describes procedures for obtaining cox type and encompassing tests for competing models estimated by gmm section 3 specializes these results to competing linear regression models estimated by instrumental variables regression forms for the statistics are presented the paper is concluded by section 4 in our presentation we eschew detailed regularity assumptions

a general approach to lagrange multiplier model diagnostics abstract a diagnostic test can be formulated by taking the current model as the null hypothesis and a particular form of misspecification as the alternative the general approach of this paper is to calculate the score for some alternative and base a test on its distribution under the null this distribution is derived in two theorems corresponding to different models such a test is a langrange multiplier test and is asymptotically optimal these tests can be formulated as ways of looking at the residuals for particular types of non randomness the tests are simple to calculate even when the alternative may be very complicated examples are given of tests for omitted variables and block recursive structures

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

realization of finite impulse response filters using coefficients 1 0 and 1 new classes of nonrecursive linear digital filters are proposed as alternatives to conventional methods for digital signal processing devices in fact the traditional approach where signal samples are represented by 8 15 bit words can be very expensive to implement due to the complexity of multibit multipliers and adders filter structures consisting of a transversal filter with tap coefficients restricted to 1 0 or 1 and cascaded with simple recursive sections are proposed using a mean square error criterion dynamic programming methods to select optimum sets of coefficient values for the taps are presented and evaluated it is shown that these structures lend themselves to very simple hardware implementations and offer a valid alternative to the conventional filtering approach designs for several example filters are presented and their implementation complexity is examined

on finite wordlength fir filter design a recent paper has investigated the use of integer linear programming for the design of chebyshev optimal finite wordlength fir digital filters we point out that for some time domain error norms coefficient rounding provides the best approximation to the infinite precision filter

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

lll algorithm and the optimal finite wordlength fir design in practical finite impulse response fir digital filter applications it is often necessary to represent the filter coefficients with a finite number of bits the finite wordlength restriction increases the filter deviation this increase can be reduced substantially if the optimal finite wordlength coefficients are used the time needed to compute these coefficients is greatly reduced with the help of a lower bound on the deviation increase derivation of an improved lower bound that uses the well known lll algorithm is presented in this correspondence

fir filter design based on successive approximation of vectors we present a novel method for the design of finite im pulse response fir filters with discrete coefficients that belong in thesumofpowers of two pot space theimportanceofthisclass of filters cannot be overstated given the ever increasing number of applications for which a specific hardware implementation is needed filters that have coefficients that belong to such a class are also referred to as multiplierless filters given that the oper ations performed by the filter can all be implemented by using appropriately designed shifts of the input data making them a perfect choice whenever implementation simplicity and processing speed are the ultimate goal to produce suc had esign we employ a vector successive approximation technique successfully used in data compression that has a very low computational complexity the matching pursuits generalized bitplanes algorithm mpgbp we derive optimality conditions for the approximation dictionary we compare filters obtained with the proposed method with those derived in previous works based on this comparative analysis we show that this new and powerful way of producing the filters co efficients is also among the simplest available in the literature indexterms signalprocessing filterdesign successiveapprox imation methods vq

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

asymptotic robustness of tests of overidentification and predeterminedness abstract many statistical test procedures have been proposed for identification restrictions on one or several equations and the econometric predeterminedness of one or several variables in a system of structural equations this study is devoted to unifying many test procedures in a systematic way and to deriving the asymptotic distributions of the test statistics under a set of local alternative hypotheses and very general conditions on the disturbances by making use of a new martingale central limit theorem and a martingale convergence theorem we show that the limiting distributions of test statistics are noncentral 2 distributions under the local alternative hypotheses and central 2 distributions under the null hypotheses these limiting distributions are robust in the sense that they hold for a variety of disturbance distributions and models our results show that many tests already known among econometricians can be carried out without making the usual relatively restrictive assumptions

a special irreducible matrix representation of the real clifford algebra c 3 1 4 4 dirac gamma matrices irreducible matrix representations of the clifford algebras c 3 1 c 1 3 c 4 0 are an essential part of many calculations in quantum physics although the final physical results do not depend on the applied representation of the dirac matrices e g due to the invariance of traces of products of dirac matrices the appropriate choice of the representation used may facilitate the analysis the present paper introduces a particularly symmetric real representation of 4 4 dirac matrices majorana representation which may prove useful in the future as a by product a compact formula for transformed pauli matrices is found the consideration is based on the role played by isoclinic 2 planes in the geometry of the real clifford algebra c 3 0 which provide an invariant geometric frame for it it can be generalized to larger clifford algebras

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

a filled function method for finding a global minimizer of a function of several variables the concept of a filled function is introduced we construct a particular filled function and analyze its properties an algorithm for global minimization is generated based on the concept and properties of the filled function some typical examples with 1 to 10 variables are tested and computational results show that in most cases this algorithm works better than the tunneling algorithm the advantages and disadvantages are analyzed and further research directions are discussed

on the power of tests for superexogeneity and structural invariance abstract this paper examines the finite sample power of tests of structural invariance and superexogeneity hypotheses in econometric models with contemporaneous conditioning variables we consider both direct parametric tests of superexogeneity as well as indirect procedures based on temporal stability tests for the parameters of interest our monte carlo analysis reveals that both types of tests may lack power in interesting classes of models an empirical illustration investigates the superexogeneity of the short term interest rate in a dynamic specification for the u s term structure

multistep detector for linear isi channels incorporating degrees of belief in past estimates this paper formulates the channel equalization problem in the framework of constrained maximum likelihood estimation this allows us to highlight key issues including the need to summarize past data and to apply a finite alphabet constraint over a sliding optimization window the approach adopted here leads to embellishments of the usual nonadaptive decision feedback equalizer and its multistep extensions it includes a provision for degrees of belief in past estimates which addresses the problem of error propagation

a unified approach to estimation and orthogonality tests in linear single equation econometric models abstract maximum likelihood estimation is considered for a generalisation of the model of anderson and rubin 1949 in which the exogenous variables in the structural equation may not be included in the reduced form equations classical and specification tests are derived for orthogonality hypotheses a necessary and sufficient condition for their equivalence is presented the classical tests are compared using bahadur s asymptotic relative efficiency criterion it is shown that a generalisation of the durbin wu hausman t 2 statistics is asymptotically bahadur efficient

design of discrete coefficient fir filters on loosely connected parallel machines this paper presents a new branch and bound mixed integer linear programming based algorithm for designing discrete coefficient finite impulse response fir filters using a cluster of workstations as the computation platform the discrete coefficient space considered is the sum of signed power of two space but the technique is also applicable to other discrete coefficient spaces the key issue determining the success of the algorithm is the ability to partition the original problem into several independent parts that can be distributed to a cluster of machines for solution the master slave model is adopted for the control of the machines test run results showed that super linear speedup i e the speedup factor is more than the number of machines running in parallel may be achieved

normally related n planes and isoclinic n planes in r2n and strongly linearly independent matrices of order n abstract we study the normally related n planes in r2n n 2 and the relationship between sets of pairwise normally related n planes and sets of mutually isoclinic n planes in r2n we also discuss an interesting link between this problem and the celebrated theorem of j f adams that the maximum number of strongly linearly independent matrices of order n is equal to the radon hurwitz number n

design of fir filters in the complex domain the design of fir digital filters with a complex valued desired frequency response using the chebyshev error is investigated the complex approximation problem is converted into a real approximation problem which is nearly equivalent to the complex problem a standard linear programming algorithm for the chebyshev solution of overdetermined equations is used to solve the real approximation problem additional constraints are introduced which allow weighting of the phase and or group delay of the approximation digital filters are designed which have nearly constant group delay in the passbands the desired constant group delay which gives the minimum chebyshev error is found to be smaller than that of a linear phase filter of the same length these filters in addition to having a smaller approximately constant group delay have better magnitude characteristics than exactly linear phase filters with the same length the filters have nearly equiripple magnitude and group delay

dynamic programming methods for designing fir filters using coefficients 1 0 and 1 in this paper we describe an efficient design procedure for designing fir filters whose general structure consists of a transversal filter with tap coefficients restricted to 1 0 or 1 and cascaded with simple recursive sections due to the multiplication free nature of this transversal filter the configuration is particularly attractive from the standpoint of implementation with very simple hardware dynamic programming methods in conjunction with a mean square error functional are presented to select the set of coefficient values for the taps the approach is based on the assumption that the approximation sequence can be described as the output of a sequential machine whose state corresponds to the state space representation of the sections in cascade with the transveral filter

oversampled sigma delta modulation oversampled sigma delta modulation has been proposed as a practical implementation for high rate analog to digital conversion because of its simplicity and its robustness against circuit imperfections to date mathematical developments of the basic properties of such systems have been based either on simplified continuous time approximate models or on linearized discrete time models where the quantizer is replaced by an additive white uniform noise source in this paper we rigorously derive several basic properties of a simple discrete time single integrator loop sigma delta modulator with an accumulate and dump demodulator the derivation does not require any assumptions on the correlation or distribution of the quantizer error and hence involves no linearization of the nonlinear system but it does show that when the input is constant the state sequence of the integrator in the encoder loop can be modeled exactly as a linear system in an appropriate space two basic properties are developed 1 the behavior of the sigma delta quantizer when driven by a constant input and its relation to uniform quantization and 2 the rate distortion tradeoffs between the oversampling ratio and the average mean squared quantization error

a discrete filled function algorithm embedded with continuous approximation for solving max cut problems in this paper a discrete filled function algorithm embedded with continuous approximation is proposed to solve max cut problems a new discrete filled function is defined for max cut problems and properties of the function are studied in the process of finding an approximation to the global solution of a max cut problem a continuation optimization algorithm is employed to find local solutions of a continuous relaxation of the max cut problem and then global searches are performed by minimizing the proposed filled function unlike general filled function methods characteristics of max cut problems are used the parameters in the proposed filled function need not to be adjusted and are exactly the same for all max cut problems that greatly increases the efficiency of the filled function method numerical results and comparisons on some well known max cut test problems show that the proposed algorithm is efficient to get approximate global solutions of max cut problems

moving horizon design of discrete coefficient fir filters we show how the discrete coefficient filter design problem can be solved with a moving horizon optimization approach the computation time of this procedure is determined by the optimization horizon and does not grow exponentially with the filter length spl sigma spl delta design methods are a special case of the proposed procedure

a discrete filled function method for the design of fir filters with signed powers of two coefficients in this paper we consider the optimal design of finite impulse response fir filters with coefficients expressed as sums of signed powers of two spt terms where the normalized peak ripple npr is taken as the performance measure this problem is formulated as a mixed integer programming problem based on a transformation between two different integer spaces and the computation of the optimal scaling factor for a given set of coefficients this mixed integer programming problem is transformed into an equivalent integer programming problem then an efficient algorithm based on a discrete filled function is developed for solving this equivalent problem for illustration some numerical examples are solved

optimal design of complex fir filters with arbitrary magnitude and group delay responses this paper presents a method for the frequency domain design of digital finite impulse response filters with arbitrary magnitude and group delay responses the method can deal with both the equiripple design problem and the peak constrained least squares pcls design problem consequently the method can also be applied to the equiripple passbands and pcls stopbands design problem as a special case of the pcls design both the equiripple and the pcls design problems are converted into weighted least squares optimization problems they are then solved iteratively with appropriately updated error weighting functions a novel scheme for updating the error weighting function is developed to incorporate the design requirements design examples are included in order to compare the performance of the filters designed using the proposed scheme and several other existing methods

spectral analysis of quantization noise in a single loop sigma delta modulator with dc input an exact discrete time analysis of the moments and spectra of the quantization noise of a discrete time single loop sigma delta modulator with a dc input is presented an exact difference equation for the discrete time nonlinear system is used to evaluate the first and second order moments and power spectrum of the binary quantizer noise and the binary quantizer output for a single loop sigma delta encoder with a dc input it is shown that the sample mean and power of the binary quantization noise are consistent with the common uniform distribution assumption but that the autocorrelation and power spectrum are not consistent with the white noise assumption the results are used to evaluate the overall sample average mean squared quantization error as a function of the decimation filter used

a new approach to the design of discrete coefficient fir digital filters in this correspondence the iterative lagrange multiplier approach is proposed for designing discrete coefficient fir digital filters the method associates the conventional lagrange multiplier approach and a tree search algorithm for each branch of the tree the lagrange multiplier approach is used to optimize the remaining unquantized coefficients of the designed fir filter in the least squares sense when one or more of the coefficients takes on discrete values design examples including general low pass filters and nyquist filters are presented to demonstrate the effectiveness of the method also the method can be extended to design discrete coefficient 2 d fir filters

design of linear phase direct form fir digital filters with quantized coefficients using error spectrum shaping a generalization of the statistical approach of d s k chan and l r rabiner ieee trans audio electroacoust vol au 21 p 354 66 aug 1973 for predicting the effects of quantized coefficients in direct form finite impulse response fir filters is presented the analysis is used on more sophisticated quantizing procedures involving linear feedback of rounding errors it is shown that the expected disturbance filter frequency response due to quantization can be controlled the effect is concentrated in tolerant frequency bands and significantly reduced in critical ones the price paid is an increase of overall expected disturbance the method is demonstrated in a practical filter design a low pass filter for factor 2 decimation that has greater margins for quantization effects in the passband than in the stopband is specified

a lattice basis reduction approach for the design of finite wordlength fir filters many applications of finite impulse response fir digital filters impose strict format constraints on the filter coefficients such requirements increase the complexity of determining optimal designs for the problem at hand we introduce a fast and efficient method based on the computation of good nodes for polynomial interpolation and euclidean lattice basis reduction experiments show that it returns quasi optimal finite wordlength fir filters compared to previous approaches it also scales remarkably well length 125 filters are treated in 9 s it also proves useful for accelerating the determination of optimal finite wordlength fir filters

how good is quantized model predictive control with horizon one model predictive control is increasingly being used in areas where decision variables are constrained to finite or countably infinite sets well known fields include power electronics signal processing and telecommunications typically the applications utilize high speed sampling and thus there is an incentive to reduce computational burden one way of achieving this is to use small optimization horizons this raises the question as to the optimality and performance of control laws with short horizons in this paper we give necessary and sufficient conditions for horizon one quantized model predictive control to be equivalent to the use of larger horizons we also explore situations where horizon one is near optimal

finite word length fir filter design using integer programming over a discrete coefficient space it is demonstrated that the improvement achieved by using integer programming over simple coefficient rounding in the design of finite impulse response fir filters with discrete coefficients is most significant when the discrete coefficient space is the powers of two space or when a specification is to be met with a given coefficient word length by increasing the filter length both minimax and least square error criteria are considered

generalized method of moments specification testing abstract this paper analyzes the asymptotic power properties of specification tests which are based on a finite set of moment conditions it shows that any such test may fail against general misspecification that causes estimator inconsistency the mutual asymptotic equivalence of maximal degree of freedom tests is shown and the form of optimal tests against specific forms of misspecification is derived applications to testing for exogeneity of a set of instrumental variables are presented

exogeneity tests incomplete models weak identification and non gaussian distributions invariance and finite sample distributional theory abstract we study the distribution of durbin wu hausman dwh and revankar hartley rh tests for exogeneity from a finite sample viewpoint under the null and alternative hypotheses we consider linear structural models with possibly non gaussian errors where structural parameters may not be identified and where reduced forms can be incompletely specified or nonparametric on level control we characterize the null distributions of all the test statistics through conditioning and invariance arguments we show that these distributions do not involve nuisance parameters in particular this applies to several test statistics for which no finite sample distributional theory is yet available such as the standard statistic proposed by hausman 1978 the distributions of the test statistics may be non standard so corrections to usual asymptotic critical values are needed but the characterizations are sufficiently explicit to yield finite sample monte carlo tests of the exogeneity hypothesis the procedures so obtained are robust to weak identification missing instruments or misspecified reduced forms and can easily be adapted to allow for parametric non gaussian error distributions we give a general invariance result block triangular invariance for exogeneity test statistics this property yields a convenient exogeneity canonical form and a parsimonious reduction of the parameters on which power depends in the extreme case where no structural parameter is identified the distributions under the alternative hypothesis and the null hypothesis are identical so the power function is flat for all the exogeneity statistics however as soon as identification does not fail completely this phenomenon typically disappears we present simulation experiments which confirm the finite sample theory the theoretical results are illustrated with an empirical example the relation between trade and economic growth

performance limit of finite wordlength fir digital filters in many practical situations it is necessary to represent the coefficients of a finite impulse response fir digital filter by a finite number of bits this not only degrades the filter frequency response but also introduces a theoretical limit on the performance of the filter derivation of a lower bound on filter degradation is the purpose of this paper we consider a general case of a length n filter with a discrete set of allowable coefficients a theorem that gives the lower bound on the increase in minimax approximation error that is caused by the finite wordlength restriction is presented its extension and application to filter design cases is demonstrated the importance of this bound is not only theoretical its practical effectiveness is shown in the algorithm for optimal finite wordlength fir filter design where it significantly reduces the amount of computation

tests of overidentification and predeterminedness in simultaneous equation models abstract a set of simultaneous equations that is a part of a larger complete system is considered one hypothesis concerning this set of equations is that it is overidentified as a block by a block of zero restrictions another hypothesis is that a subset of the current endogenous variables is uncorrelated with the disturbances in the set of simultaneous equations econometric predeterminedness likelihood ratio lagrange multiplier and wald tests are derived for the overidentification hypothesis against unrestricted alternatives for the predeterminedness hypothesis against unrestricted alternatives and for the predeterminedness hypothesis against overidentified alternatives the tests are derived on the basis of normality but are asymptotically valid under very general conditions this study generalizes and unifies many test procedures proposed previously some new tests are developed

an interpolation technique for computing the dft of a sparse sequence an interpolation technique for the approximate computation of the dft of a sparse sequence is presented this new method is more efficient than fft pruning particularly for long sequences where the effectiveness of fft pruning diminishes this interpolation method for computing the dft of a sparse sequence is very useful in filter design and spectrum analysis

conditions for optimality of naive quantized finite horizon control this paper presents properties of a control law which quantizes the unconstrained solution to a unitary horizon quadratic programme this naive quantized control law underlies many popular algorithms such as converters and decision feedback equalities and is easily shown to be globally optimal for horizon one however the question arises as to whether it is also globally optimal for horizons greater than one i e whether it solves a finite horizon quadratic programme where decision variables are restricted to belonging to a quantized set by using dynamic programming we develop sufficient conditions for this to hold the present analysis is restricted to first order plants however this case already raises a number of highly non trivial issues the results can be applied to arbitrary horizons and quantized sets which may contain a finite or an infinite though countable number of elements

double loop sigma delta modulation with dc input a discrete time model having a two bit 2 b quantizer is analyzed exactly and an analytical expression for the quantizer noise sequence is found rigorous answers are then provided to two fundamental questions for a double loop sigma delta modulation system with dc input 1 what is the long term statistical behavior of the internal quantizer noise 2 how does the asymptotic mean square sigma delta quantization error vary as a function of the oversampling ratio

efficient special purpose linear programming for fir filter design a high efficiency special purpose linear programming algorithm for fir filter design is introduced this algorithm incorporates fft and fir zero phase filters to assist in the computation compared to the general purpose linear programming this special purpose linear programming produces large savings in the computing cost when used to design fir filters the savings increase with the length of the filter being designed

decimation for sigma delta modulation decimation is an important component of oversampled analog to digital conversion it transforms the digitally modulated signal from short words occurring at high sampling rate to longer words at the nyquist rate here we are concerned with the initial stage of decimation where the word rate decreases to about four times the nyquist rate we show that digital filters comprising cascades of integrate and dump functions can match the structure of the noise from sigma delta modulation to provide decimation with negligible loss of signal to noise ratio explicit formulas evaluate particular tradeoffs between modulation rate signal to noise ratio length of digital words and complexity of the modulating and decimating functions

control of constrained discrete time linear systems using quantized controls abstract the theory of control of continuous time systems with control constraints is extended to the case where the controls are of the form u i n i s where n i is an integer and s is a scaling factor these results permit the analysis of the controllability of digital control systems with quantized controls they also provide the theoretical framework for recently suggested real time suboptimal controllers based on the application of artificial intelligence techniques such an application is presented at the end of the paper

fir filter design over a discrete powers of two coefficient space fir digital filters with discrete coefficient values selected from the powers of two coefficient space are designed using the methods of integer programming the frequency responses obtained are shown to be superior to those obtained by simply rounding the coefficients both the weighted minimax and the weighted least square error criteria are considered using a weighted least square error criterion it is shown that it is possible to predict the improvement that can be expected when integer quadratic programming is used instead of simple coefficient rounding

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

a use of double integration in sigma delta modulation sigma delta modulation is viewed as a technique that employs integration and feedback to move quantization noise out of baseband this technique may be iterated by placing feedback loop around feedback loop but when three or more loops are used the circuit can latch into undesirable overloading modes in the desired mode a simple linear theory gives a good description of the modulation even when the quantization has only two levels a modulator that employs double integration and two level quantization is easy to implement and is tolerant of parameter variation at sampling rates of 1 mhz it provides resolution equivalent to 16 bit pcm for voiceband signals digital filters that are suitable for converting the modulation to pcm are also described

design of discrete coefficient fir filters by a fast entropy directed deterministic annealing algorithm we present an entropy directed deterministic annealing optimization algorithm and show its applicability to the problem of designing digital filters with discrete coefficients each implemented as a sum of signed power of two terms and additional general hardware constraints the algorithm is based on analogies from statistical mechanics and is related to the well known mean field annealing algorithm it utilizes estimates of conditional entropy to prune the problem during the optimization thereby reducing the computational time by 30 to 50 in conjunction with a scheme to compute the value of the objective function as a sequence of updates this approach leads to a very fast algorithm as an application example demonstrating the potential of the new method we consider the design of digital filters with discrete coefficients consisting of a minimum number of signed power of two terms

noise reduction in oversampled filter banks using predictive quantization we introduce two methods for quantization noise reduction in oversampled filter banks these methods are based on predictive quantization noise shaping or linear prediction it is demonstrated that oversampled noise shaping or linear predictive subband coders are well suited for subband coding applications where for technological or other reasons low resolution quantizers have to be used in this case oversampling combined with noise shaping or linear prediction improves the effective resolution of the subband coder at the expense of increased rate simulation results are provided to assess the achievable quantization noise reduction and resolution enhancement and to investigate the rate distortion properties of the proposed methods

quantization noise spectra several results describing the behavior of quantization noise in a unified and simplified manner are discussed exact formulas for quantizer noise spectra are developed they are applied to a variety of systems and inputs including scalar quantization pcm dithered pcm sigma delta modulation dithered sigma delta modulation two stage sigma delta modulation and second order sigma delta modulation

a new technique for the design of two dimensional fir and iir filters the design problem of two dimensional digital filters is the subject of this paper the problem is formulated for both fir and iir filters in such a way that the performance index is a convex function of the optimization vector the design technique is based on newton s method each iteration consists of n easily computed steps where n is the number of parameters to be optimized the coefficients can be obtained in the quantization levels according to the desired number representation illustrative examples and comparisons with existing techniques are also included