the vinnicombe metric for nonlinear operators describes an extension of the vinnicombe metric on linear operators to a pseudometric on nonlinear operators a metric for finite dimensional time varying operators is shown to be capable of guaranteeing stability and performance robustness and reduces to the standard vinnicombe metric for the time invariant operator case which is known to be less conservative than the gap metric the analysis exploits the time varying operator equivalents of unstable poles and normalized coprime fractional descriptions in addition a time varying operator equivalent of the winding number is defined

the arithmetic cosine transform exact and approximate algorithms in this paper we introduce a new class of transform method the arithmetic cosine transform act we provide the central mathematical properties of the act necessary in designing efficient and accurate implementations of the new transform method the key mathematical tools used in the paper come from analytic number theory in particular the properties of the riemann zeta function additionally we demonstrate that an exact signal interpolation is achievable for any block length approximate calculations were also considered the numerical examples provided show the potential of the act for various digital signal processing applications

pseudopolar based estimation of large translations rotations and scalings in images one of the major challenges related to image registration is the estimation of large motions without prior knowledge this work presents a fourier based approach that estimates large translations scalings and rotations the algorithm uses the pseudopolar pp fourier transform to achieve substantial improved approximations of the polar and log polar fourier transforms of an image thus rotations and scalings are reduced to translations which are estimated using phase correlation by utilizing the pp grid we increase the performance accuracy speed and robustness of the registration algorithms scales up to 4 and arbitrary rotation angles can be robustly recovered compared to a maximum scaling of 2 recovered by state of the art algorithms the algorithm only utilizes one dimensional fast fourier transform computations whose overall complexity is significantly lower than prior works experimental results demonstrate the applicability of the proposed algorithms

the scale representation the authors considers scale a physical attribute of a signal and develop its properties he presents an operator which represents scale and study its characteristics and representation this allows one to define the scale transform and the energy scale density spectrum which is an indication of the intensity of scale values in a signal he obtains explicit expressions for the mean scale scale bandwidth instantaneous scale and scale group delay furthermore he derives expressions for mean time mean frequency duration frequency bandwidth in terms of the scale variable the short time transform is defined and used to obtain the conditional value of scale for a given time he shows that as the windows narrows one obtains instantaneous scale convolution and correlation theorems for scale are derived a formulation is devised for studying linear scale invariant systems he derives joint representations of time scale and frequency scale general classes for each are presented using the same methodology as for the time frequency case as special cases the joint distributions of marinovich altes 1978 1986 and bertrand bertrand 1984 are recovered also joint representations of the three quantities time frequency scale are devised a general expression for the local scale autocorrelation function is given uncertainty principles for scale and time and scale and frequency are derived

sensitivity and robust stability of general input output systems the author considers a general model of an input output system that is governed by nonlinear operator equations which relate the input the state and the output of the system this model encompasses feedback systems as a special case assuming that the governing equations depend on a parameter a which is allowed to vary in a neighborhood of a nominal value a sub 0 in a linear space the author studies the dependence of the system behavior on a a system is considered insensitive if for any fixed input the output depends continuously on a similarly the system is robust if it is stable for each a in a neighborhood of a sub 0 stability is defined as an appropriate continuity of the input output operator the results give various sufficient conditions for insensitivity and robustness applications of the theory are discussed including the estimation of the difference of operator inverses and the insensitivity and robust stability of a hilbert network a feedback feedforward system a traditional feedback system and a time varying dynamical system described by a linear vector differential equation on 0 infinity

approximating filtered scale variant signals we develop theorems that place limits on the point wise approximation of the responses of filters both linear shift invariant lsi and linear shift variant lsv to input signals and images that are lsv in the following sense they can be expressed as the outputs of systems with lsv impulse responses where the shift variance is with respect to the filter scale of a single prototype filter the approximations take the form of lsi approximations to the responses we develop tight bounds on the approximation errors expressed in terms of filter durations and derivative sobolev norms finally we find application of the developed theory to defoveation of images deblurring of shift variant blurs and shift variant edge detection

a penalized likelihood approach to image warping discussion a warping is a function that deforms images by mapping between image domains the choice of function is formulated statistically as maximum penalized likelihood where the likelihood measures the similarity between images after warping and the penalty is a measure of distortion of a warping the paper addresses two issues simultaneously of how to choose the warping function and how to assess the alignment a new fourier von mises image model is identified with phase differences between fourier transformed images having von mises distributions also new null set distortion criteria are proposed with each criterion uniquely minimized by a particular set of polynomial functions a conjugate gradient algorithm is used to estimate the warping function which is numerically approximated by a piecewise bilinear function the method is motivated by and used to solve three applied problems to register a remotely sensed image with a map to align microscope images obtained by using different optics and to discriminate between species of fish from photographic images

on the stabilization of nonlinear systems we extend the applicability of the global q parametrization method of controller design to a large class of unstable nonlinear plants the main result is a two step compensation theorem analogous to that of zames for unstable linear plants if p l e2 rightarrow l e1 is a nonlinear possibly unstable plant and f 0 is any incrementally stable controller such that p 1 p i f 0 p 1 is incrementally stable then the class of controllers f which yields an f g stable closed loop system in the unity feedback configuration for p is globally parametrized by finite gain stable maps q l e1 rightarrow l e2 with f f 0 q i p 1 q 1

permuted difference coefficient realization of fir digital filters a new realization for fir digital filters using permuted difference coefficients is proposed in this paper its coefficients are obtained as the difference between the successive values of the original coefficients reordered in a sequence with falling magnitude the proposed realization can hold desirable properties in fir filters such as an exactly linear phase characteristic and stable implementation and is effectively applied to a wide range filter response quantization error analysis shows that the internal data word lengths must be somewhat increased to maintain the same roundoff noise as in a direct form realization computational complexity becomes about 23 percent and 18 percent for 99th and 299th order filters taking the excess data word lengths into account compared with the direct form

construction of the left coprime fractional representation for a class of nonlinear control systems abstract a constructive approach to the left coprime fractional representations for a class of stable and unstable nonlinear control systems described by certain multi input multi output nonlinear ordinary differential equations is proposed the method works for the coprimeness defined by verma 15

characterization of all nonlinear stabilizing controllers via observer based kernel representations this paper deals with the characterization of all nonlinear stabilizing controllers observer based kernel representations are introduced to avoid the difficulty which occurs in constructing the state space realizations of the parametrization of input output operators the parametrization of all stabilizing controllers for a given plant and a class of stabilizing plant controller pairs are derived by employing observer based kernel representations furthermore the relationship between the results via kernel representation approach and the existing results via state space approach is clarified

a high resolution data adaptive time frequency representation a data adaptive time frequency representation is developed that overcomes some limitations of the short time fourier transform while avoiding the cross terms that make the wigner distribution and other bilinear representations difficult to interpret the adaptive time frequency representations uses gaussian basis functions but varies their time width and chirp rate with time and frequency to achieve high signal concentration everywhere a measure of local signal concentration allows fully automated determination of the optimal basis parameters the adaptive method is computationally expensive but may provide much better performance than any currently known technique

a parametrization for closed loop identification of nonlinear systems based on differentially coprime kernel representations in this paper we use the notion of a differentially coprime kernel representation to parametrize the set of all nonlinear plants stabilized by a given nonlinear controller using a so called youla parameter and to unify understanding of some stability concepts for nonlinear systems by utilizing the differential kernel representation concept we are able to convert a closed loop identification problem into one of open loop identification the main advantage of our approach using kernel representations over fractional descriptions is that we address a larger class of nonlinear systems the idea of a differential kernel representation allows us also to clarify the relationship between three different notions of internal stability available in the literature the results in the paper thus provide new insights to the stability of nonlinear feedback systems

robust right coprime factorization and robust stabilization of nonlinear feedback control systems robust right coprime factorization and robust stabilization of nonlinear feedback control systems are studied the concept of robust right coprime factorization of nonlinear operators for feedback control systems is introduced some conditions for the robustness of a right coprime factorization of a nonlinear plant under unknown but bounded perturbations are derived an example with a closed form solution is included to illustrate the general theory and a step by step construction of the robust factorization and the robust stabilization

further results on stability of xd t ax t bx t t abstract our aim in this communication is to improve the existing results concerning the stability of x dot t ax t bx t it is shown that the unstable characteristic roots could be more accurately located in a bounded and restrictive region of the complex plane an iterative scheme is presented for numerical implementation of the results numerical computations are presented for illustration and comparison with previous results

a vlsi architecture for simplified arithmetic fourier transform algorithm the arithmetic fourier transform aft is a number theoretic approach to fourier analysis which has been shown to perform competitively with the classical fft in terms of accuracy complexity and speed theorems developed by i s reed et al 1990 for the aft algorithm are used here to derive the original aft algorithm which bruns found in 1903 this is shown to yield an algorithm of less complexity and of improved performance over certain aft algorithms a vlsi architecture is suggested for this simplified aft algorithm this architecture uses a butterfly structure which reduces the number of additions by 25 of that used in the direct method

the design and use of steerable filters the authors present an efficient architecture to synthesize filters of arbitrary orientations from linear combinations of basis filters allowing one to adaptively steer a filter to any orientation and to determine analytically the filter output as a function of orientation steerable filters may be designed in quadrature pairs to allow adaptive control over phase as well as orientation the authors show how to design and steer the filters and present examples of their use in the analysis of orientation and phase angularly adaptive filtering edge detection and shape from shading one can also build a self similar steerable pyramid representation the same concepts can be generalized to the design of 3 d steerable filters

on computing and implementing the running bispectra the paper extends recursion to bispectrum estimation problems and presents the systolic array implementation of the recursive higher order spectrum in which the bispectrum estimate is updated every data sample forward and reverse sequence running fourier transforms are first systolically realized the results are then used to drive a second systolic array whose outputs represent the ft of the data third order moment the proposed systolic arrays have no global communications with a number of processing elements independent of the size of the employed 2d lag window

algebraic rings of integers and some 2d lattice problems in physics this paper develops the mobius inversion formula for the gaussian integers and eisenstein s integers and gives two applications the first application is to the two dimensional arithmetic fourier transform aft which is suitable for parallel processing the second application is to two dimensional inverse lattice problems and is illustrated with the recovery of interatomic potentials from the cohesive energy for monolayer graphite the paper demonstrates the potential application in the physical science of integral domains other than the standard integers

stabilisation of nonlinear systems by discontinuous dynamic state feedback in this paper a dynamic state feedback that stabilizes general nonlinear affine in the control systems is proposed it is deduced from the solution of an hamilton jacobi like equality with two boundary conditions the asymptotic stability of the closed loop system is proved and some examples are given an interesting feature of this method is that the so obtained feedback takes the form of a generalised sliding mode control in the sense that it is a dynamic feedback on one half part of the space and a static feedback on the other half with eventually a discontinuity on the surface dividing the space

the fast discrete radon transform i theory an inversion scheme for reconstruction of images from projections based on the slope intercept form of the discrete radon transform is presented a seminal algorithm for the forward and the inverse transforms proposed by g beylkin 1987 demonstrated poor dispersion characteristics for steep slopes and could not invert transforms based on nonlinear slope variations by formulating the computation of a discrete computation of the continuous radon transform formula the authors explicitly derive fast generalized inversion methods that overcome the original shortcomings the generalized forward frt and inverse ifrt algorithms proposed are fast eliminate interpolation calculations and convert directly between a raster scan grid and a rectangular polar grid in one step

image denoising using scale mixtures of gaussians in the wavelet domain we describe a method for removing noise from digital images based on a statistical model of the coefficients of an overcomplete multiscale oriented basis neighborhoods of coefficients at adjacent positions and scales are modeled as the product of two independent random variables a gaussian vector and a hidden positive scalar multiplier the latter modulates the local variance of the coefficients in the neighborhood and is thus able to account for the empirically observed correlation between the coefficient amplitudes under this model the bayesian least squares estimate of each coefficient reduces to a weighted average of the local linear estimates over all possible values of the hidden multiplier variable we demonstrate through simulations with images contaminated by additive white gaussian noise that the performance of this method substantially surpasses that of previously published methods both visually and in terms of mean squared error

duality of log polar image representations in the space and spatial frequency domains in this paper we study the result of applying a lowpass variant filtering using scaling rotating kernels to both the spatial and spatial frequency representations of a two dimensional 2 d signal image it is shown that if we apply this transformation to a fourier pair the two resulting signals can also form a fourier pair when the filters used in each domain maintain a dual relationship for a large class of self dual filters a perfect symmetry exists so that the lowpass scaling rotating variant filtering srvf is the same in both domains thus commuting with the fourier transform operator the lowpass srvf of an image is often referred to as a foveated image whereas its fourier pair the lowpass srvf of its spectrum can be realized as a local spectrum estimation around the point of attention this lowpass srvf is equivalent to a log polar warping of the image representation followed by a lowpass invariant filtering and the corresponding inverse warping the use of the log polar warped representation allows us to extend the one dimensional 1 d scale transform to higher dimensions in particular to images for which we have defined a scale rotation invariant representation we also present an efficient implementation using steerable filters to compute both the foveated image and the local spectrum

internally stable nonlinear systems with disturbances a parameterization this paper deals with the control of a nonlinear system whose output is subjected to an additive disturbance the main result is a simple parameterization of the set of all system responses that can be obtained through internally stable control of the given system the parameterization provides a clear indication of the effects of the disturbance on the response of the stabilized closed loop system the class of achievable responses is determined by the numerator of a right coprime fraction representation of the system being controlled

coprime fractional representations and stability of non linear feedback systems fractional representation methods for finite dimensional linear time invariant fdlti systems have been developed in an algebraic framework of principal ideal domains the concept of coprime fractional representations has been generalized to discrete time non linear systems by hammer 1985 1987 by viewing the bezout identity as the basis of the definition of coprimeness in this paper we view the role of right coprime fractional representation in representing the set of all stable input output pairs of a possibly unstable non linear system this notion of coprimeness is shown to be equivalent to that of fdlti systems using coprime fractional representations of non linear systems we obtain a characterization of the stability of non linear feedback systems this characterization is similar to that obtained in the case of fdlti systems we also obtain a parameterization of all non linear and time varying stabilizing controllers for linear possibly time varying plants which has the same form as t

fourier analysis and signal processing by use of the mobius inversion formula a novel fourier technique for digital signal processing is developed this approach to fourier analysis is based on the number theoretic method of the mobius inversion of series the fourier transform method developed is shown also to yield the convolution of two signals a computer simulation shows that this method for finding fourier coefficients is quite suitable for digital signal processing it competes with the classical fft fast fourier transform approach in terms of accuracy complexity and speed

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

sensitivity and robust stability of some control systems containing a nonlinear plant sufficient conditions for insensitivity and robust stability of some frequently used control systems which contain a nonlinear plant and are not of a feedback type are presented these conditions are derived from some results of the author 1991 on general input output systems they are stated in terms of the transmission operators that describe the blocks constituting the system

on the parametrization of nonlinear finite gain over set stabilizing controllers the concepts of gain and incremental gain over set have been introduced to alleviate some of the limitations of the conventional notions of gain and incremental gain in this paper the class of all finite gain over set stabilizing controllers is parametrized in terms of a finite gain over set stable map q provided that the plant p is finite incremental gain over set stable an alternate theorem for finite gain over ball stability of the closed loop is also developed which provides a superset and a subset of the set of all finite gain over set stabilizing compensators for the feedback system

left coprime factorizations and a class of stabilizing controllers for non linear systems abstract the problem of representing a class of non linear systems by both left and right bounded input bounded output bibo coprime factors is studied based on the coprime factorizations the class of all stabilizing controllers of a particular structure for the set of plants under consideration is then characterized in term of a bibo stable map q the results specialize to the youla kucera parametrization in the linear case results giving the various conditions for a non linear feedback system to be well posed are also presented

global parametrization of feedback systems with nonlinear plants for unity feedback systems with a plant p and controller c we show that given a nonlinear stable p the class of all controller stabilizing the feedback system is globally parametrized by a stable map q we also show how q is useful in studying the effects of modeling errors on the stability

weighted optimization theory for nonlinear systems in this paper the solution of a nonlinear version of the weighted sensitivity h infty optimization problem is discussed it is shown that the natural object to be considered in this context is a certain sensitivity operator which will be optimized locally in a given energy ball see 5 for the details in the linear case the authors are reduced again to the classical sensitivity minimization technique of zames 21 the methods were very strongly influenced by the complex analytic power series ideas of 3 4 5 see also the recent results of ball and helton 6 for another approach to this subject

on robust stabilization on nonlinear control systems abstract a robust stabilization problem for general mimo nonlinear systems is formulated in a banach space setting in the time domain existence and uniqueness theorems are established a general procedure for solving the problem is illustrated and a simple example is included to show how the results can be applied

uniformly optimal control of linear time invariant plants nonlinear time varying controllers abstract it is shown that in the problems of uniformly or h optimal control of linear time invariant plants arbitrary nonlinear time varying controllers offer no advantage over linear time invariant controllers

non linear systems stability and rationality the problem of when a non linear system can be represented as a quotient of two stable non linear systems is considered attention is mainly directed toward nonlinear discrete time recursive systems where recursive means that the relationship between an input sequence and the corresponding output sequence can be expressed in terms of a finite number of recursive equations necessary and sufficient conditions are derived for the existence of a fraction representation of a recursive system where the numerator and the denominator are stable recursive systems the explicit construction of such a fraction representation is described

notes on the interpolation of discrete periodic signals using sinc function related approaches considering the sinc interpolation of discrete periodic signals this correspondence establishes the equivalence of two recently published methods furthermore the interpolation methods are equivalent to a fractional delay filter designed using the frequency sampling technique a numerically stable and computationally attractive form of the equivalent methods is presented

right factorization of a class of time varying nonlinear systems a class of nonlinear continuous time time varying plants with a state space description which has a uniformly completely controllable linear part is considered for this class a right factorization is obtained for the case in which the state is available for feedback a normalized right coprime factorization is realized

a theory for multiresolution signal decomposition the wavelet representation multiresolution representations are effective for analyzing the information content of images the properties of the operator which approximates a signal at a given resolution were studied it is shown that the difference of information between the approximation of a signal at the resolutions 2 sup j 1 and 2 sup j where j is an integer can be extracted by decomposing this signal on a wavelet orthonormal basis of l sup 2 r sup n the vector space of measurable square integrable n dimensional functions in l sup 2 r a wavelet orthonormal basis is a family of functions which is built by dilating and translating a unique function psi x this decomposition defines an orthogonal multiresolution representation called a wavelet representation it is computed with a pyramidal algorithm based on convolutions with quadrature mirror filters wavelet representation lies between the spatial and fourier domains for images the wavelet representation differentiates several spatial orientations the application of this representation to data compression in image coding texture discrimination and fractal analysis is discussed

technical communique recursive identification of nonlinear plants operating in closed loop using kernel representations in this paper we extend the family of algorithms presented in algorithms for identification of continuous time nonlinear systems a passivity approach in a isidori f ramnabhi lagarrigue w respondek eds nonlinear control in the year 2000 vol 2 pp 13 44 berlin springer automatica 37 2000 469 for the identification of continuous time nonlinear plants operating in closed loop the new algorithms presuppose that one can construct a stable kernel representation for the to be identified model structure the new theory results in a less restrictive passivity condition the main novelty is that the identification of unstable plants can be tackled by an appropriate choice of the kernel representation i e there is an additional degree of freedom when constructing the kernel representation the implicit stability of the controller is still required by the new passivity condition

a parametric texture model based on joint statistics of complex wavelet coefficients we present a universal statistical model for texture images in the context of an overcomplete complex wavelet transform the model is parameterized by a set of statistics computed on pairs of coefficients corresponding to basis functions at adjacent spatial locations orientations and scales we develop an efficient algorithm for synthesizing random images subject to these constraints by iteratively projecting onto the set of images satisfying each constraint and we use this to test the perceptual validity of the model in particular we demonstrate the necessity of subgroups of the parameter set by showing examples of texture synthesis that fail when those parameters are removed from the set we also demonstrate the power of our model by successfully synthesizing examples drawn from a diverse collection of artificial and natural textures

sinc interpolation of discrete periodic signals the paper introduces a method for the sinc interpolation of discrete periodic signals the convolution of the sinc kernel with the infinite sequence of a periodic function is rewritten as a finite summation the method is equivalent to trigonometrical interpolation by fourier series expansion

nonlinear unity feedback systems and q parametrization this paper concerns nonlinear systems defines a new concept of stability and extends to unity feedback systems the technique of q parametrization introduced by zames and developed by desoer chen and gustafson we specify 1 a global parametrization of all controllers that s stabilize a given s stable plant 2 a parametrization of a class of controllers that stabilize an unstable plant 3 necessary and sufficient conditions for a nonlinear controller to simultaneously stabilize two nonlinear plants

the poorman s transform approximating the fourier transform without multiplication a time domain to frequency domain transformation for sampled signals which is computed with only additions and trivial complex multiplications is described this poorman s transform is an approximation to the usual fourier transform obtained by quantizing the fourier coefficients to the four values or 1 or j and is especially useful when multiplication is expensive for the general case of an n point quantization an analytic formula is given for the error in the approximation which involves only contributions from aliased harmonics continuous time signals are considered in this case the approximation is exact for bandlimited signals

mobius transform pairs a continuous version of a theorem from classical number theory due to mobius has recently been derived and used to solve some inverse problems in physics that are otherwise difficult to solve explicitly using standard results a table of mobius transform pairs is presented that may be useful in identifying other applications of the transform to physical problems

remarks on computing coprime factors for distributed parameter systems presents an indirect method for computing coprime factors for a class of linear time invariant distributed parameter systems the method overcomes the numerical instability of an existing direct decomposition method it is shown that coprime factorization can be reduced to constructing simultaneously stabilizing finite dimensional controllers for which an efficient iterative procedure is developed

an algorithm for computing the inverse z transform the authors determine an infinite impulse response of a causal system via a sampling algorithm applied to the transform on the unit circle

on implementing the arithmetic fourier transform the arithmetic fourier transform aft a method for computing the fourier coefficients of a complex valued periodic function is based on a formula which has the advantage of eliminating many of the multiplications usually associated with computing discrete fourier coefficients but has the disadvantage of requiring samples of the signal at nonuniformly spaced time values a method for computing the fourier coefficients which allows uniform sampling at arbitrarily chosen sampling rates is developed the technique still requires few multiplications albeit at the expense of a limited amount of linear interpolation of the sample values efficient hardware implementations of this algorithm are presented

on the equivalence between a minimal codomain cardinality riesz basis construction a system of hadamard sylvester operators and a class of sparse binary optimization problems piecewise low order polynomial riesz basis families are constructed such that they share the same coefficient functionals of smoother orthonormal bases in a localized indexing subset it is shown that a minimal cardinality basis codomain can be realized by inducing sparsity via l1 regularization in the distributional derivatives of the basis functions and that the optimal construction can be found numerically by constrained binary optimization over a suitably large dictionary furthermore it is shown that a subset of these solutions are equivalent to a specific constrained analytical solution derived via sylvester type hadamard operators

on the stabilizing conic sectors obtained using small gain techniques abstract this paper is concerned with the analysis of the scope and properties of the stabilizing conic sectors obtained using small gain and loop transformation sglt techniques first it is shown how sglt techniques are able to generate the set of all nonlinear stabilizing controllers by using transformations based on dynamical 2 2 block systems configurations then stabilizing cones obtained from static configurations are considered they induce only subsets of all stabilizing controllers however providing simplification and tractability for these cones maximality is characterized in terms of mu values and frequency responses finally an algorithm for deriving maximal cones is presented

a state space approach to parameterization of stabilizing controllers for nonlinear systems a state space approach to the youla parameterization of stabilizing controllers for linear and nonlinear systems is suggested the stabilizing controllers or a class of stabilizing controllers for nonlinear systems are characterized as fractional transformations of stable parameters the main idea behind this approach is to decompose the output feedback stabilization problem into state feedback and state estimation problems the parameterized output feedback controllers have separation structures this machinery allows the parameterization of stabilizing controllers to be conducted directly in state space without using coprime factorization

conditions for abstract nonlinear regulation this paper studies the general problem of the existence of output dynamic stabilizers for a control system the controller is not assumed to have any special structure necessary and sufficient conditions are given in terms of new notions which generalize the usual ones of stabilizability and detectability in the particular cases of analytic and bilinear systems these conditions are considerably simplified

fast algorithms for the discrete cosine transform several fast algorithms for computing discrete cosine transforms dcts and their inverses on multidimensional inputs of sizes which are powers of 2 are introduced because the 1 d 8 point dct and the 2 d 8 8 point dct are so widely used they are discussed in detail algorithms for computing scaled dcts and their inverses are also presented these have applications in compression of continuous tone image data where the dct is generally followed by scaling and quantization

a note on the computational complexity of the arithmetic fourier transform it is shown that the number of data points the arithmetic fourier transform aft needs for an n point fourier transform is proportional to n sup 2 thus for example while a standard fast fourier transform algorithm requires 1024 samples to yield 1024 spectral components aft would take more than 300000 samples to do the same job

a note on the coprime fractional representation of nonlinear feedback systems abstract a very large infinite dimensional banach space of bounded nonlinear operators is suggested as an underlying framework for studies of nonlinear systems control meanwhile it is pointed out that all results obtained in verma 6 can be extended to this much larger family of nonlinear control systems

state feedback control of nonlinear systems a simple approach a simple methodology for the design of state feedback controllers for nonlinear continuous time systems is introduced the objective is to develop controllers that drive a nonlinear system from an initial condition into an assigned region of state space it is shown that such state feedback controllers can be derived by solving a set of inequalities obtained directly from quantities given in the controlled system s equation the results are applied to the design of state feedback controllers that achieve robust asymptotic stabilisation for a rather general class of nonlinear systems

efficient algorithm for 2 d arithmetic fourier transform this article presents an efficient algorithm for the two dimensional 2 d arithmetic fourier transform aft based on the mobius inversion formula of odd number series it requires fewer multiplications and has less complexity over previous algorithms in addition a technique is proposed to carry out the on axis fourier coefficients a parallel vlsi architecture is developed for the new algorithm

a new factorization of special nonlinear discrete systems and their applications in this paper a new factorization of discrete nonlinear systems is presented this factorization is based on the star product an operation corresponding to the linear connection of systems a relevant algorithm is developed based on a theoretical background finally some applications to system analysis bibo stability and feedback design are provided

right coprime factorizations and stabilization for nonlinear systems the problem of constructing right coprime factorizations which are based on the graph of an input output map instead of the bezout identity of nonlinear input output maps is considered the map is assumed to arise from a state variable realization with a fixed initial state the main result is that the existence of a stabilizing state feedback implies the existence of a right coprime factorization for the map the technique is illustrated by application to nonlinear systems which are affine in the control and have a controllable linear past and nonlinear systems which are feedback linearizable a notion of input output stability that requires a bound on the magnitude of the input signals is introduced methods of constructing such bounds are developed for a locally feedback linearizable system the problem of input bounds is transferred to the equivalent linear system this leads to a technique that allows state and input constraints for a feedback linearizable system to be mapped to the equivalent linear system

a new algorithm for the solution of a polynomial matrix diophantine equation the main contribution of this work is to provide a new algorithm for the general solution of a polynomial matrix diophantine equation the theory is implemented via illustrative examples

fraction representations of non linear systems a simplified approach abstract a non linear system has a right fraction representation if it can be represented as pq 1 where p and q are stable systems and it has a left fraction representation if it can be represented as g 1 t where g and t are stable systems we develop here a theory of right and of left fraction representations for discrete time non linear systems with bounded input sequences we indicate the connection between fraction representations and the stabilization problem for non linear systems

shiftable multiscale transforms one of the major drawbacks of orthogonal wavelet transforms is their lack of translation invariance the content of wavelet subbands is unstable under translations of the input signal wavelet transforms are also unstable with respect to dilations of the input signal and in two dimensions rotations of the input signal the authors formalize these problems by defining a type of translation invariance called shiftability in the spatial domain shiftability corresponds to a lack of aliasing thus the conditions under which the property holds are specified by the sampling theorem shiftability may also be applied in the context of other domains particularly orientation and scale jointly shiftable transforms that are simultaneously shiftable in more than one domain are explored two examples of jointly shiftable transforms are designed and implemented a 1 d transform that is jointly shiftable in position and scale and a 2 d transform that is jointly shiftable in position and orientation the usefulness of these image representations for scale space analysis stereo disparity measurement and image enhancement is demonstrated

rapid convergence of some seismic processing algorithms the rate of convergence of many numerical algorithms can be greatly improved by repeated application of the method of summation by parts cases of interest in seismology arise when we need to resample the spectrum of a function at unevenly spaced frequency values related examples include the time domain evaluation of the hilbert transform and the extrapolation to the real axis of spectra evaluated in the complex domain a formula of this type was first presented by lanczos 1956 the validity of the algorithms depends upon the fact that summation by parts of the cardinal series representation is justified as long as a function is somewhat oversampled

diophantine equations in control a survey abstract this survey is also a tutorial whose aim is to explain the role of diophantine equations in the synthesis of feedback control systems these are linear equations in a ring and result from a fractional representation of the systems involved the cornerstone of the exposition is a simple parametrization of all stabilizing controllers for a given plant one can then choose in principle the best controllers for various applications these ideas evolved from early attempts to use polynomial equations in the design of discrete time linear systems by now they have been extended to continuous time infinite dimensional time varying and non linear systems

deformable kernels for early vision early vision algorithms often have a first stage of linear filtering that extracts from the image information at multiple scales of resolution and multiple orientations a common difficulty in the design and implementation of such schemes is that one feels compelled to discretize coarsely the space of scales and orientations in order to reduce computation and storage costs a technique is presented that allows 1 computing the best approximation of a given family using linear combinations of a small number of basis functions and 2 describing all finite dimensional families i e the families of filters for which a finite dimensional representation is possible with no error the technique is based on singular value decomposition and may be applied to generating filters in arbitrary dimensions and subject to arbitrary deformations the relevant functional analysis results are reviewed and precise conditions for the decomposition to be feasible are stated experimental results are presented that demonstrate the applicability of the technique to generating multiorientation multi scale 2d edge detection kernels the implementation issues are also discussed

comments on a note on the computational complexity of the arithmetic fourier transform by n tepedelenlioglu the commenter states that because of the use of farey sequences the result stated by n tepedelenlioglu ibid vol 37 no 7 p 1146 7 1989 becomes a statement about d sub n the number of elements in a farey sequence of order n tepedelenlioglu s formula is then equivalent to a formula about farey sequences given by m r schroder 1986 c m rader 1977 thus for example while a standard ftt algorithm requires 1024 samples to yield 1024 spectral components aft would take more than 300000 samples to do the same job

inverse z transform by mobius inversion and the error bounds of aliasing in sampling a general algorithm based on two special mobius inversion formulae is developed to compute the inverse z transform this approach to fourier analysis uses what is called the arithmetic fourier transform aft with the new aft algorithm one can compute the inverse z transform of an infinite two sided sequence it is compared with the conventional dft approach both methods have aliasing errors due to sampling the error bounds of the aliasing effects in the dft and the new proposed method are established and compared in general the aft algorithm is not so vulnerable to the aliasing errors in the high frequency components as the dft approach

the mobius inversion and fourier coefficients the mobius inversion formula is extended to the unique factorization semigroup based on the theory of generalized function and the theory of algebraic numbers we obtain the relation between high dimensional fourier coefficients and the extended mobius inversion formula i e high dimensional arithmetic fourier transform

method for the global analysis of non linear parametrized systems a method for the global analysis of non linear systems is presented which provides a framework for the analysis of both continuous and discrete time non linear systems for the diverse range of model types by extending a numerical approach to enable the analysis of non linear parametrized non linear systems a global perspective is achieved that is difficult to obtain using analytical methods alone simple examples are used to illustrate how the method characterizes the system stability at the same time as detecting typical qualitative bifurcation phenomena a non linear feedback system is analysed in order to show how the approach provides both qualitative and quantitative information over a defined region of the system parameter space the method proves to be a powerful tool which can be used to probe the non linear characteristics of a system

optimal disturbance rejection for nonlinear control systems the problem of optimal disturbance rejection for a general class of multiinput multioutput mimo nonlinear systems achieved over a set of stabilizing compensator operators is formulated in a banach space setting conditions on the operators are imposed on the basis of the inputs as well as the outputs an existence theorem for optimal solutions is established under some realistic and verifiable conditions for solving the optimization problem a generalized recursive nonlinear programming algorithm is passed and a simple example of nonlinear optimal feedback design is given to show that the problem can be reduced to standard min max optimization and is hence solvable

operator based robust control design for nonlinear plants with perturbation in this article operator based robust control design for nonlinear plants with perturbation is considered by using robust right coprime factorisation approach in detail the property of unimodular operator is studied and a control design structure is proposed based on the proposed design scheme the designed system is robustly stable also output tracking performance can be realised simultaneously finally the effectiveness of the proposed design scheme is demonstrated by a simulation example

a generalized mobius transform and arithmetic fourier transforms a general approach to arithmetic fourier transforms aft is developed the implementation is based on the concept of killer polynomials and the solution of an arithmetic deconvolution problem pertaining to a generalized mobius transform this results in an extension of the bruns 1903 procedure valid for all prime numbers and in an aft that extracts directly the sine coefficients from the fourier series

a combinatorial limit to the computing power of vlsi circuits we introduce a property of boolean functions called transitivity which consists of integer polynomial and matrix products as well as of many interesting related computational problems we show that the area of any circuit computing a transitive function grows quadratically with the circuit s maximum data rate expressed in bits s this result provides a precise analytic expression of an area time tradeoff for a wide class of vlsi circuits furthermore as shown elsewhere this tradeoff is achievable we have thus matching to within a constant multiplicative factor upper and lower complexity bounds for the three above products in the vlsi circuits computational model

improved square root forms of fast linear least squares estimation algorithms improving the numerical stability of fast algorithms by square root factorization generally requires the use of hypernormal transformations which do not always exhibit a satisfactory numerical behavior an alternate approach adapted from a paper by a w bojanczyk and a o steinhardt see ibid vol 37 p 1286 8 1989 is proposed it uses orthogonal transformations which leads to more stable fast square root algorithms applications to the generalized levinson algorithm and the chandrasekhar equations are detailed

a generalized mobius transform arithmetic fourier transforms and primitive roots a general approach to arithmetic fourier transforms is developed the implementation is based on sine and cosine killer procedures pertaining to a generalized mobius transform involving reduced periodic multiplicative arithmetical functions it is shown that cosine killer procedures exist whenever one half of euler s totient function of the order of the transform is odd primitive roots and indices with respect to primitive roots play an important part in the derivation of the results