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Circuits and Systems I: Fundamental Theory and Applications, IEEE Transactions on

Issue 6 • Date June 2002

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Displaying Results 1 - 21 of 21
  • Editorial preface to special issue on multidimensional signals and systems

    Publication Year: 2002 , Page(s): 709 - 714
    Cited by:  Papers (6)
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    Freely Available from IEEE
  • LMIs - a fundamental tool in analysis and controller design for discrete linear repetitive processes

    Publication Year: 2002 , Page(s): 768 - 778
    Cited by:  Papers (42)
    Save to Project icon | Request Permissions | Click to expandQuick Abstract | PDF file iconPDF (345 KB) |  | HTML iconHTML  

    Discrete linear repetitive processes are a distinct class of two-dimensional (2-D) linear systems with applications in areas ranging from long-wall coal cutting through to iterative learning control schemes. The feature which makes them distinct from other classes of 2-D linear systems is that information propagation in one of the two distinct directions only occurs over a finite duration. This, in turn, means that a distinct systems theory must be developed for them. In this paper, an LMI approach is used to produce highly significant new results on the stability analysis of these processes and the design of control schemes for them. These results are, in the main, for processes with singular dynamics and for those with so-called dynamic boundary conditions. Unlike other classes of 2-D linear systems, these feedback control laws have a firm physical basis, and the LMI setting is also shown to provide a (potentially) very powerful setting in which to characterize the robustness properties of these processes View full abstract»

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  • Analytical design of multidimensional IIR digital notch filter

    Publication Year: 2002 , Page(s): 882 - 887
    Cited by:  Papers (1)
    Save to Project icon | Request Permissions | Click to expandQuick Abstract | PDF file iconPDF (382 KB) |  | HTML iconHTML  

    This paper is concerned with the multidimensional (M-D) IIR notch filter design problem. First, a dimension updating formula is derived to reduce the M-D notch filter design problem to two types of 1-D filter design problems. Then, we develop a simple algebraic method for the design of two types of 1-D IIR filters. This approach not only has closed form transfer function but also satisfies bounded input/output (BIBO) stability condition. Finally, one example is used to demonstrate the performance of the proposed method and an efficient implementation is presented View full abstract»

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  • A unified approach for the design of 2-D digital filters via semidefinite programming

    Publication Year: 2002 , Page(s): 814 - 826
    Cited by:  Papers (42)
    Save to Project icon | Request Permissions | Click to expandQuick Abstract | PDF file iconPDF (510 KB) |  | HTML iconHTML  

    This paper attempts to demonstrate that a modem optimization methodology known as semidefinite programming (SDP) can serve as the algorithmic core of a unified design tool for a variety of two-dimensional (2-D) digital filters. Representative SDP-based designs presented in the paper include minimax and weighted least-squares designs of FIR filters with continuous and discrete coefficients, and minimax design of stable separable-denominator IIR filters. Our studies are motivated by the fact that SDP as a subclass of convex programming can be solved efficiently using recently developed interior-point methods and, more importantly, constraints on amplitude/phase responses in certain frequency regions and on stability (for IIR filters), that are often encountered in many filter design problems, can be formulated in a natural way as linear matrix inequalities (LMI) which allow SDP to apply. Design examples for each class of filters are included to demonstrate that SDP-based methods can in many cases be useful in producing optimal or near-optimal 2-D filters with reduced computational complexity View full abstract»

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  • Recent results on the robust stability of multivariate polynomials

    Publication Year: 2002 , Page(s): 715 - 724
    Cited by:  Papers (4)
    Save to Project icon | Request Permissions | Click to expandQuick Abstract | PDF file iconPDF (374 KB) |  | HTML iconHTML  

    This paper presents a detailed account of recent results on stability and robust stability of multivariate polynomials, First, a new stability concept is introduced. Then, it is shown that polynomials stable in this new sense have many properties that are known to hold for Hurwitz stable univariate polynomials. Finally, basic robust stability results for such polynomials are presented View full abstract»

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  • A new method for computing the stability margin of two-dimensional continuous systems

    Publication Year: 2002 , Page(s): 869 - 872
    Cited by:  Papers (3)
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    This paper presents a new method for computing the stability margin of two-dimensional (2-D) continuous systems. The method is based on the computation of the Hermite matrix in 2-D continuous systems, one of its partial derivatives and their resultant. The theoretical result is illustrated by examples View full abstract»

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  • Spectral transformations for two-dimensional filters via FFT

    Publication Year: 2002 , Page(s): 827 - 831
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    In this paper, a new fast algorithm for spectral transformations for two-dimensional digital filters is presented. The algorithm is based on the use of the fast Fourier transform. The computational complexity of this algorithm is evaluated. The simplicity and efficiency of the algorithm is illustrated by a numerical example View full abstract»

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  • A new two-dimensional interleaving technique using successive packing

    Publication Year: 2002 , Page(s): 779 - 789
    Cited by:  Papers (13)
    Save to Project icon | Request Permissions | Click to expandQuick Abstract | PDF file iconPDF (360 KB) |  | HTML iconHTML  

    Correction of two-dimensional (2-D) and three-dimensional (3-D) error bursts finds wide applications in secure data handling such as 2-D and 3-D magnetic and optical data storage, charged-coupled devices (CCDs), 2-D barcodes, and information hiding in digital images and video sequences, to name a few. In this paper, we present a new 2-D interleaving technique, called successive packing, to combat 2-D spot burst errors, with potential for extending to multidimensional (M-D) interleaving. Square arrays of 2n × 2n are considered. It is shown that the proposed successive packing technique can spread any error burst of 2k × 2k (with 1 ⩽ k ⩽ n-1), 2k × 2k+1 (with 0 ⩽ k ⩽ n-1), and 2k+1 × 2k (with 0 ⩽ k ⩽ n-1) effectively so that the error burst can be corrected with some simple random-error-correction code (provided the error-correction code is available). It is further shown that the technique is optimal for combating all the above-mentioned error bursts in the sense that the interleaving degree reaches its lower bound. This implies that the algorithm needs to be implemented only once for a given 2-D array and is thereafter optimal for the set of error bursts having different sizes. A performance comparison between the proposed method and some existing techniques is given and the future research is discussed View full abstract»

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  • Parametric Bernstein polynomial for least squares design of 3-D wavelet filter banks

    Publication Year: 2002 , Page(s): 887 - 891
    Cited by:  Papers (6)
    Save to Project icon | Request Permissions | Click to expandQuick Abstract | PDF file iconPDF (536 KB) |  | HTML iconHTML  

    The design of nonseparable three-dimensional (3-D) biorthogonal wavelet filter banks is addressed in this paper. The sampling is on the face centered orthorhombic (FCO) lattice and the ideal low-pass filter's passband shape is the truncated octahedron (TRO). We introduce a 3-D parametric Bernstein polynomial that preserves biorthogonality and gives a good approximation to the TRO shape. Furthermore, filters with arbitrarily flat frequency response for giving regular wavelet systems are readily obtainable. The free parameters of the Bernstein polynomial can be chosen to sharpen the frequency response of the filter. A least squares approach is employed for the design of the parameters. The design process is efficient as it involves solving linear equations and is noniterative. This approach provides a trade-off mechanism between the sharpness of roll-off and the degree of flatness View full abstract»

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  • Analysis of displacement errors in high-resolution image reconstruction with multisensors

    Publication Year: 2002 , Page(s): 806 - 813
    Cited by:  Papers (28)
    Save to Project icon | Request Permissions | Click to expandQuick Abstract | PDF file iconPDF (359 KB) |  | HTML iconHTML  

    An image-acquisition system composed of an array of sensors, where each sensor has a subarray of sensing elements of suitable size, has recently been popular for increasing the spatial resolution with high signal-to-noise ratio beyond the performance bound of technologies that constrain the manufacture of imaging devices. Small perturbations around the ideal subpixel locations of the sensing elements (responsible for capturing the sequence of undersampled degraded frames), because of imperfections in fabrication, limit the performance of the signal-processing algorithms for processing and integrating the acquired images for the desired enhanced resolution and quality. The contributions of this paper include an analysis of the displacement errors on the convergence rate of the iterative approach for solving the transform based preconditioned system of equations. Subsequently, it is established that the use of the MAP, L2 norm or H1 norm regularization functional leads to a proof of linear convergence of the conjugate gradient method in terms of the displacement errors caused by the imperfect subpixel locations. Results of simulation support the analytical results View full abstract»

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  • 2-D stable polynomials with parameter-dependent coefficients: generalizations and new results

    Publication Year: 2002 , Page(s): 725 - 731
    Cited by:  Papers (2)
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    Stability of multidimensional systems is a field of intensive research. In this context, different classes of Hurwitz polynomials (in the continuous case) and Schur polynomials (in the discrete case) are in the focus of interest. Although there exist various methods for testing whether a given polynomial belongs to a certain class of the afore mentioned. The type of converse problem, namely the design of stable polynomials is much more tedious. In this paper, a parametric model for the characterization of real or complex two-variable scattering Schur polynomials is given. In other words, the coefficients of the two-dimensional (2-D) polynomial model are functions of real parameters. The following features make it best suited for the design of 2-D systems: no dependencies between the real valued parameters, coverage of the whole class of 2-D scattering Schur polynomials, and the coefficients of the polynomial are rational functions of the parameters. The synthesis of 2-D lossless networks and unitary matrices play a key role in our considerations View full abstract»

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  • Two-dimensional analysis of an iterative nonlinear optimal control algorithm

    Publication Year: 2002 , Page(s): 872 - 878
    Cited by:  Papers (30)
    Save to Project icon | Request Permissions | Click to expandQuick Abstract | PDF file iconPDF (353 KB) |  | HTML iconHTML  

    Nonlinear optimal control problems usually require solutions using iterative procedures and, hence, they fall naturally in the realm of 2-D systems where the two dimensions are response time horizon and iteration index, respectively. The paper uses this observation to employ 2-D systems theory, in the form of unit memory repetitive process techniques, to investigate optimality, local stability, and global convergence behavior of an algorithm, based on integrated-system optimization and parameter estimation, for solving continuous nonlinear dynamic optimal control problems. It is shown that 2-D systems theory can be usefully applied to analyze the properties of iterative procedures for solving these problems View full abstract»

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  • The wave-digital method and some of its relativistic implications

    Publication Year: 2002 , Page(s): 862 - 868
    Cited by:  Papers (5)
    Save to Project icon | Request Permissions | Click to expandQuick Abstract | PDF file iconPDF (247 KB) |  | HTML iconHTML  

    The advantageous robustness properties obtainable in digital filtering and numerical integration by using the wave-digital principles are essentially due to the extensive use of concepts such as passivity and losslessness, which in turn rely directly on the use of the energy concept. If some of the ideas developed in this context are carried over to relativity theory, one discovers some alternative results that show interesting similarities as well as noteworthy differences to the classical ones. It is shown that by making some assumptions that, although differing from the conventional ones, are at least not a priori physically unreasonable, one is almost naturally led to the alternative expressions. This fact alone justifies the present interest in the subject View full abstract»

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  • Multidimensional causal, stable, perfect reconstruction filter banks

    Publication Year: 2002 , Page(s): 832 - 842
    Cited by:  Papers (3)
    Save to Project icon | Request Permissions | Click to expandQuick Abstract | PDF file iconPDF (414 KB) |  | HTML iconHTML  

    Following our earlier one-dimensional (1-D) work, we show that it is possible to have a large family of biorthogonal perfect reconstruction multidimensional (n-D) subband coding filter banks, which are causal and IIR both at the analysis and at the synthesis ends. While the need for perfect reconstruction IIR filter banks are more apparent for multidimensional signals than for 1-D signals, lack of design techniques have made it impossible to use such schemes. We argue that such filter banks, including their multichannel counterparts, should not only exist in a large variety, but we also indicate a number of tools potentially useful in their design. Specifically, a complete parameterization of such filters leading to design methods in 2-D are given. Parameterizations in frequency domain terms as well as in terms of state space descriptions of filters are provided. These latter techniques have potential for better numerical implementation. The development is valid for two-band as well as for multiband subband coding schemes. Examples of bi-orthogonal version of continuous multidimensional wavelets generated by these iterated filter banks, that have not been previously constructed, are worked out View full abstract»

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  • Recent advances in digital halftoning and inverse halftoning methods

    Publication Year: 2002 , Page(s): 790 - 805
    Cited by:  Papers (32)  |  Patents (1)
    Save to Project icon | Request Permissions | Click to expandQuick Abstract | PDF file iconPDF (1084 KB)  

    Halftoning is the rendition of continuous-tone pictures on displays, paper or other media that are capable of producing only two levels. In digital halftoning, we perform the gray scale to bilevel conversion digitally using software or hardware. In the last three decades, several algorithms have evolved for halftoning. Examples of algorithms include ordered dither, error diffusion, blue noise masks, green noise halftoning, direct binary search (DBS), and dot diffusion. In this paper, we first review some of the algorithms which have a direct bearing on our paper and then describe some of the more recent advances in the field. The dot-diffusion method for digital halftoning has the advantage of pixel-level parallelism unlike the error-diffusion method, which is a popular halftoning method. However, the image quality offered by error diffusion is still regarded as superior to most of the other known methods. We first review error diffusion and dot diffusion, and describe a recent method to improve the image quality of the dot-diffusion algorithm which takes advantage of the Human Visual System (HVS) function. Then, we discuss the inverse halftoning problem View full abstract»

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  • Design of 2-D multiplierless IIR filters using the genetic algorithm

    Publication Year: 2002 , Page(s): 878 - 882
    Cited by:  Papers (11)  |  Patents (1)
    Save to Project icon | Request Permissions | Click to expandQuick Abstract | PDF file iconPDF (296 KB) |  | HTML iconHTML  

    When digital filters are designed with power-of-two coefficients, the multiplications can be implemented by simple shifting operations. For VLSI implementations, multiplierless filters are faster and more compact than filters with multipliers. In this paper, the genetic algorithm (GA) is used to design two-dimensional (2-D) IIR multiplierless filters. The 2-D filter is designed to have periodically shift variant (PSV) coefficients. This increases the degrees of freedom for the multiplierless coefficients so that a better approximation can be achieved. The design involves finding the impulse response of the 2-D PSV filter in closed form and then using the GA to find the filter coefficients. Two different types of GA are used, namely, the Binary-GA and the Integer-GA. Some design examples are presented to illustrate the results View full abstract»

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  • Simple learning control made practical by zero-phase filtering: applications to robotics

    Publication Year: 2002 , Page(s): 753 - 767
    Cited by:  Papers (50)
    Save to Project icon | Request Permissions | Click to expandQuick Abstract | PDF file iconPDF (345 KB)  

    Iterative learning control (ILC) applies to control systems that perform the same finite-time tracking command repeatedly. It iteratively adjusts the command from one repetition to the next in order to reduce the tracking error. This creates a two-dimensional (2-D) system, with time step and repetition number as independent variables. The simplest form of ILC uses only one gain times one error in the previous repetition, and can be shown to converge to the zero-tracking error independent of the system dynamics. Hence, it appears very effective from a mathematical perspective. However, in practice, there are unacceptable learning transients. A zero-phase low-pass filter is introduced here to eliminate the worst transients. The main purpose of this paper is to supply a presentation of experiments on a commercial robot that demonstrate the effectiveness of this approach, improving the tracking accuracy of the robot performing a high speed maneuver by a factor of 100 in six repetitions. Experiments using a two-gain ILC reaches this error level in only three iterations. It is suggested that these two simple ILC laws are the equivalent for learning control of proportional and PD control in classical control system design. Thus, what was an impractical approach, becomes practical, easy to apply, and effective View full abstract»

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  • Multidimensional transfer function models

    Publication Year: 2002 , Page(s): 852 - 861
    Cited by:  Papers (5)
    Save to Project icon | Request Permissions | Click to expandQuick Abstract | PDF file iconPDF (345 KB) |  | HTML iconHTML  

    Transfer functions are a standard description of one-dimensional linear and time-invariant systems. They provide an alternative to the conventional representation by ordinary differential equations and are suitable for computer implementation. This article extends that concept to multidimensional (MD) systems, normally described by partial differential equations (PDEs). Transfer function modeling is presented for scalar and for vector PDEs. Vector PDEs contain multiple dependent output variables, e.g., a potential and a flux quantity. This facilitates the direct formulation of boundary and interface conditions in their physical context. It is shown how carefully constructed transformations for the space variable lead to transfer function models for scalar and vector PDEs. They are the starting point for the derivation of discrete models by standard methods for one-dimensional systems. The presented functional transformation approach is suitable for a number of technical applications, like electromagnetics, optics, acoustics and heat and mass transfer View full abstract»

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  • Optimal design of synthesis filters in multidimensional perfect reconstruction FIR filter banks using Grobner bases

    Publication Year: 2002 , Page(s): 843 - 851
    Cited by:  Papers (10)
    Save to Project icon | Request Permissions | Click to expandQuick Abstract | PDF file iconPDF (473 KB) |  | HTML iconHTML  

    For a given low-pass analysis filter in an n-dimensional (n-D) perfect reconstruction (PR) FIR filter bank, there exists certain degree of freedom in designing a synthesis filter to make the overall filter bank have PR property, and Quillen-Suslin Theorem can be used to precisely determine the degree of freedom. Designing a PR synthesis filter with optimal frequency response amounts to minimizing the deviation between the frequency responses of the synthesis filter and an ideal filter under the PR constraint. In this paper, a method based on Grobner bases computation is developed for optimally designing critically sampled n-D PR FIR filter banks when one analysis filter is known. This design method can be easily combined with various existing design methods including minimax optimization and weighted least squares optimization, and can incorporate additional design goals including linear phase and bandpass characteristic View full abstract»

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  • On homomorphisms of n-D behaviors

    Publication Year: 2002 , Page(s): 732 - 742
    Cited by:  Papers (9)
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    Different modeling procedures applied to a physical system may result in behaviors which are distinct but nevertheless share many structural properties. Such behaviors are isomorphic in a sense which we formalize and characterize in this paper. More generally, we introduce a natural notion of homomorphisms between behaviors of multidimensional systems, generalizing recent work of Fuhrmann. A generalization of strict system equivalence (in the sense of Fuhrmann) is shown to describe the relationship between generalized state-space descriptions in the nD case View full abstract»

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  • Parameterization of stabilizing controllers over commutative rings with application to multidimensional systems

    Publication Year: 2002 , Page(s): 743 - 752
    Cited by:  Papers (13)
    Save to Project icon | Request Permissions | Click to expandQuick Abstract | PDF file iconPDF (400 KB) |  | HTML iconHTML  

    The objective of this paper is to present a parameterization method of all stabilizing controllers of the given plant even in the case where there do not exist right-/left-coprime factorizations. The coordinate-free approach is employed to present it. The parameterization is applied to the multidimensional systems with structural stability View full abstract»

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