Multiple Exchange Algorithm Research Articles

Network Security System with Optimized Randomized Multiple Key Exchange Algorithm

This paper illustrates three different algorithms to provide shared secret key for security of the system. The proposed three algorithms namely 1) Modified Simple Password Key Exchange Scheme 2) Modified Diffie-Hellman Key exchange Scheme 3) Modified Elliptic Curve Scheme are meant to provide shared secret key for authentication process. Enhancements in terms of memory requirement, storage and other security properties such as authentication among mutual users, fraud prevention, attack etc., prove the validity of the proposed algorithms in proving authentication for the cryptographic identification of networks.

Theory and Design of Linear-Phase Minimax FIR Filters with Mixed Constraints in the Frequency Domain

The alternation theorem is the core of efficient approximation algorithms for the minimax design of finite-impulse response (FIR) filters. In this paper, an extended alternation theorem with additional mixed constraints, i.e., equality-and-inequality constraints, is obtained. Then, an efficient multiple-exchange algorithm based on the extended theorem is presented for designing linear-phase FIR filters with frequency mixed constraints in the minimax sense. Further, convergence of the algorithm is established. Several design examples and comparisons with existing techniques are presented, and the simulation results show that the proposed algorithm is numerically more efficient and guaranteed to converge to the optimal solution.

Use Of The Remez Algorithm For Designing FRM Based FIRr Filters

A very efficient technique for drastically reducing the number of multipliers and adders in narrow transition-band linear-phase finite impulse response (FIR) filters is to use the one-stage or multistage frequency-response masking (FRM) approach as originally introduced by Lim. In the original synthesis techniques developed by Lim and Lian, the subfilters in the overall approach were designed using time-consuming linear programming. In order to perform the overall synthesis faster, this paper shows how these subfilters can be designed with the aid of the the Remez multiple exchange algorithm, the most powerful technique for designing arbitrary-magnitude linear-phase FIR filters in the minimax sense. In addition to speeding up the overall procedure, the use of the Remez algorithm enables one to generate a very fast MATLAB program for the overall synthesis so that after being given the filter specifications as well as the number of stages, the program automatically provides the solution with the minimum number of multipliers and adders required in the overall implementation. This is possible because the MATLAB Remez routine is directly available and thus can be used for this purpose after appropriate modifications.

Design of equiripple FIR filters with constraint using a multiple exchange algorithm

We propose a method of designing equiripple linear-phase FIR filters with linear constraint by using the Remez exchange algorithm. A novel technique is derived to convert a linearly constrained problem into an equivalent unconstrained one. We proposed a technique to modify the original desired frequency response so that the original linear constraint can be reduced to a simpler one (the null constraint) for the new target frequency response. The filter with null constraint can be designed without constraint by transformation of the original basis functions. The transformation is represented by a basis for the null space of the constraint. In this paper, we show that the transformed basis set also forms a Tchebycheff set. This fact indicates the proposed design is optimal in the Tchebycheff sense. The optimal filter is deigned by the Remez method according to the new target frequency response in transformed basis. Design examples suggest that the proposed algorithm converges fast and stably.

On the use of Remes multiple exchange algorithm for linear-phase FIR filters with general specifications

The celebrated Remes multiple exchange algorithm for linear-phase digital FIR filter design is most commonly described for ordinary filter types (low-pass, high-pass, etc.) where it is sufficient to consider only the magnitude of the error function. Convergence for general specifications will be guaranteed only when the sign of the error function is incorporated. However, a discussion of this feature of the Remes algorithm is lacking in the literature on digital signal processing. The aim of this presentation is to fill in this gap by recasting the Remes exchange algorithm for the design of linear-phase finite-impulse response (FIR) filters with a general amplitude response specification.

Complex Chebyshev approximation for IIR digital filters based on eigenvalue problem

This paper presents an efficient method for designing complex infinite impulse response digital filters in the complex Chebyshev sense. The proposed method is based on the formulation of a generalized eigenvalue problem by using the Remez multiple exchange algorithm. Hence, the filter coefficients can be easily obtained by solving the eigenvalue problem to find the absolute minimum eigenvalue, and then the complex Chebyshev approximation is attained through a few iterations starting from a given initial guess. The proposed algorithm is computationally efficient because it not only retains the speed inherent in the Remez exchange algorithm but also simplifies the interpolation step. Some design examples are presented and compared with the conventional methods. It is shown that the results obtained by using the method proposed in this paper are better than those obtained by the conventional methods.

Design of an equiripple FIR notch filter using a multiple exchange algorithm

This paper presents a multiple exchange algorithm for designing linear phase equiripple FIR notch filters. The algorithm is first discussed for designing a single notch filter. Compared with conventional linear programming methods, the design speed can be improved significantly. Then, two modified algorithms are developed to reduce the ripple in the low-frequency passband because the energy of biomedical ECG signals is usually occupied in the low-frequency band. Next, we extend the proposed algorithm to design an equiripple multiple-notch filter. Finally, several design examples are presented to demonstrate its effectiveness.

Design of FIR Nyquist filters with low group delay

A new method is proposed for designing FIR Nyquist filters with zero-crossing impulse response and low group delay. It is first shown that FIR Nyquist filters that satisfy the zero-crossing time-domain condition have a frequency response property where both the magnitude and phase responses in the passband are dependent on the stopband response. Therefore, the design problem will become a magnitude approximation in the stopband. The proposed procedure is based on the formulation of a linear problem by using the multiple Remez exchange algorithm in the stopband directly. Hence, the filter coefficients can be computed by solving linear equations, and the optimal solution with an equiripple stopband response is easily obtained after applying an iteration procedure. Although the proposed Nyquist filters have an approximate linear phase response, its group delay is lower than the conventional FIR Nyquist filters. The proposed procedure is computationally efficient because it only solves a set of linear equations. Finally, the characteristics of the low-delay FIR Nyquist filters are examined, and the performance is compared with the conventional FIR Nyquist filters.

Design of equiripple log FIR and IIR filters using multiple exchange algorithm

In this paper, an efficient design method for linear phase FIR filter with equiripple log magnitude response is first investigated. Then, we extend this method to design a class of IIR filter having equiripple behavior in both log magnitude and group delay response. Both design procedures are mainly based on the multiple exchange algorithm. Also, the log FIR and IIR filters are designed in three cases where the passband and stopband error ratio, or the passband error, or the stopband error are specified. Several design examples for lowpass log filters are presented to demonstrate the effectiveness of the proposed methods.

A Multiple-Exchange Algorithm for Complex Chebyshev Approximation by Polynomials on the Unit Circle

This paper presents a generalization of the Remez multiple-exchange (ME) algorithm for solving complex Chebyshev approximation by polynomials on the unit circle. The difficulties of implementing the two fundamental steps of the Remez algorithm in the complex case are pointed out and methods for overcoming these difficulties are proposed. It is shown that generalization of the first step, which involves solving a complex Chebyshev approximation subproblem over a set of guessed extremal points, can be implemented by solving a maximization problem with simple bound constraints using Newton’s method. Furthermore, generalization of the second step, which involves finding a new set of guessed extremal points, can be realized by use of an effective exchange rule derived from the concept of extremal signatures. Numerical results suggest that the proposed ME algorithm has fast convergence rate and good numerical properties even for large-scale problems.

Constrained least square design of FIR filters without specified transition bands

This paper puts forth the notion that explicitly specified transition bands have been introduced in the filter design literature in part as an indirect approach for dealing with discontinuities in the desired frequency response. We suggest that the use of explicitly specified transition bands is sometimes inappropriate because to satisfy a meaningful optimality criterion, their use implicitly assumes a possibly unrealistic assumption on the class of input signals. This paper also presents an algorithm for the design of peak constrained lowpass FIR filters according to an integral square error criterion that does not require the use of specified transition bands. This rapidly converging, robust, simple multiple exchange algorithm uses Lagrange multipliers and the Kuhn-Tucker conditions on each iteration. The algorithm will design linear- and minimum-phase FIR filters and gives the best L/sub 2/ filter and a continuum of Chebyshev filters as special cases. It is distinct from many other filter design methods because it does not exclude from the integral square error a region around the cut-off frequency, and yet, it overcomes the Gibbs' phenomenon without resorting to windowing or 'smoothing out' the discontinuity of the ideal lowpass filter.

An efficient implementation of Lawson's algorithm with application to complex Chebyshev FIR filter design

This paper presents an efficient implementation of Lawson's algorithm and illustrates its application in complex Chebyshev FIR filter design. It is shown that the update terms in Lawson's algorithm can be efficiently achieved by computing a proper subspace projection, provided that the number of points involved in Lawson's algorithm is sufficiently small (not much greater than n where n is the number of variables). An application of this particular implementation form for Lawson's algorithm is then demonstrated by using it to solve the subproblems involved in a multiple exchange algorithm. In particular, this exchange algorithm is based on generalizing Remez second exchange algorithm to the complex case which requires solving a sequence of subproblems where each subproblem is itself a complex Chebyshev approximation problem defined over a finite number of points; the subproblems are systematically defined using a simple exchange procedure. The effectiveness of this multiple exchange algorithm for designing complex FIR filters is illustrated through various design examples, including a long filter with length n=125. >

A Multiple Exchange Algorithm for Multivariate Chebyshev Approximation

Previous article Next article A Multiple Exchange Algorithm for Multivariate Chebyshev ApproximationG. A. WatsonG. A. Watsonhttps://doi.org/10.1137/0712004PDFBibTexSections ToolsAdd to favoritesExport CitationTrack CitationsEmail SectionsAboutAbstractA Remes-type algorithm based on linear programming is presented for computing linear best Chebyshev approximations to multivariate functions. Numerical results are given for some 2-variable examples.[1] R. H. Bartels and , G. H. Golub, The simplex method of linear programming using $LU$ decompo-sition, Comm. ACM, 12 (1969), 266–268 10.1145/362946.362974 0181.19104 CrossrefISIGoogle Scholar[2] L. Bittner, Das Austauschverfahren der linearen Tschebyscheff-Approximation bei nicht erfüllter Haarscher Bedingung, Z. Angew. Math. Mech., 41 (1961), 238–256 MR0175289 0103.28501 CrossrefGoogle Scholar[3] E. W. Cheney, Introduction to approximation theory, McGraw-Hill Book Co., New York, 1966xii+259 MR0222517 0161.25202 Google Scholar[4] J. 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Anal., 11 (1974), 693–699 10.1137/0711056 MR0388735 0256.65006 LinkISIGoogle Scholar Previous article Next article FiguresRelatedReferencesCited byDetails Multivariable quantum signal processing (M-QSP): prophecies of the two-headed oracle20 September 2022 | Quantum, Vol. 6 Cross Ref Membership Function, Time Delay-Dependent $\eta$-Exponential Stabilization of the Positive Discrete-Time Polynomial Fuzzy Model Control SystemIEEE Transactions on Fuzzy Systems, Vol. 30, No. 7 Cross Ref Membership-Function-Dependent Stability Analysis for Polynomial-Fuzzy-Model-Based Control Systems via Chebyshev Membership FunctionsIEEE Transactions on Fuzzy Systems, Vol. 29, No. 11 Cross Ref An Efficient Algorithm for Min-Max Convex Semi-Infinite Programming Problems26 May 2016 | Numerical Functional Analysis and Optimization, Vol. 37, No. 8 Cross Ref A smoothing Levenberg–Marquardt algorithm for semi-infinite programming12 September 2014 | Computational Optimization and Applications, Vol. 60, No. 3 Cross Ref Stability of non-polynomial systems using differential inclusions and polynomial Lyapunov functions Cross Ref A new smoothing Newton-type algorithm for semi-infinite programming1 August 2009 | Journal of Global Optimization, Vol. 47, No. 1 Cross Ref Approximation in normed linear spaces Cross Ref Approximation in normed linear spacesJournal of Computational and Applied Mathematics, Vol. 121, No. 1-2 Cross Ref Chebyshev digital FIR filter designSignal Processing, Vol. 76, No. 1 Cross Ref Numerical Methods for Semi-Infinite Programming: A Survey Cross Ref Optimal design of FIR filters with the complex Chebyshev error criteriaIEEE Transactions on Signal Processing, Vol. 43, No. 3 Cross Ref Discretization methods for the solution of semi-infinite programming problemsJournal of Optimization Theory and Applications, Vol. 71, No. 1 Cross Ref Modifications of the First Remez AlgorithmRembert Reemtsen14 July 2006 | SIAM Journal on Numerical Analysis, Vol. 27, No. 2AbstractPDF (1305 KB)An adaptive differential-correction algorithmJournal of Approximation Theory, Vol. 37, No. 3 Cross Ref A Review of Numerical Methods for Semi-Infinite Optimization Cross Ref A Lagrangian Method for Multivariate Continuous Chebyshev Approximation Problems Cross Ref Chebyshev approximation with non-negative derivativeJournal of Approximation Theory, Vol. 31, No. 2 Cross Ref Bemerkungen zur Fehlerabschätzung bei Linearer Tschebyscheff — Approximation Cross Ref Comparison of algorithms for multivariate rational approximation1 January 1977 | Mathematics of Computation, Vol. 31, No. 138 Cross Ref Computing the strict Chebyshev solution of overdetermined linear equations1 January 1977 | Mathematics of Computation, Vol. 31, No. 140 Cross Ref Linear Chebyshev approximation without Chebyshev setsBIT, Vol. 16, No. 4 Cross Ref Computational Methods in Special Functions-A Survey Cross Ref A stable multiple exchange algorithm for linear sip Cross Ref A comparison of some numerical methods for semi-infinite programming Cross Ref Optimal minimax two-dimensional FIR design using a multiple simplex exchange Cross Ref Volume 12, Issue 1| 1975SIAM Journal on Numerical Analysis History Submitted:26 October 1973Published online:14 July 2006 InformationCopyright © 1975 Society for Industrial and Applied MathematicsPDF Download Article & Publication DataArticle DOI:10.1137/0712004Article page range:pp. 46-52ISSN (print):0036-1429ISSN (online):1095-7170Publisher:Society for Industrial and Applied Mathematics

Restricted range approximation and its application to digital filter design

The multiple exchange algorithm for restricted range approximation is discussed. Efficient formulas are derived for the numerical implementation of the method. Discretization effects are analyzed mathematically. The method is applied to a certain problem arising in digital filter design.

A Multiple Exchange Algorithm for Calculation of Best Restricted Approximations

In this paper, a multiple exchange algorithm for calculation of best restricted approximations is presented and its convergence is proved. The algorithm presented is an extension of the single exchange algorithm for calculation of best restricted approximations which was recently given by Taylor and Winter [1]. Based on computational experience with a class of approximation problems encountered in linear phase digital filter design, a comparison of single exchange and multiple exchange convergence rates and C.P.U. times per iteration is given.