The Experts below are selected from a list of 3018 Experts worldwide ranked by ideXlab platform

Alden H Wright - One of the best experts on this subject based on the ideXlab platform.

  • the simple genetic algorithm and the Walsh Transform part ii the inverse
    1998
    Co-Authors: Michael D Vose, Alden H Wright
    Abstract:

    This paper continues the development, begun in Part I, of the relationship between the simple genetic algorithm and the Walsh Transform. The mixing scheme (comprised of crossover and mutation) is essentially “triangularized” when expressed in terms of the Walsh basis. This leads to a formulation of the inverse of the expected next generation operator. The fixed points of the mixing scheme are also determined, and a formula is obtained giving the fixed point corresponding to any starting population. Geiringer's theorem follows from these results in the special case corresponding to zero mutation.

  • the simple genetic algorithm and the Walsh Transform part i theory
    1998
    Co-Authors: Michael D Vose, Alden H Wright
    Abstract:

    This paper is the first part of a two-part series. It proves a number of direct relationships between the Fourier Transform and the simple genetic algorithm. (For a binary representation, the Walsh Transform is the Fourier Transform.) The results are of a theoretical nature and are based on the analysis of mutation and crossover. The Fourier Transform of the mixing matrix is shown to be sparse. An explicit formula is given for the spectrum of the differential of the mixing Transformation. By using the Fourier representation and the fast Fourier Transform, one generation of the infinite population simple genetic algorithm can be computed in time O(cl log2 3), where c is arity of the alphabet and l is the string length. This is in contrast to the time of O(c3l) for the algorithm as represented in the standard basis. There are two orthogonal decompositions of population space that are invariant under mixing. The sequel to this paper will apply the basic theoretical results obtained here to inverse problems and asymptotic behavior.

Xiuqiao Xiang - One of the best experts on this subject based on the ideXlab platform.

  • weak signal detection based on the information fusion and chaotic oscillator
    2010
    Co-Authors: Xiuqiao Xiang, Baochang Shi
    Abstract:

    Based on the chaotic oscillator, a method for weak signal detection using information fusion technology is proposed in this paper. On the one hand, various methods are employed to the amplitude detection of the same weak periodic signal, then the detection outcomes are fused by the adaptive weighted fusion method. On the other hand, during the detection course, information entropy, statistic distance, and Walsh Transform are, respectively, used in the state recognition of chaotic oscillator from the viewpoint of time domain or frequency domain, then the recognition results are fused by the k/l fusion method. Numerical results show that the proposed approach detects signal more precisely, identifies state more accurately, and represents information more completely compared with traditional methods.

  • fault diagnosis based on Walsh Transform and rough sets
    2009
    Co-Authors: Xiuqiao Xiang, Jianzhong Zhou, Zhimeng Luo
    Abstract:

    An accurate and fast method for fault diagnosis is an important issue most techniques have sought to. For this reason, a fast fault diagnosis method based on Walsh Transform and rough sets is proposed in this paper. Firstly, fault signals are fast Transformed by Walsh matrix, and the Walsh spectrums are obtained, whose statistical characteristics constitute feature vectors. Secondly, the feature vectors are discretized and reduced by the rough sets theory, as a result, key features are retained and diagnosis rules are provided. Finally, utilized these diagnosis rules, fault diagnosis is carried out experimentally in the spectrum domain and its performance is compared with that of other methods, the higher accuracy is achieved and much time is saved, which fully validates the effectiveness of our approach.

  • fault diagnosis based on Walsh Transform and support vector machine
    2008
    Co-Authors: Xiuqiao Xiang, Jianzhong Zhou, Bing Peng, Junjie Yang
    Abstract:

    Recognition of shaft orbit plays an important role in the fault diagnosis. In this paper, a novel recognition method for the shaft orbit based on Walsh Transform and support vector machine is proposed. In the method, distance vector between the point on the shaft orbit and its center is first calculated. Then, the distance vector is Transformed by Walsh matrix, and the Walsh spectrum obtained has property of invariance to rotation, scaling and translation. In the end, the Walsh spectrum, viewed as the feature of shaft orbit, is trained and tested by means of support vector machine. In addition, a comparison with the previous methods is performed, and experimental results are encouraging, which fully demonstrates the effectiveness and superiority of the proposed approach.

Palash Sarkar - One of the best experts on this subject based on the ideXlab platform.

  • computing partial Walsh Transform from the algebraic normal form of a boolean function
    2009
    Co-Authors: Chand K Gupta, Palash Sarkar
    Abstract:

    We study the relationship between the Walsh Transform and the algebraic normal form (ANF) of a Boolean function. In the first part of the paper, we obtain a formula for the Walsh Transform at a certain point in terms of parameters derived from the algebraic normal form. We use previous results by Carlet and Guillot to obtain an explicit expression for the Walsh Transform at a point in terms of parameters derived from the ANF. The second part of the paper is devoted to simplify this formula and develop an algorithm to evaluate it. This algorithm can be applied in situations where it is practically impossible to use the fast Walsh Transform algorithm. Experimental results show that under certain conditions it is possible to execute our algorithm to evaluate the Walsh Transform (at a small set of points) of functions on a few scores of variables having a few hundred terms in the algebraic normal form.

  • computing Walsh Transform from the algebraic normal form of a boolean function
    2003
    Co-Authors: Kishan Chand Gupta, Palash Sarkar
    Abstract:

    Abstract We study the relationship between the Walsh Transform and the algebraic normal form of a Boolean function. In the first part of the paper, we carry out a combinatorial analysis to obtain a formula for the Walsh Transform at a certain point in terms of parameters derived from the algebraic normal form. The second part of the paper is devoted to simplify this formula and develop an algorithm to evaluate it. Our algorithm can be applied in situations where it is practically impossible to use the fast Walsh Transform algorithm. Experimental results show that under certain conditions it is possible to execute our algorithm to evaluate the Walsh Transform (at a small set of points) of functions on a few scores of variables having a few hundred terms in the algebraic normal form.

  • Spectral Domain Analysis of Correlation Immune and Resilient Boolean Functions
    2002
    Co-Authors: Claude Carlet, Palash Sarkar
    Abstract:

    We use a general property of Fourier Transform to obtain direct proofs of recent divisibility results on the Walsh Transform of correlation immune and resilient functions. Improved upper bounds on the nonlinearity of these functions are obtained from the divisibility results. We deduce further information on correlation immune and resilient functions. In particular, we obtain a necessary condition on the algebraic normal form of correlation immune functions attaining the maximum possible nonlinearity.

Michael D Vose - One of the best experts on this subject based on the ideXlab platform.

  • the simple genetic algorithm and the Walsh Transform part ii the inverse
    1998
    Co-Authors: Michael D Vose, Alden H Wright
    Abstract:

    This paper continues the development, begun in Part I, of the relationship between the simple genetic algorithm and the Walsh Transform. The mixing scheme (comprised of crossover and mutation) is essentially “triangularized” when expressed in terms of the Walsh basis. This leads to a formulation of the inverse of the expected next generation operator. The fixed points of the mixing scheme are also determined, and a formula is obtained giving the fixed point corresponding to any starting population. Geiringer's theorem follows from these results in the special case corresponding to zero mutation.

  • the simple genetic algorithm and the Walsh Transform part i theory
    1998
    Co-Authors: Michael D Vose, Alden H Wright
    Abstract:

    This paper is the first part of a two-part series. It proves a number of direct relationships between the Fourier Transform and the simple genetic algorithm. (For a binary representation, the Walsh Transform is the Fourier Transform.) The results are of a theoretical nature and are based on the analysis of mutation and crossover. The Fourier Transform of the mixing matrix is shown to be sparse. An explicit formula is given for the spectrum of the differential of the mixing Transformation. By using the Fourier representation and the fast Fourier Transform, one generation of the infinite population simple genetic algorithm can be computed in time O(cl log2 3), where c is arity of the alphabet and l is the string length. This is in contrast to the time of O(c3l) for the algorithm as represented in the standard basis. There are two orthogonal decompositions of population space that are invariant under mixing. The sequel to this paper will apply the basic theoretical results obtained here to inverse problems and asymptotic behavior.

B J Falkowski - One of the best experts on this subject based on the ideXlab platform.

  • fixed sign Walsh Transform and its iterative hardware architecture
    2005
    Co-Authors: B J Falkowski, Shixing Yan
    Abstract:

    The paper describes an efficient way of implementing the hardware of a sign Walsh Transform. Such a nonlinear Transforms convert binary/ternary vectors into the spectral domain and is important in many signal processing applications including CDMA coding and the analysis of logic design. The approach used here is based on fixed butterfly diagrams that can be easily implemented in hardware.

  • identification of complement single variable symmetry in boolean functions through Walsh Transform
    2002
    Co-Authors: S Kannurao, B J Falkowski
    Abstract:

    In this paper, we present a new method to detect complement single variable symmetry (CSVS) in Boolean functions. The Walsh spectral coefficients are used to identify all the four types of complement single variable symmetries. To reduce the time and to increase the efficiency in identifying the symmetries, necessary and spectral conditions are highlighted. Properties of the functions with CSVS in terms of Walsh spectral coefficients are also discussed.

  • Walsh like functions and their relations
    1996
    Co-Authors: B J Falkowski, S Rahardja
    Abstract:

    A new discrete Transform, the 'Haar-Walsh Transform', has been introduced. Similar to well known Walsh and non-normalised Haar Transforms, the new Transform assumes only +1 and -1 values, hence it is a Walsh-like function and can be used in different applications of digital signal and image processing. In particular, it is extremely well suited to the processing of two-valued binary logic signals. Besides being a discrete Transform on its own, the proposed Transform can also convert Haar and Walsh spectra uniquely between themselves. Besides the fast algorithm that can be implemented in the form of in-place flexible architecture, the new Transform may be conveniently calculated using recursive definitions of a new type of matrix, a 'generator matrix'. The latter matrix can also be used to calculate some chosen Haar-Walsh spectral coefficients which is a useful feature in applications of the new Transform in logic synthesis.

  • recursive relationships fast Transforms generalisations and vlsi iterative architecture for gray code ordered Walsh functions
    1995
    Co-Authors: B J Falkowski
    Abstract:

    Two Walsh Transforms in Gray code ordering are introduced. The generation of two Walsh Transforms in Gray code ordering from the binary code is shown. Recursive relationship between higher and lower matrix orders for Gray code ordering of Walsh functions, using the concepts of operator matrices with symmetric and shift copy, are developed. The generalisation of the introduced Gray code ordered Walsh functions for arbitrary polarity is shown. Another recursive algorithm for a fast Gray code ordered Walsh Transform, which is based on the new operators on matrices, joint Transformations and a bisymmetrical pseudo-Kronecker product, is introduced. The latter recursive algorithm is the basis for the implementation of a constant-geometry iterative architecture for the Gray code ordered Walsh Transform. This architecture can be looped n times or cascaded n times to produce a useful VLSI integrated circuit.

  • calculation of the rademacher Walsh spectrum from a reduced representation of boolean functions
    1992
    Co-Authors: B J Falkowski, I Schafer, Marek Perkowski
    Abstract:

    A theory has been developed to calculate the Rademacher-Walsh Transform from a reduced representation (disjoint cubes) of incompletely specified Boolean functions. The Transform algorithm makes use of the properties of an array of disjoint cubes and allows the determination of the spectral coefficients in an independent way. The program for the algorithms uses advantages of C language to speed up the execution. The comparison of different versions of the algorithm has been carried out. The algorithm successfully overcomes all drawbacks in the calculation of the Transform from the design automation system based on spectral methods. >