The Experts below are selected from a list of 26115 Experts worldwide ranked by ideXlab platform
K. Egiazarian - One of the best experts on this subject based on the ideXlab platform.
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Fibonacci Arithmetic Expressions
Automation and Remote Control, 2004Co-Authors: J. T. Astola, K. Egiazarian, M. Stanković, R. S. StankovićAbstract:In this paper, we extend the arithmetic (AR) expressions for functions on finite dyadic groups to functions used in Fibonacci interconnection topologies. We have introduced the Fibonacci-Arithmetic (FibAR) expressions for representation of these functions. We discussed the optimization of FibARs with respect to the number of non-zero coefficients through the Fixed-Polarity FibARs defined by using different polarities for the Fibonacci variables. In this way, we provide a base to extend the application of ARs and related powerful CAD design tools for switching functions to functions in Fibonacci interconnection topologies.
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Fibonacci decision diagrams and spectral Fibonacci decision diagrams
Proceedings 30th IEEE International Symposium on Multiple-Valued Logic (ISMVL 2000), 2000Co-Authors: R.s. Stankovic, J. Astola, M. Stankovic, K. EgiazarianAbstract:The authors define the Fibonacci decision diagrams (FibDDs) permitting representation of functions defined in a number of points different from N=2/sup n/ by decision diagrams consisting of nodes with two outgoing edges. We show the relationships between the FibDDs and the contracted Fibonacci codes. Then, we define the Spectral Fibonacci DDs (FibSTDDs) in terms of the generalized Fibonacci transforms. This broad family of transforms provides a corresponding family of FibSTDDs. These DDs allow compact representations of functions with simple Fibonacci spectra. Such representations may be useful in various tasks of signal processing, including image processing and systems design, where the generalized Fibonacci transforms have been efficiently used.
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Generalized Fibonacci cubes and trees for DSP applications
1996 IEEE International Symposium on Circuits and Systems. Circuits and Systems Connecting the World. ISCAS 96, 1996Co-Authors: K. Egiazarian, J. AstolaAbstract:We present a new interconnection topology called generalized Fibonacci cubes, which unifies a wide range of connection topologies such as the Boolean cube (or hypercube), classical Fibonacci cube, etc. We study the properties of generalized Fibonacci corresponding codes, e.g. we find an Zeckendorfs' theorem for the generalized Fibonacci codes. Some basic properties of generalized Fibonacci cubes and graphs, especially, their topological properties, are also established. Finally, the classes of unitary generalized Fibonacci-Walsh and Fibonacci-Haar transforms are proposed for which efficient computation algorithms and corresponding generalized Fibonacci flowcharts are presented.
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Discrete orthogonal transforms based on Fibonacci-type recursions
1996 IEEE Digital Signal Processing Workshop Proceedings, 1996Co-Authors: K. Egiazarian, J. AstolaAbstract:The idea of unified Fibonacci-type topology is used for construction of wide classes of discrete orthogonal transforms, including Rademacher-Fibonacci, Walsh-Fibonacci, Haar-Fibonacci-type transforms, etc. Efficient algorithms for proposed transforms directly related with the generalized Fibonacci topology are derived. The generation of discrete wavelets and wavelet packets based on Fibonacci-type recursions is established.
Hiroshi Fujisaki - One of the best experts on this subject based on the ideXlab platform.
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On embedding conditions of shifts of finite type into the Fibonacci-Dyck shift
2012 IEEE International Symposium on Information Theory Proceedings, 2012Co-Authors: Hiroshi FujisakiAbstract:We consider the embedding problem for shifts of finite type (SFT) into the Fibonacci-Dyck shift. First, we find the reflection principle does not hold for the path in the Fibonacci-Dyck shift. Then, we obtain the limit of a sequence of topological entropies of a class of irreducible (d - 1)-step SFT of the Fibonacci-Dyck shift, where d(≥ 2) are even integers. This limit provide one of the embedding conditions for the Fibonacci-Dyck shift. Finally, we generalize the result on computing the above limit of a sequence of topological entropies to the Markov-Dyck shift.
J. Astola - One of the best experts on this subject based on the ideXlab platform.
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Fibonacci decision diagrams and spectral Fibonacci decision diagrams
Proceedings 30th IEEE International Symposium on Multiple-Valued Logic (ISMVL 2000), 2000Co-Authors: R.s. Stankovic, J. Astola, M. Stankovic, K. EgiazarianAbstract:The authors define the Fibonacci decision diagrams (FibDDs) permitting representation of functions defined in a number of points different from N=2/sup n/ by decision diagrams consisting of nodes with two outgoing edges. We show the relationships between the FibDDs and the contracted Fibonacci codes. Then, we define the Spectral Fibonacci DDs (FibSTDDs) in terms of the generalized Fibonacci transforms. This broad family of transforms provides a corresponding family of FibSTDDs. These DDs allow compact representations of functions with simple Fibonacci spectra. Such representations may be useful in various tasks of signal processing, including image processing and systems design, where the generalized Fibonacci transforms have been efficiently used.
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Generalized Fibonacci cubes and trees for DSP applications
1996 IEEE International Symposium on Circuits and Systems. Circuits and Systems Connecting the World. ISCAS 96, 1996Co-Authors: K. Egiazarian, J. AstolaAbstract:We present a new interconnection topology called generalized Fibonacci cubes, which unifies a wide range of connection topologies such as the Boolean cube (or hypercube), classical Fibonacci cube, etc. We study the properties of generalized Fibonacci corresponding codes, e.g. we find an Zeckendorfs' theorem for the generalized Fibonacci codes. Some basic properties of generalized Fibonacci cubes and graphs, especially, their topological properties, are also established. Finally, the classes of unitary generalized Fibonacci-Walsh and Fibonacci-Haar transforms are proposed for which efficient computation algorithms and corresponding generalized Fibonacci flowcharts are presented.
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Discrete orthogonal transforms based on Fibonacci-type recursions
1996 IEEE Digital Signal Processing Workshop Proceedings, 1996Co-Authors: K. Egiazarian, J. AstolaAbstract:The idea of unified Fibonacci-type topology is used for construction of wide classes of discrete orthogonal transforms, including Rademacher-Fibonacci, Walsh-Fibonacci, Haar-Fibonacci-type transforms, etc. Efficient algorithms for proposed transforms directly related with the generalized Fibonacci topology are derived. The generation of discrete wavelets and wavelet packets based on Fibonacci-type recursions is established.
Omprakash Sikhwal - One of the best experts on this subject based on the ideXlab platform.
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On Fibonacci and Fibonacci-Like Numbers by Matrix Method
2016Co-Authors: Shikha Bhatnagar, Omprakash SikhwalAbstract:The Fibonacci, Lucas and Fibonacci-Like sequences are famous for possessing amazing properties and identities. There is a long tradition of using matrices and determinants to study Fibonacci numbers, Lucas numbers and other numbers of various celebrated sequences. In this paper, we present 2x2 order matrix representation of Fibonacci-Like numbers with some identities of Fibonacci-Like numbers and Fibonacci numbers. Sum of product of Fibonacci numbers and Fibonacci-Like numbers are taken in various pattern and identities derive by relevant matrix.
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Generalized Fibonacci – Like Sequence Associated with Fibonacci and Lucas Sequences
Turkish Journal of Analysis and Number Theory, 2016Co-Authors: Yogesh Kumar Gupta, Mamta Singh, Omprakash SikhwalAbstract:The Fibonacci sequence, Lucas numbers and their generalization have many interesting properties and applications to almost every field. Fibonacci sequence is defined by the recurrence formula Fn=Fn-1+Fn-2, , and F0=0, F1=1, where Fn is a nth number of sequence. Many authors have been defined Fibonacci pattern based sequences which are popularized and known as Fibonacci-Like sequences. In this paper, Generalized Fibonacci-Like sequence is introduced and defined by the recurrence relation Bn=Bn-1+Bn-2, with B0=2s, B1=s+1, where s being a fixed integers. Some identities of Generalized Fibonacci-Like sequence associated with Fibonacci and Lucas sequences are presented by Binet’s formula. Also some determinant identities are discussed.
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Fibonacci triple sequences and some fundamental properties
Tamkang Journal of Mathematics, 2010Co-Authors: Bijendra Singh, Omprakash SikhwalAbstract:Fibonacci sequence stands as a kind of super sequence with fabulous properties. This note presents Fibonacci-Triple sequences that may also be called 3-F sequences. This is the explosive development in the region of Fibonacci sequence. Our purpose of this paper is to demonstrate fundamental properties of Fibonacci-Triple sequence.
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Fibonacci like sequence and its properties
2010Co-Authors: Bijendra Singh, Omprakash Sikhwal, Shikha BhatnagarAbstract:The Fibonacci sequence is a source of many nice and interesting identities. A similar interpretation exists for Lucas sequence. In this paper, we study Fibonacci-Like sequence that is defined by the recurrence 12 0 1 ,f or all 2, 2, 2 nn n SS S n S S −− =+ ≥ = =. The associated initial conditions are the sum of initial conditions of Fibonacci and Lucas sequences respectively. We shall define Binet’s formula and generating function of Fibonacci-Like sequence. Mainly, Inducion method and Binet’s formula will be used to establish properties of Fibonacci-Like sequence.
Karen Egiazarian - One of the best experts on this subject based on the ideXlab platform.
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ISMVL - Fibonacci decision diagrams and spectral Fibonacci decision diagrams
Proceedings 30th IEEE International Symposium on Multiple-Valued Logic (ISMVL 2000), 2000Co-Authors: R.s. Stankovic, M. Stankovic, Jaakko Astola, Karen EgiazarianAbstract:The authors define the Fibonacci decision diagrams (FibDDs) permitting representation of functions defined in a number of points different from N=2/sup n/ by decision diagrams consisting of nodes with two outgoing edges. We show the relationships between the FibDDs and the contracted Fibonacci codes. Then, we define the Spectral Fibonacci DDs (FibSTDDs) in terms of the generalized Fibonacci transforms. This broad family of transforms provides a corresponding family of FibSTDDs. These DDs allow compact representations of functions with simple Fibonacci spectra. Such representations may be useful in various tasks of signal processing, including image processing and systems design, where the generalized Fibonacci transforms have been efficiently used.
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On Generalized Fibonacci Cubes and Unitary Transforms
Applicable Algebra in Engineering Communication and Computing, 1997Co-Authors: Karen Egiazarian, Jaakko AstolaAbstract:We present a new interconnection topology called generalized Fibonacci topology, which unifies a wide range of connection topologies such as the Boolean cube (or hypercube), classical Fibonacci cube, etc. Some basic topological properties of generalized Fibonacci cubes are established. Finally, we developed new classes of the discrete orthogonal transforms, based on the generalized Fibonacci recursions. They can be implemented efficiently by butterfly-type networks (like the Fourier, or the Haar transforms). A generalized Fibonacci cube based processor architecture (generalizing the known SIMD architecture — hypercube processor) can be efficiently used for hardware implementation of the proposed discrete orthogonal transforms.
