The Experts below are selected from a list of 7128 Experts worldwide ranked by ideXlab platform
Giovanni Vincenzi - One of the best experts on this subject based on the ideXlab platform.
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from Fibonacci Sequence to the golden ratio
Journal of Mathematics, 2013Co-Authors: Alberto Fiorenza, Giovanni VincenziAbstract:We consider the well-known characterization of the Golden ratio as limit of the ratio of consecutive terms of the Fibonacci Sequence, and we give an explanation of this property in the framework of the Difference Equations Theory. We show that the Golden ratio coincides with this limit not because it is the root with maximum modulus and multiplicity of the characteristic polynomial, but, from a more general point of view, because it is the root with maximum modulus and multiplicity of a restricted set of roots, which in this special case coincides with the two roots of the characteristic polynomial. This new perspective is the heart of the characterization of the limit of ratio of consecutive terms of all linear homogeneous recurrences with constant coefficients, without any assumption on the roots of the characteristic polynomial, which may be, in particular, also complex and not real.
Alberto Fiorenza - One of the best experts on this subject based on the ideXlab platform.
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from Fibonacci Sequence to the golden ratio
Journal of Mathematics, 2013Co-Authors: Alberto Fiorenza, Giovanni VincenziAbstract:We consider the well-known characterization of the Golden ratio as limit of the ratio of consecutive terms of the Fibonacci Sequence, and we give an explanation of this property in the framework of the Difference Equations Theory. We show that the Golden ratio coincides with this limit not because it is the root with maximum modulus and multiplicity of the characteristic polynomial, but, from a more general point of view, because it is the root with maximum modulus and multiplicity of a restricted set of roots, which in this special case coincides with the two roots of the characteristic polynomial. This new perspective is the heart of the characterization of the limit of ratio of consecutive terms of all linear homogeneous recurrences with constant coefficients, without any assumption on the roots of the characteristic polynomial, which may be, in particular, also complex and not real.
Haruo Kobayashi - One of the best experts on this subject based on the ideXlab platform.
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redundant sar adc algorithm based on Fibonacci Sequence
Key Engineering Materials, 2016Co-Authors: Yutaro Kobayashi, Haruo KobayashiAbstract:This paper describes a redundant Successive Approximation Register Analog-to-Digital Converter (SAR ADC) design method which enables high-reliability and high-speed AD conversion by using digital error correction. Especially we introduce to apply Fibonacci Sequence and its property called Golden ratio to SAR ADC design to improve conventional redundant search algorithms. We also present some derived equations and many beautiful properties for well-balanced redundancy design for SAR ADC
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Fibonacci Sequence weighted SAR ADC algorithm and its DAC topology
2015 IEEE 11th International Conference on ASIC (ASICON), 2015Co-Authors: Takuya Arafune, Yutaro Kobayashi, Shohei Shibuya, Haruo KobayashiAbstract:This paper describes redundant successive approximation register (SAR) ADC design methods to improve reliability and conversion speed by digital error correction. Especially we show that redundant SAR ADC using Fibonacci Sequence and its property called Golden ratio can be well-balanced design. We also present some simple golden-ratio-weighted DAC topologies for easy realization of the redundant SAR ADC by utilizing many interesting properties of Fibonacci Sequence.
Leiran Wang - One of the best experts on this subject based on the ideXlab platform.
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high channel count plasmonic filter with the metal insulator metal Fibonacci Sequence gratings
Optics Letters, 2010Co-Authors: Yongkang Gong, Leiran WangAbstract:Fibonacci-Sequence gratings based on metal–insulator–metal waveguides are proposed. The spectrum properties of this structure are numerically investigated by using the transfer matrix method. Numerical results demonstrate that the proposed structure can generate high-channel-count plasmonic stop bands and can find significant applications in highly integrated dense wavelength division multiplexing networks.
Chrissavgi Triantafillou - One of the best experts on this subject based on the ideXlab platform.
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lainiotis filter golden section and Fibonacci Sequence
Signal Processing, 2013Co-Authors: Nicholas Assimakis, Maria Adam, Chrissavgi TriantafillouAbstract:The relation between the discrete time Lainiotis filter on the one side and the golden section and the Fibonacci Sequence on the other is established. As far as the random walk system is concerned, the relation between the Lainiotis filter and the golden section is derived through the Riccati equation since the steady state estimation error covariance is related to the golden section. The relation between the closed form of the Lainiotis filter and the Fibonacci Sequence is also derived. It is shown that the steady state Lainiotis filter computes the state estimate using a linear combination of the previous estimate and of the current measurement with coefficients related to the golden section. A Finite Impulse Response (FIR) implementation of the steady state Lainiotis filter is also proposed, where the filter computes the state estimate as a linear combination of a well-defined set of the last measurements with coefficients which are powers of the golden section. Finally, the scalar generic stochastic dynamic system is considered and the relation between its parameters and the golden section is investigated.