Design of IIR fractional differentiator With Peano kernel

2008 ◽  
Author(s):  
Soo-Chang Pei ◽  
Peng-Hua Wang ◽  
Chia-Huei Lin
Keyword(s):  
Fractional Differentiator ◽  
Peano Kernel

scholarly journals RF and microwave fractional differentiation with transversal filters using a soliton crystal microcomb multiwavelength source

2020 ◽  
Author(s):  
David Moss ◽  
Arnan Mitchell ◽  
Roberto Morandotti ◽  
xingyuan xu
Keyword(s):  
High Performance ◽  
Free Spectral Range ◽  
Fractional Differentiation ◽  
Temporal Response ◽  
Pulse Input ◽  
Transversal Filters ◽  
Multi Wavelength ◽  
Fractional Orders ◽  
Fractional Differentiator ◽  
Good Agreement

We report a photonic radio frequency (RF) fractional differentiator based on an integrated Kerr micro-comb source. The micro-comb source has a free spectral range (FSR) of 49 GHz, generating a large number of comb lines that serve as a high-performance multi-wavelength source for the differentiator. By programming and shaping the comb lines according to calculated tap weights, arbitrary fractional orders ranging from 0.15 to 0.90 are achieved over a broad RF operation bandwidth of 15.49 GHz. We experimentally characterize the frequency-domain RF amplitude and phase response as well as the temporal response with a Gaussian pulse input. The experimental results show good agreement with theory, confirming the effectiveness of our approach towards high-performance fractional differentiators featuring broad processing bandwidth, high reconfigurability, and potentially reduced sized and cost.

FREQUENCY BAND-LIMITED FRACTIONAL DIFFERENTIATOR IN PATH TRACKING DESIGN

2006 ◽  
Vol 39 (11) ◽  
pp. 468-474
Author(s):  
Alexandre Poty ◽  
Pierre Melchior ◽  
Alain Oustaloup
Keyword(s):  
Frequency Band ◽  
Path Tracking ◽  
Band Limited ◽  
Fractional Differentiator

scholarly journals TOWARDS A MORE GENERAL TYPE OF UNIVARIATE CONSTRAINED INTERPOLATION WITH FRACTAL SPLINES

Fractals ◽  
2015 ◽  
Vol 23 (04) ◽  
pp. 1550040 ◽  
Author(s):  
A. K. B. CHAND ◽  
P. VISWANATHAN ◽  
K. M. REDDY
Keyword(s):  
Fractal Interpolation ◽  
Quadratic Spline ◽  
Constrained Interpolation ◽  
New Class ◽  
Background Theory ◽  
Fractal Interpolation Functions ◽  
Numer Anal ◽  
Shape Preserving Properties ◽  
Peano Kernel ◽  
Interpolation Functions

Recently, in [Electron. Trans. Numer. Anal. 41 (2014) 420–442] authors introduced a new class of rational cubic fractal interpolation functions with linear denominators via fractal perturbation of traditional nonrecursive rational cubic splines and investigated their basic shape preserving properties. The main goal of the current paper is to embark on univariate constrained fractal interpolation that is more general than what was considered so far. To this end, we propose some strategies for selecting the parameters of the rational fractal spline so that the interpolating curves lie strictly above or below a prescribed linear or a quadratic spline function. Approximation property of the proposed rational cubic fractal spine is broached by using the Peano kernel theorem as an interlude. The paper also provides an illustration of background theory, veined by examples.

Order-Frequency Characteristics of a Promising Circuit Element: Fractor

2016 ◽  
Vol 25 (12) ◽  
pp. 1650156 ◽  
Author(s):  
Yi-Fei Pu ◽  
Ni Zhang ◽  
Huai Wang ◽  
Shu-Shu Chen ◽  
Xiao Yuan ◽  
...  
Keyword(s):  
Electrical Properties ◽  
Fractional Order ◽  
Time Constant ◽  
Mathematical Analysis ◽  
Analog Circuit ◽  
Frequency Characteristics ◽  
Circuit Element ◽  
Simulation Results ◽  
Fractional Differentiator

This paper mainly discusses the order-frequency characteristics of a promising circuit element: fractor. The concept of fractance, as the fractional-order impedance of a fractor, arose following the successful synthesis of a fractional differentiator or integrator in an analog circuit. In this paper, we studied some electrical properties of a fractor. In particular, the order-frequency characteristics of a fractor are introduced. First, the order-sensitivity characteristics of a fractor are proposed. Second, the order-frequency characteristics of a fractor are studied. Third, the time constant of a fractor is analyzed. Last, through mathematical analysis and simulation results, we discussed in detail some issues of the electrical properties of a fractor, especially its time constant.

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