Best two-parameter rational approximation algorithm of given order: a variation of adaptive Fourier decomposition

2014 ◽  
Vol 38 (13) ◽  
pp. 2816-2829 ◽  
Author(s):  
Chao Huang ◽  
Lihui Tan ◽  
Lihua Yang
Keyword(s):  
Approximation Algorithm ◽  
Rational Approximation ◽  
Fourier Decomposition ◽  
Adaptive Fourier Decomposition ◽  
Two Parameter

Adaptive Fourier decomposition and rational approximation — Part II: Software system design and development

2014 ◽  
Vol 12 (05) ◽  
pp. 1461009 ◽  
Author(s):  
Liming Zhang ◽  
Wei Hong ◽  
Weixiong Mai ◽  
Tao Qian
Keyword(s):  
System Design ◽  
Rational Approximation ◽  
Finite Energy ◽  
Software System ◽  
Design And Development ◽  
Frequency Distributions ◽  
Fourier Decomposition ◽  
Time Frequency ◽  
Adaptive Fourier Decomposition

This paper proposes a new software system which provides algorithms for three variations of adaptive Fourier decomposition (AFD), including Core AFD, Cyclic AFD and Unwending AFD. The related time frequency distributions (TFDs) are also provided. Remarks are made for the algorithms design and development. The software system can be used to analyze any signal with finite energy.

Adaptive Fourier decomposition in

2019 ◽  
Vol 42 (6) ◽  
pp. 2016-2024
Author(s):  
Yanbo Wang ◽  
Tao Qian
Keyword(s):  
Fourier Decomposition ◽  
Adaptive Fourier Decomposition

scholarly journals New Fast Arctangent Approximation Algorithm for Generic Real-Time Embedded Applications

Sensors ◽  
2019 ◽  
Vol 19 (23) ◽  
pp. 5148
Author(s):  
Mohieddine Benammar ◽  
Abdulrahman Alassi ◽  
Adel Gastli ◽  
Lazhar Ben-Brahim ◽  
Farid Touati
Keyword(s):  
Approximation Algorithm ◽  
Power Systems ◽  
Rational Approximation ◽  
Zero Point ◽  
Approximation Formula ◽  
Practical Implementation ◽  
Approximation Techniques ◽  
Accuracy Requirement ◽  
Practical Evaluation ◽  
Main Approximation

Fast and accurate arctangent approximations are used in several contemporary applications, including embedded systems, signal processing, radar, and power systems. Three main approximation techniques are well-established in the literature, varying in their accuracy and resource utilization levels. Those are the iterative coordinate rotational digital computer (CORDIC), the lookup tables (LUTs)-based, and the rational formulae techniques. This paper presents a novel technique that combines the advantages of both rational formulae and LUT approximation methods. The new algorithm exploits the pseudo-linear region around the tangent function zero point to estimate a reduced input arctangent through a modified rational approximation before referring this estimate to its original value using miniature LUTs. A new 2nd order rational approximation formula is introduced for the first time in this work and benchmarked against existing alternatives as it improves the new algorithm performance. The eZDSP-F28335 platform has been used for practical implementation and results validation of the proposed technique. The contributions of this work are summarized as follows: (1) introducing a new approximation algorithm with high precision and application-based flexibility; (2) introducing a new rational approximation formula that outperforms literature alternatives with the algorithm at higher accuracy requirement; and (3) presenting a practical evaluation index for rational approximations in the literature.

A NOVEL SIGNAL DECOMPOSITION APPROACH — ADAPTIVE FOURIER DECOMPOSITION

2011 ◽  
Vol 03 (03) ◽  
pp. 325-338
Author(s):  
LIMING ZHANG ◽  
HONG LI
Keyword(s):  
Greedy Algorithm ◽  
Fast Convergence ◽  
Signal Decomposition ◽  
Theoretical Studies ◽  
Decomposition Approach ◽  
Fourier Decomposition ◽  
Energy Effectiveness ◽  
Adaptive Fourier Decomposition ◽  
Instantaneous Frequencies ◽  
The Greedy Algorithm

This paper presents a novel signal decomposition approach — adaptive Fourier decomposition (AFD), which decomposes a given signal based on its physical characters. The algorithm is described in detail, that is based on recent theoretical studies on analytic instantaneous frequencies and stands as a realizable variation of the greedy algorithm. The principle of the algorithm gives rise to fast convergence in terms of energy. Effectiveness of the algorithm is evaluated by comparison experiments with the classical Fourier decomposition (FD) algorithm. The results are promising.

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