Passive constrained rational approximation algorithm using Nevanlinna-Pick interpolation

2003 ◽  
Author(s):  
C.P. Coelho ◽  
J.R. Phillips ◽  
L.M. Silveira
Keyword(s):  
Approximation Algorithm ◽  
Rational Approximation

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.

scholarly journals 3-adic complexity of ternary generalized cyclotomic sequences with period

2021 ◽  
Vol 2052 (1) ◽  
pp. 012008
Author(s):  
V A Edemskiy ◽  
S A Koltsova
Keyword(s):  
Approximation Algorithm ◽  
Rational Approximation ◽  
Generalized Cyclotomic Classes ◽  
Definition Of ◽  
Cyclotomic Sequences

Abstract In this paper, we study the ternary generalized cyclotomic sequences with a period equal to a power of an odd prime. Ding-Helleseth’s generalized cyclotomic classes of order three are used for the definition of these sequences. We derive the symmetric 3-adic complexity of above mention sequences and obtain the estimate of symmetric 3-adic complexity of sequences. It is shown that 3-adic complexity of these sequences is large enough to resist the attack of the rational approximation algorithm for feedback with carry shift registers.

scholarly journals Symmetric 2-adic complexity of generalized cyclotomic sequences of order six with period p n

2021 ◽  
Vol 2052 (1) ◽  
pp. 012009
Author(s):  
V A Edemskiy ◽  
S A Koltsova
Keyword(s):  
Approximation Algorithm ◽  
Rational Approximation ◽  
Cyclotomic Sequences

Abstract In this paper, the symmetric 2-adic complexity of generalized cyclotomic sequences of order six with period equals a power of an odd prime is studied. The estimate of symmetric 2-adic complexity of these sequences is obtained. It is shown that above sequences have high symmetric 2-adic complexity and the 2-adic complexity of this class of sequences is large enough to resist the attack of the rational approximation algorithm for feedback with carry shift registers.

Rational Approximation of Real Functions

1988 ◽  
Author(s):  
P. P. Petrushev ◽  
Vasil Atanasov Popov
Keyword(s):  
Rational Approximation ◽  
Real Functions
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