Abstract
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.
Highlights
Efficient and fast arctangent approximation is utilized in various applications ranging from signal processing, sensors, and measurements to large-scale power systems [1,2,3,4]
Sinusoidal encoders provide electrical signals related to the sine and cosine values of their mechanical shaft angle θ; and conventional ratiometric converters associated with these devices employ the tangent/cotangent method to decode the signal and obtain the position angle through arctangent approximation [3,5]
The new arctangent approximation algorithm presented in this paper for the first time, combines the advantages of both Lookup Tables (LUT) and rational techniques, while covering the full 360° implementation the advantages of both LUT and rational techniques, while covering the full 360◦ implementation range and guaranteeing a very small estimation error
Summary
Efficient and fast arctangent approximation is utilized in various applications ranging from signal processing, sensors, and measurements to large-scale power systems [1,2,3,4]. The new arctangent approximation algorithm presented in this paper for the first time, combines. The new arctangent approximation algorithm presented in this paper for the first time, combines the advantages of both LUT and rational techniques, while covering the full 360° implementation the advantages of both LUT and rational techniques, while covering the full 360◦ implementation range and guaranteeing a very small estimation error. Introducing a new rational approximation formula that outperforms published alternatives with the algorithm at higher accuracies; (3) presenting a practical evaluation index for the existing with the algorithm atapproximation higher accuracies;. Section introduces a new second order rational arctangent approximation describes it in details the proposed approximation algorithm that incorporates the new in and compares to state-of-the-art approximation expressions from literature.
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