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

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  • 1Department of Electrical Engineering, Qatar University, Doha 2713, Qatar.

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Summary
This summary is machine-generated.

This study introduces a novel arctangent approximation technique combining rational formulae and lookup tables for enhanced precision and flexibility in embedded systems. The new method offers improved performance over existing approaches.

Keywords:
CORDICarctangent approximationlook-up-tablesminimax optimizationnovel algorithmposition sensorsrational approximationssignals processing

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Area of Science:

  • Digital Signal Processing
  • Computer Engineering

Background:

  • Accurate arctangent approximations are crucial for embedded systems, signal processing, radar, and power systems.
  • Established methods include Coordinate Rotational Digital Computer (CORDIC), Lookup Tables (LUTs), and rational formulae, each with trade-offs in accuracy and resource use.

Purpose of the Study:

  • To present a novel arctangent approximation algorithm that merges the benefits of rational formulae and LUTs.
  • To introduce and evaluate a new 2nd order rational approximation formula.
  • To validate the proposed technique through practical implementation and benchmarking.

Main Methods:

  • A hybrid algorithm exploiting the pseudo-linear region of the tangent function.
  • Utilizing a modified rational approximation for reduced input arctangent estimation.
  • Employing miniature LUTs to map estimates to original arctangent values.
  • Introducing and benchmarking a new 2nd order rational approximation formula.
  • Implementation and validation on the eZDSP-F28335 platform.

Main Results:

  • The proposed algorithm achieves high precision and application-based flexibility.
  • The new 2nd order rational approximation formula demonstrates superior performance compared to existing alternatives, especially at higher accuracy requirements.
  • Practical evaluation of rational approximations is presented.

Conclusions:

  • The novel hybrid arctangent approximation technique offers a significant advancement in accuracy and flexibility.
  • The new rational approximation formula enhances performance, particularly for demanding applications.
  • The work provides a practical framework for evaluating and implementing efficient arctangent approximations.