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Electronics 2017, 6(1), 22; doi:10.3390/electronics6010022

Real-Time and High-Accuracy Arctangent Computation Using CORDIC and Fast Magnitude Estimation

Dipartimento Ingegneria della Informazione, Università di Pisa, via G. Caruso 16, 56122 Pisa, Italy
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Academic Editors: Christos Koulamas and Mihai Lazarescu
Received: 11 February 2017 / Revised: 9 March 2017 / Accepted: 13 March 2017 / Published: 16 March 2017
(This article belongs to the Special Issue Real-Time Embedded Systems)
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Abstract

This paper presents an improved VLSI (Very Large Scale of Integration) architecture for real-time and high-accuracy computation of trigonometric functions with fixed-point arithmetic, particularly arctangent using CORDIC (Coordinate Rotation Digital Computer) and fast magnitude estimation. The standard CORDIC implementation suffers of a loss of accuracy when the magnitude of the input vector becomes small. Using a fast magnitude estimator before running the standard algorithm, a pre-processing magnification is implemented, shifting the input coordinates by a proper factor. The entire architecture does not use a multiplier, it uses only shift and add primitives as the original CORDIC, and it does not change the data path precision of the CORDIC core. A bit-true case study is presented showing a reduction of the maximum phase error from 414 LSB (angle error of 0.6355 rad) to 4 LSB (angle error of 0.0061 rad), with small overheads of complexity and speed. Implementation of the new architecture in 0.18 µm CMOS technology allows for real-time and low-power processing of CORDIC and arctangent, which are key functions in many embedded DSP systems. The proposed macrocell has been verified by integration in a system-on-chip, called SENSASIP (Sensor Application Specific Instruction-set Processor), for position sensor signal processing in automotive measurement applications. View Full-Text
Keywords: real-time; Digital Signal Processing (DSP); Embedded Systems; CORDIC (Coordinate Rotation Digital Computer); ASIC (Application Specific Integrated Circuit); FPGA (Field Programmable Gate Array); IP (Intellectual Property); automotive sensors real-time; Digital Signal Processing (DSP); Embedded Systems; CORDIC (Coordinate Rotation Digital Computer); ASIC (Application Specific Integrated Circuit); FPGA (Field Programmable Gate Array); IP (Intellectual Property); automotive sensors
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This is an open access article distributed under the Creative Commons Attribution License which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited. (CC BY 4.0).

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MDPI and ACS Style

Pilato, L.; Fanucci, L.; Saponara, S. Real-Time and High-Accuracy Arctangent Computation Using CORDIC and Fast Magnitude Estimation. Electronics 2017, 6, 22.

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