{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,1,27]],"date-time":"2026-01-27T22:53:57Z","timestamp":1769554437035,"version":"3.49.0"},"reference-count":17,"publisher":"MDPI AG","issue":"23","license":[{"start":{"date-parts":[[2019,11,25]],"date-time":"2019-11-25T00:00:00Z","timestamp":1574640000000},"content-version":"vor","delay-in-days":0,"URL":"https:\/\/creativecommons.org\/licenses\/by\/4.0\/"}],"content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["Sensors"],"abstract":"<jats:p>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.<\/jats:p>","DOI":"10.3390\/s19235148","type":"journal-article","created":{"date-parts":[[2019,11,25]],"date-time":"2019-11-25T05:52:58Z","timestamp":1574661178000},"page":"5148","update-policy":"https:\/\/doi.org\/10.3390\/mdpi_crossmark_policy","source":"Crossref","is-referenced-by-count":9,"title":["New Fast Arctangent Approximation Algorithm for Generic Real-Time Embedded Applications"],"prefix":"10.3390","volume":"19","author":[{"ORCID":"https:\/\/orcid.org\/0000-0001-5340-1981","authenticated-orcid":false,"given":"Mohieddine","family":"Benammar","sequence":"first","affiliation":[{"name":"Department of Electrical Engineering, Qatar University, Doha 2713, Qatar"}]},{"given":"Abdulrahman","family":"Alassi","sequence":"additional","affiliation":[{"name":"Department of Electrical Engineering, Qatar University, Doha 2713, Qatar"},{"name":"R&amp;D Laboratory, Iberdrola Innovation Middle East, Doha 210177, Qatar"}]},{"ORCID":"https:\/\/orcid.org\/0000-0002-6818-3320","authenticated-orcid":false,"given":"Adel","family":"Gastli","sequence":"additional","affiliation":[{"name":"Department of Electrical Engineering, Qatar University, Doha 2713, Qatar"}]},{"given":"Lazhar","family":"Ben-Brahim","sequence":"additional","affiliation":[{"name":"Department of Electrical Engineering, Qatar University, Doha 2713, Qatar"}]},{"ORCID":"https:\/\/orcid.org\/0000-0001-9495-2157","authenticated-orcid":false,"given":"Farid","family":"Touati","sequence":"additional","affiliation":[{"name":"Department of Electrical Engineering, Qatar University, Doha 2713, Qatar"}]}],"member":"1968","published-online":{"date-parts":[[2019,11,25]]},"reference":[{"key":"ref_1","doi-asserted-by":"crossref","first-page":"108","DOI":"10.1109\/MSP.2006.1628884","article-title":"Efficient Approximations for the Arctangent Function","volume":"23","author":"Rajan","year":"2006","journal-title":"IEEE Signal Process. Mag."},{"key":"ref_2","doi-asserted-by":"crossref","unstructured":"Ukil, A., Shah, V.H., and Deck, B. (2011, January 27\u201330). Fast computation of arctangent functions for embedded applications: A comparative analysis. Proceedings of the 2011 IEEE International Symposium on Industrial Electronics, Gdansk, Poland.","DOI":"10.1109\/ISIE.2011.5984330"},{"key":"ref_3","doi-asserted-by":"crossref","first-page":"574","DOI":"10.1109\/TIE.2008.2002719","article-title":"A Resolver Angle Estimator Based on Its Excitation Signal","volume":"56","author":"Benammar","year":"2009","journal-title":"IEEE Trans. Ind. Electron."},{"key":"ref_4","doi-asserted-by":"crossref","first-page":"267","DOI":"10.1108\/SR-12-2015-0208","article-title":"Study on high precision magnetic encoder based on PMSM sensorless control","volume":"36","author":"Wang","year":"2016","journal-title":"Sens. Rev."},{"key":"ref_5","doi-asserted-by":"crossref","first-page":"5169","DOI":"10.1109\/JSEN.2017.2723619","article-title":"A Sinusoidal Encoder-to-Digital Converter Based on an Improved Tangent Method","volume":"17","author":"Benammar","year":"2017","journal-title":"IEEE Sens. J."},{"key":"ref_6","doi-asserted-by":"crossref","first-page":"1580","DOI":"10.1109\/TIM.2009.2028208","article-title":"Instrument-Based Noncontact Doppler Radar Vital Sign Detection System Using Heterodyne Digital Quadrature Demodulation Architecture","volume":"59","author":"Gu","year":"2010","journal-title":"IEEE Trans. Instrum. Meas."},{"key":"ref_7","doi-asserted-by":"crossref","unstructured":"Gu, C. (2016). Short-Range Noncontact Sensors for Healthcare and Other Emerging Applications: A Review. Sensors, 16.","DOI":"10.3390\/s16081169"},{"key":"ref_8","doi-asserted-by":"crossref","first-page":"130","DOI":"10.1109\/MSP.2012.2219677","article-title":"Full Quadrant Approximations for the Arctangent Function [Tips and Tricks]","volume":"30","author":"Girones","year":"2013","journal-title":"IEEE Signal Process. Mag."},{"key":"ref_9","doi-asserted-by":"crossref","unstructured":"Pilato, L., Fanucci, L., and Saponara, S. (2017). Real-Time and High-Accuracy Arctangent Computation Using CORDIC and Fast Magnitude Estimation. Electronics, 6.","DOI":"10.3390\/electronics6010022"},{"key":"ref_10","doi-asserted-by":"crossref","first-page":"109","DOI":"10.1109\/MSP.2004.1267054","article-title":"Another contender in the arctangent race","volume":"21","author":"Lyons","year":"2004","journal-title":"IEEE Signal Process. Mag."},{"key":"ref_11","doi-asserted-by":"crossref","first-page":"164","DOI":"10.1109\/MSP.2017.2730898","article-title":"Fast- and Low-Complexity atan2(a,b) Approximation [Tips and Tricks]","volume":"34","author":"Torres","year":"2017","journal-title":"IEEE Signal Process. Mag."},{"key":"ref_12","doi-asserted-by":"crossref","first-page":"133","DOI":"10.1049\/iet-spr:20070117","article-title":"Error reduction technique for four-quadrant arctangent approximations","volume":"2","author":"Rajan","year":"2008","journal-title":"IET Signal Process."},{"key":"ref_13","doi-asserted-by":"crossref","first-page":"2663","DOI":"10.1109\/TVLSI.2017.2700519","article-title":"A Fast and Low-Complexity Operator for the Computation of the Arctangent of a Complex Number","volume":"25","author":"Torres","year":"2017","journal-title":"IEEE Trans. VLSI Syst."},{"key":"ref_14","unstructured":"Zarowski, C. (Differential Evolution for a Better Approximation to the Arctangent Function, 2006). Differential Evolution for a Better Approximation to the Arctangent Function, Nanodottek Report NDT3-04-2006."},{"key":"ref_15","doi-asserted-by":"crossref","first-page":"155","DOI":"10.1007\/s12239-010-0021-5","article-title":"Approximations to the magic formula","volume":"11","author":"Moriano","year":"2010","journal-title":"Int. J. Automot. Technol."},{"key":"ref_16","doi-asserted-by":"crossref","first-page":"30","DOI":"10.1016\/j.sna.2015.04.026","article-title":"Precise and robust position estimation for optical incremental encoders using a linearization technique","volume":"232","author":"Ye","year":"2015","journal-title":"Sensors Actuators A Phys."},{"key":"ref_17","doi-asserted-by":"crossref","unstructured":"Saber, M., Jitsumatsu, Y., and Kohda, T. (2009, January 19\u201323). A low-power implementation of arctangent function for communication applications using FPGA. Proceedings of  the 2009 Fourth International Workshop on Signal Design and Its Applications in Communications, Fukuoka, Japan.","DOI":"10.1109\/IWSDA.2009.5346438"}],"container-title":["Sensors"],"original-title":[],"language":"en","link":[{"URL":"https:\/\/www.mdpi.com\/1424-8220\/19\/23\/5148\/pdf","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2025,10,11]],"date-time":"2025-10-11T13:37:18Z","timestamp":1760189838000},"score":1,"resource":{"primary":{"URL":"https:\/\/www.mdpi.com\/1424-8220\/19\/23\/5148"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2019,11,25]]},"references-count":17,"journal-issue":{"issue":"23","published-online":{"date-parts":[[2019,12]]}},"alternative-id":["s19235148"],"URL":"https:\/\/doi.org\/10.3390\/s19235148","relation":{},"ISSN":["1424-8220"],"issn-type":[{"value":"1424-8220","type":"electronic"}],"subject":[],"published":{"date-parts":[[2019,11,25]]}}}