{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2025,6,19]],"date-time":"2025-06-19T04:08:34Z","timestamp":1750306114399,"version":"3.41.0"},"reference-count":20,"publisher":"Association for Computing Machinery (ACM)","issue":"4","license":[{"start":{"date-parts":[[2017,1,11]],"date-time":"2017-01-11T00:00:00Z","timestamp":1484092800000},"content-version":"vor","delay-in-days":0,"URL":"https:\/\/www.acm.org\/publications\/policies\/copyright_policy#Background"}],"content-domain":{"domain":["dl.acm.org"],"crossmark-restriction":true},"short-container-title":["SIGARCH Comput. Archit. News"],"published-print":{"date-parts":[[2017,1,11]]},"abstract":"<jats:p>A radio telescope analyzes radio frequency (RF) received from celestial objects. It consists of an antenna, a receiver, and a spectrometer. The spectrometer converts the time domain into the frequency domain by an FFT operation. This paper applies an FFT circuit based on nested residue number system (NRNS), which recursively decompose the RNS. It can decompose the MAC unit into circuits with small sizes. In the FFT using the NRNS, a MAC unit is decomposed into 4-bit ones realized by look-up tables of the FPGA. Also, to realize the scaling (truncation) circuit, we propose a constant division algorithm on the FPGA. The truncation is realized by the division of a dynamic range for a subset of moduli. We implemented the proposed NRNS FFT on the Xilinx Inc. Virtex 6 FPGA. Compared with a Xilinx Inc. binary FFT library, although the number of block RAMs (BRAMs) was increased by 38%, in the RNS FFT, the number of LUTs was decreased by 42-45% and the maximum clock frequency was increased by 38-74%. With this technique, we successfully implemented an FFT that satisfied the required size and speed specifications on an available FPGA, since the excessive number of LUTs was the bottleneck of the binary FFT.<\/jats:p>","DOI":"10.1145\/3039902.3039911","type":"journal-article","created":{"date-parts":[[2017,1,17]],"date-time":"2017-01-17T13:42:08Z","timestamp":1484660528000},"page":"44-49","update-policy":"https:\/\/doi.org\/10.1145\/crossmark-policy","source":"Crossref","is-referenced-by-count":3,"title":["An FFT Circuit for a Spectrometer of a Radio Telescope using the Nested RNS including the Constant Division"],"prefix":"10.1145","volume":"44","author":[{"given":"Hiroki","family":"Nakahara","sequence":"first","affiliation":[{"name":"Tokyo Institute of Technology"}]},{"given":"Hiroyuki","family":"Nakanishi","sequence":"additional","affiliation":[{"name":"Kagoshima University"}]},{"given":"Kazumasa","family":"Iwai","sequence":"additional","affiliation":[{"name":"Nobeyama Solar Radio Observatory"}]},{"given":"Tsutomu","family":"Sasao","sequence":"additional","affiliation":[{"name":"Meiji University"}]}],"member":"320","published-online":{"date-parts":[[2017,1,11]]},"reference":[{"key":"e_1_2_1_1_1","volume-title":"No. 3568","author":"Benz A. O.","year":"2008","unstructured":"A. O. Benz , P. C. Grigis , V. Hungerbuhler , H. Meyer , C. Monstein , B. Stuber , and D. Zardet , \" A broadband FFT spectrometer for radio and millimeter astronomy,\" Astronomy and Astrophysics , No. 3568 , 2008 . A. O. Benz, P. C. Grigis, V. Hungerbuhler, H. Meyer, C. Monstein, B. Stuber, and D. Zardet, \"A broadband FFT spectrometer for radio and millimeter astronomy,\" Astronomy and Astrophysics, No. 3568, 2008."},{"key":"e_1_2_1_2_1","first-page":"190","article-title":"Some modular adders and multipliers for field programmable gate arrays","author":"Beuchat J. L.","year":"2003","unstructured":"J. L. Beuchat , \" Some modular adders and multipliers for field programmable gate arrays ,\" IPDPS 2003, 2003 , pp. 190 .2. J. L. Beuchat, \"Some modular adders and multipliers for field programmable gate arrays,\" IPDPS2003, 2003, pp.190.2.","journal-title":"IPDPS"},{"key":"e_1_2_1_3_1","unstructured":"CASPER : Collaboration for Astronomy Signal Processing and Electronics Research https:\/\/casper.berkeley.edu\/ CASPER: Collaboration for Astronomy Signal Processing and Electronics Research https:\/\/casper.berkeley.edu\/"},{"key":"e_1_2_1_4_1","doi-asserted-by":"publisher","DOI":"10.1090\/S0025-5718-1965-0178586-1"},{"key":"e_1_2_1_5_1","volume-title":"Van Nostrand Co.","author":"Curtis H. A.","year":"1962","unstructured":"H. A. Curtis , \"A new approach to the design of switching circuits,\" D . Van Nostrand Co. , Princeton, NJ , 1962 . H. A. Curtis, \"A new approach to the design of switching circuits,\" D. 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Gusten, \"High-resolution wide-band Fast Fourier Transform spectrometers,\" Astronomy and Astrophysics, 2012."},{"key":"e_1_2_1_8_1","first-page":"1","volume-title":"A deep convolutional neural network based on nested residue number system,\" 25th International Conference on Filed-Programmable Logic and Applications (FPL","author":"Nakahara H.","year":"2015","unstructured":"H. Nakahara and T. Sasao , \" A deep convolutional neural network based on nested residue number system,\" 25th International Conference on Filed-Programmable Logic and Applications (FPL 2015 ), 2015, pp. 1 -- 6 . H. Nakahara and T. Sasao, \"A deep convolutional neural network based on nested residue number system,\" 25th International Conference on Filed-Programmable Logic and Applications (FPL 2015), 2015, pp.1--6."},{"key":"e_1_2_1_9_1","doi-asserted-by":"publisher","DOI":"10.1109\/ISMVL.2015.41"},{"key":"e_1_2_1_10_1","doi-asserted-by":"publisher","DOI":"10.1007\/978-3-642-33078-0_15"},{"key":"e_1_2_1_11_1","first-page":"109","volume-title":"On a wideband fast Fourier transform for a radio telescope,\" 3rd Int'l Workshop on Highly-Efficient Accelerators and Reconfigurable Technologies (HEART","author":"Nakahara H.","year":"2012","unstructured":"H. Nakahara , H. Nakanishi , and T. Sasao , \" On a wideband fast Fourier transform for a radio telescope,\" 3rd Int'l Workshop on Highly-Efficient Accelerators and Reconfigurable Technologies (HEART 2012 ), May 31-June 1, 2012, pp. 109 -- 114 . H. Nakahara, H. Nakanishi, and T. Sasao, \"On a wideband fast Fourier transform for a radio telescope,\" 3rd Int'l Workshop on Highly-Efficient Accelerators and Reconfigurable Technologies (HEART 2012), May 31-June 1, 2012, pp.109--114."},{"key":"e_1_2_1_12_1","doi-asserted-by":"crossref","DOI":"10.1142\/p523","volume-title":"Residue Number Systems,\" Imperial College Press","author":"Omondi A. R.","year":"2007","unstructured":"A. R. Omondi and B. Premkumar , \" Residue Number Systems,\" Imperial College Press , 2007 . A. R. Omondi and B. Premkumar, \"Residue Number Systems,\" Imperial College Press, 2007."},{"key":"e_1_2_1_13_1","volume-title":"of the Asilomar Conference on Signals, Systems, and Computers","author":"A.","year":"2006","unstructured":"A. Parsons et.al, \"PetaOp\/Second FPGA signal processing for SETI and radio astronomy,\" Proc. of the Asilomar Conference on Signals, Systems, and Computers , 2006 . A. 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