{"title":"通用- N Winograd dft程序与逆选项","authors":"J. Masse, D. Cante","doi":"10.1109/ICASSP.1983.1171940","DOIUrl":null,"url":null,"abstract":"S. Winograd's papers \"On computing the discrete Fourier transform\" (1976 and 1978) allow one to know the minimum number of multiplications to compute a DFT if the length is a power of a prime and to build such algorithms for small lengths. It is suggested that longer transforms be 'built up' with the short algorithms. For this Winograd proposes and Kolba & Parks detail two ways I.J Good's prime factor algorithm and Winograd's modified by J.H McClellan nested prime factor algorithm. In 1979 J.H McClellan publishes a General-N FORTRAN program (WFTA) using the nested algorithm. In 1981 C.S Burrus publishes a very simple program (PFA1) using in place the prime factor algorithm. In 1982 J.H Rothweller extends an idea of Burrus to developp an in place and in order version of the program (PFA2). These two last programs do not perform the inverse DFT. In this work ways to implement this as an option of the same program are systematically derived from the general properties of the prime factor index maps and tested.","PeriodicalId":403091,"journal":{"name":"ICASSP '83. IEEE International Conference on Acoustics, Speech, and Signal Processing","volume":"13 1","pages":"0"},"PeriodicalIF":0.0000,"publicationDate":"1983-04-14","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":"0","resultStr":"{\"title\":\"General - N Winograd D.F.T. programs with inverse option\",\"authors\":\"J. Masse, D. Cante\",\"doi\":\"10.1109/ICASSP.1983.1171940\",\"DOIUrl\":null,\"url\":null,\"abstract\":\"S. Winograd's papers \\\"On computing the discrete Fourier transform\\\" (1976 and 1978) allow one to know the minimum number of multiplications to compute a DFT if the length is a power of a prime and to build such algorithms for small lengths. It is suggested that longer transforms be 'built up' with the short algorithms. For this Winograd proposes and Kolba & Parks detail two ways I.J Good's prime factor algorithm and Winograd's modified by J.H McClellan nested prime factor algorithm. In 1979 J.H McClellan publishes a General-N FORTRAN program (WFTA) using the nested algorithm. In 1981 C.S Burrus publishes a very simple program (PFA1) using in place the prime factor algorithm. In 1982 J.H Rothweller extends an idea of Burrus to developp an in place and in order version of the program (PFA2). These two last programs do not perform the inverse DFT. In this work ways to implement this as an option of the same program are systematically derived from the general properties of the prime factor index maps and tested.\",\"PeriodicalId\":403091,\"journal\":{\"name\":\"ICASSP '83. IEEE International Conference on Acoustics, Speech, and Signal Processing\",\"volume\":\"13 1\",\"pages\":\"0\"},\"PeriodicalIF\":0.0000,\"publicationDate\":\"1983-04-14\",\"publicationTypes\":\"Journal Article\",\"fieldsOfStudy\":null,\"isOpenAccess\":false,\"openAccessPdf\":\"\",\"citationCount\":\"0\",\"resultStr\":null,\"platform\":\"Semanticscholar\",\"paperid\":null,\"PeriodicalName\":\"ICASSP '83. IEEE International Conference on Acoustics, Speech, and Signal Processing\",\"FirstCategoryId\":\"1085\",\"ListUrlMain\":\"https://doi.org/10.1109/ICASSP.1983.1171940\",\"RegionNum\":0,\"RegionCategory\":null,\"ArticlePicture\":[],\"TitleCN\":null,\"AbstractTextCN\":null,\"PMCID\":null,\"EPubDate\":\"\",\"PubModel\":\"\",\"JCR\":\"\",\"JCRName\":\"\",\"Score\":null,\"Total\":0}","platform":"Semanticscholar","paperid":null,"PeriodicalName":"ICASSP '83. IEEE International Conference on Acoustics, Speech, and Signal Processing","FirstCategoryId":"1085","ListUrlMain":"https://doi.org/10.1109/ICASSP.1983.1171940","RegionNum":0,"RegionCategory":null,"ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":null,"EPubDate":"","PubModel":"","JCR":"","JCRName":"","Score":null,"Total":0}
引用次数: 0
摘要
S. Winograd的论文“计算离散傅里叶变换”(1976年和1978年)允许人们知道如果长度是素数的幂次计算DFT的最小乘法次数,并为小长度建立这样的算法。有人建议用较短的算法“建立”较长的变换。为此,Winograd提出和Kolba & Parks详细介绍了i.j. Good的素因子算法和由j.h. McClellan改进的Winograd嵌套素因子算法两种方法。1979年,j.h.麦克莱伦出版了一个使用嵌套算法的通用n FORTRAN程序(WFTA)。1981年,c.s. Burrus发表了一个非常简单的程序(PFA1),它使用了原因子算法。1982年,j.h. Rothweller扩展了Burrus的思想,开发了一个适当的、有序的程序版本(PFA2)。最后两个程序不执行逆DFT。在本工作中,系统地推导出了原因子索引图的一般性质,并进行了测试。
General - N Winograd D.F.T. programs with inverse option
S. Winograd's papers "On computing the discrete Fourier transform" (1976 and 1978) allow one to know the minimum number of multiplications to compute a DFT if the length is a power of a prime and to build such algorithms for small lengths. It is suggested that longer transforms be 'built up' with the short algorithms. For this Winograd proposes and Kolba & Parks detail two ways I.J Good's prime factor algorithm and Winograd's modified by J.H McClellan nested prime factor algorithm. In 1979 J.H McClellan publishes a General-N FORTRAN program (WFTA) using the nested algorithm. In 1981 C.S Burrus publishes a very simple program (PFA1) using in place the prime factor algorithm. In 1982 J.H Rothweller extends an idea of Burrus to developp an in place and in order version of the program (PFA2). These two last programs do not perform the inverse DFT. In this work ways to implement this as an option of the same program are systematically derived from the general properties of the prime factor index maps and tested.