{"title":"新的实乘法器FFT-j算法","authors":"Yiquan Wu, Zhaoda Zhu","doi":"10.1109/NAECON.1993.290899","DOIUrl":null,"url":null,"abstract":"In this paper four different versions of the DFT (DFT-j,j=I,II,III,IV) are first introduced, Then, the relationship among four different versions of the DFT and their inherent properties are explored. The new real-multiplier FFT-j algorithms are proposed for all four versions of the N=2/sup m/ DFT. The algorithm formulae are derived, represented by Kronecker product and direct sum. Finally, the signal flowgraph for the length-2/sup 3/ FFT-j is given to illustrate the proposed algorithms. The computational complexity is analysed and a comparison is made with other existing real-multiplier FFT algorithms. The proposed algorithms require the minimum number of arithmetic operations and use real multipliers and allow in-place computation. Besides, the proposed algorithms have very simple and regular structure. They have been implemented by software and have been finding practical applications.<<ETX>>","PeriodicalId":183796,"journal":{"name":"Proceedings of the IEEE 1993 National Aerospace and Electronics Conference-NAECON 1993","volume":"260 1","pages":"0"},"PeriodicalIF":0.0000,"publicationDate":"1993-05-24","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":"3","resultStr":"{\"title\":\"The new real-multiplier FFT-j algorithms\",\"authors\":\"Yiquan Wu, Zhaoda Zhu\",\"doi\":\"10.1109/NAECON.1993.290899\",\"DOIUrl\":null,\"url\":null,\"abstract\":\"In this paper four different versions of the DFT (DFT-j,j=I,II,III,IV) are first introduced, Then, the relationship among four different versions of the DFT and their inherent properties are explored. The new real-multiplier FFT-j algorithms are proposed for all four versions of the N=2/sup m/ DFT. The algorithm formulae are derived, represented by Kronecker product and direct sum. Finally, the signal flowgraph for the length-2/sup 3/ FFT-j is given to illustrate the proposed algorithms. The computational complexity is analysed and a comparison is made with other existing real-multiplier FFT algorithms. The proposed algorithms require the minimum number of arithmetic operations and use real multipliers and allow in-place computation. Besides, the proposed algorithms have very simple and regular structure. They have been implemented by software and have been finding practical applications.<<ETX>>\",\"PeriodicalId\":183796,\"journal\":{\"name\":\"Proceedings of the IEEE 1993 National Aerospace and Electronics Conference-NAECON 1993\",\"volume\":\"260 1\",\"pages\":\"0\"},\"PeriodicalIF\":0.0000,\"publicationDate\":\"1993-05-24\",\"publicationTypes\":\"Journal Article\",\"fieldsOfStudy\":null,\"isOpenAccess\":false,\"openAccessPdf\":\"\",\"citationCount\":\"3\",\"resultStr\":null,\"platform\":\"Semanticscholar\",\"paperid\":null,\"PeriodicalName\":\"Proceedings of the IEEE 1993 National Aerospace and Electronics Conference-NAECON 1993\",\"FirstCategoryId\":\"1085\",\"ListUrlMain\":\"https://doi.org/10.1109/NAECON.1993.290899\",\"RegionNum\":0,\"RegionCategory\":null,\"ArticlePicture\":[],\"TitleCN\":null,\"AbstractTextCN\":null,\"PMCID\":null,\"EPubDate\":\"\",\"PubModel\":\"\",\"JCR\":\"\",\"JCRName\":\"\",\"Score\":null,\"Total\":0}","platform":"Semanticscholar","paperid":null,"PeriodicalName":"Proceedings of the IEEE 1993 National Aerospace and Electronics Conference-NAECON 1993","FirstCategoryId":"1085","ListUrlMain":"https://doi.org/10.1109/NAECON.1993.290899","RegionNum":0,"RegionCategory":null,"ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":null,"EPubDate":"","PubModel":"","JCR":"","JCRName":"","Score":null,"Total":0}
In this paper four different versions of the DFT (DFT-j,j=I,II,III,IV) are first introduced, Then, the relationship among four different versions of the DFT and their inherent properties are explored. The new real-multiplier FFT-j algorithms are proposed for all four versions of the N=2/sup m/ DFT. The algorithm formulae are derived, represented by Kronecker product and direct sum. Finally, the signal flowgraph for the length-2/sup 3/ FFT-j is given to illustrate the proposed algorithms. The computational complexity is analysed and a comparison is made with other existing real-multiplier FFT algorithms. The proposed algorithms require the minimum number of arithmetic operations and use real multipliers and allow in-place computation. Besides, the proposed algorithms have very simple and regular structure. They have been implemented by software and have been finding practical applications.<>
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