{"title":"New radix-3 fast algorithm for the discrete cosine transform","authors":"Yiquan Wu, Zhaoda Zhu","doi":"10.1109/NAECON.1993.290898","DOIUrl":null,"url":null,"abstract":"In this paper a new radix-3 fast algorithm for the length -3/sup m/ discrete cosine transform (DCT) is proposed, to further extend the applicability of the fast cosine transform (FCT) algorithm. First, the basic 3-point DCT is considered. Then, the formulae of the new radix-3 FCT algorithm are derived. Next, a block diagram of the radix-3 FCT algorithm is shown and the signal flowgraph for length-3/sup 2/ FCT is given to illustrate the proposed algorithm. Finally, the computational complexity is analysed. The proposed algorithm requires less number of arithmetic operations and allows in-place computation. The simple and regular structure makes it easy to be implemented. One can compute effectively the length-2/sup 1/.3/sup m/ DCT using this length-3/sup m/ algorithm together with the existing length-2/sup 1/ algorithm by prime factor decomposition. The proposed new radix-3 FCT algorithm is expected to find wide practical applications.<<ETX>>","PeriodicalId":183796,"journal":{"name":"Proceedings of the IEEE 1993 National Aerospace and Electronics Conference-NAECON 1993","volume":"52 1","pages":"0"},"PeriodicalIF":0.0000,"publicationDate":"1993-05-24","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":"2","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.1993.290898","RegionNum":0,"RegionCategory":null,"ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":null,"EPubDate":"","PubModel":"","JCR":"","JCRName":"","Score":null,"Total":0}
引用次数: 2
Abstract
In this paper a new radix-3 fast algorithm for the length -3/sup m/ discrete cosine transform (DCT) is proposed, to further extend the applicability of the fast cosine transform (FCT) algorithm. First, the basic 3-point DCT is considered. Then, the formulae of the new radix-3 FCT algorithm are derived. Next, a block diagram of the radix-3 FCT algorithm is shown and the signal flowgraph for length-3/sup 2/ FCT is given to illustrate the proposed algorithm. Finally, the computational complexity is analysed. The proposed algorithm requires less number of arithmetic operations and allows in-place computation. The simple and regular structure makes it easy to be implemented. One can compute effectively the length-2/sup 1/.3/sup m/ DCT using this length-3/sup m/ algorithm together with the existing length-2/sup 1/ algorithm by prime factor decomposition. The proposed new radix-3 FCT algorithm is expected to find wide practical applications.<>