{"title":"使用拉马努金数的快速无乘子递归变换","authors":"K. Geetha, V. K. Ananthashayana","doi":"10.1109/MSPCT.2009.5164188","DOIUrl":null,"url":null,"abstract":"A special class of multiplierless transforms for computing discrete cosine transform (DCT) is introduced. This algorithm is completely multiplierless to compute an N-point DCT using Ramanujan Number of order -1 and order-2. The algorithm requires evaluation of Cosine angles which are multiples of 2π/N. If the transform size N is a Ramanujan Number and if 2π/N ≅ 2−a, then the cosine functions can be computed by shifts and adds employing Chebyshev type of recursion. In this paper, an analytical extension of the algorithm is made for 2-D Ramanujan DCT for image coding applications.","PeriodicalId":179541,"journal":{"name":"2009 International Multimedia, Signal Processing and Communication Technologies","volume":null,"pages":null},"PeriodicalIF":0.0000,"publicationDate":"2009-03-14","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":"5","resultStr":"{\"title\":\"Fast multiplierless recursive transforms using Ramanujan numbers\",\"authors\":\"K. Geetha, V. K. Ananthashayana\",\"doi\":\"10.1109/MSPCT.2009.5164188\",\"DOIUrl\":null,\"url\":null,\"abstract\":\"A special class of multiplierless transforms for computing discrete cosine transform (DCT) is introduced. This algorithm is completely multiplierless to compute an N-point DCT using Ramanujan Number of order -1 and order-2. The algorithm requires evaluation of Cosine angles which are multiples of 2π/N. If the transform size N is a Ramanujan Number and if 2π/N ≅ 2−a, then the cosine functions can be computed by shifts and adds employing Chebyshev type of recursion. In this paper, an analytical extension of the algorithm is made for 2-D Ramanujan DCT for image coding applications.\",\"PeriodicalId\":179541,\"journal\":{\"name\":\"2009 International Multimedia, Signal Processing and Communication Technologies\",\"volume\":null,\"pages\":null},\"PeriodicalIF\":0.0000,\"publicationDate\":\"2009-03-14\",\"publicationTypes\":\"Journal Article\",\"fieldsOfStudy\":null,\"isOpenAccess\":false,\"openAccessPdf\":\"\",\"citationCount\":\"5\",\"resultStr\":null,\"platform\":\"Semanticscholar\",\"paperid\":null,\"PeriodicalName\":\"2009 International Multimedia, Signal Processing and Communication Technologies\",\"FirstCategoryId\":\"1085\",\"ListUrlMain\":\"https://doi.org/10.1109/MSPCT.2009.5164188\",\"RegionNum\":0,\"RegionCategory\":null,\"ArticlePicture\":[],\"TitleCN\":null,\"AbstractTextCN\":null,\"PMCID\":null,\"EPubDate\":\"\",\"PubModel\":\"\",\"JCR\":\"\",\"JCRName\":\"\",\"Score\":null,\"Total\":0}","platform":"Semanticscholar","paperid":null,"PeriodicalName":"2009 International Multimedia, Signal Processing and Communication Technologies","FirstCategoryId":"1085","ListUrlMain":"https://doi.org/10.1109/MSPCT.2009.5164188","RegionNum":0,"RegionCategory":null,"ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":null,"EPubDate":"","PubModel":"","JCR":"","JCRName":"","Score":null,"Total":0}
Fast multiplierless recursive transforms using Ramanujan numbers
A special class of multiplierless transforms for computing discrete cosine transform (DCT) is introduced. This algorithm is completely multiplierless to compute an N-point DCT using Ramanujan Number of order -1 and order-2. The algorithm requires evaluation of Cosine angles which are multiples of 2π/N. If the transform size N is a Ramanujan Number and if 2π/N ≅ 2−a, then the cosine functions can be computed by shifts and adds employing Chebyshev type of recursion. In this paper, an analytical extension of the algorithm is made for 2-D Ramanujan DCT for image coding applications.