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題 名 | Maximum Coset Decomposition of Prime-Factor DCT=質因數餘弦轉換之最大陪基分解演算法 |
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作 者 | 胡能忠; | 書刊名 | 中國工程學刊 |
卷 期 | 20:4 1997.07[民86.07] |
頁 次 | 頁423-433 |
分類號 | 448.5 |
關鍵詞 | 質因數DCT; 陪基分解; 斜迴旋積; 迴旋積; Prime-factor DCT; Coset decomposition; Skew-circular convolution; SCC; Circular convolution; CC; |
語 文 | 英文(English) |
中文摘要 | 長度為二個質因數乘積之DCT,可分解為斜迴旋積及迴旋積。而本文將此演算法之 長度推廣為數個互質之質因數之乘積。故此質因數DCT輸出部份形成數個矩陣為斜迴旋積或 迴旋積之矩陣與向量乘積,再利用三角等式,某些矩陣可被基底矩陣以係數為土1之矩陣以 線性組合方式取代,故將矩陣與向量乘積之個數減少同時亦減少了加法乘法運算量。因各個 輸出部份係獨立,故本法亦適合以平行方法來實現。 |
英文摘要 | The prime-factor DCT algorithm of two relatively prime factors decomposing the DCT matrix into skew-circular correlation (SCC) matrices and circular correlation (CC) matrices is generalized to many factors. As a result, the DCT output components are divided into several parts, each part is a sum of many SCC/CC matrix-vector products. The number of matrix-vector products is further reduced since some SCC/CC matrices can be represented by linear combination of other SCC/CC matrices with ± 1 coefficients. Thus the number of multiplications and additions is also reduced achieving less number of multi- plications and additions compared with other algorithms. Besides each part of the output components being independent, parallel implementation of the proposed algorithm is feasible. |
本系統中英文摘要資訊取自各篇刊載內容。