N阶整数DCT变换基通用生成算法

刘华; 吴云; 赵勇; 田伟森

doi:10.11834/jig.20101210

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专辑

N阶整数DCT变换基通用生成算法
Generic generating algorithm for N-order integer DCT transform radix
2010年15卷第12期页码：1742
网络出版：2010-12-13，

纸质出版：2010
DOI： 10.11834/jig.20101210
稿件说明：

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刘华, 吴云, 赵勇, 田伟森. N阶整数DCT变换基通用生成算法[J]. 中国图象图形学报, 2010,15(12):1742. DOI： 10.11834/jig.20101210.

Liuhua, wuyun, zhaoyong, tianweisen. Generic generating algorithm for N-order integer DCT transform radix[J]. Journal of Image and Graphics, 2010, 15(12): 1742. DOI： 10.11834/jig.20101210.

摘要

为了使DCT变换能够通用，首先通过对DCT变换原理进行研究，发现了变换基系数的取值个数与阶数的关系，并结合余弦函数的性质对其进行了证明；然后以此为基础，提出了一种N(N=2

k>0，下同）阶整数DCT变换基的通用生成算法（该算法无需对相应的浮点基进行具体分析）；接着通过巧妙排列系数的序号，使得生成的中间多项式具有极强的规律性；最后设计了一个N位M进制数，用来实现N重循环，以穷举所有的可能解，并成功对任意N元多项式组进行了求解。实验结果表明，只要计算机的能力足够强大，应用此算法便可以发现任意N×N整数DCT变换的所有可用基。

Abstract

The relationship between amounts of coefficients and order in radix is discovered through research of DCT principle and proven in combination with the nature of cosine function. On this basis

a generic generating algorithm for N-order (N=2

k>0

sic passim) integer DCT transform radix is presented

which we do not need to analyze floating radix corresponding to integer’s. Through rearrange variations of coefficient

the mid-polynomials are extremely regularity. The group of polynomials in arbitrary N-variable is resolved by designing a N-digits with M as radix implementing N-loops to exhaust all possible solutions. The experimental results show that the algorithm can find all available radix for arbitrary N×N integer DCT as long as the computing capacity is enough.