摘要
利用Walsh-Haar矩阵HKRm+1的递归性以及Walsh序的离散Walsh变换的快速算法,提出了一类特殊的Walsh序的离散Walsh-Haar变换的快速算法.该变换的特殊性在于Walsh-Haar函数系与Haar函数系一样,其演化生成时的伸缩比均为R=2.采用对输入数据奇偶二分及对变换结果数据对半二分,如此对一个KRm+1点的数据经过m+1步加上logK步二分以及若干次调序后,便得到变换结果.本设计方法可用于研究其他序的伸缩比为2的离散Walsh-Haar变换的快速算法.
In this paper, using the recursive property of the matrix HKR^m＋1 and the fast algorithm of Walsh ordering discrete Walsh transformation, the author designed a fast algorithm of a special type Walsh ordering discrete Walsh-Haar transformation based on bisection technique. In this algorithm, the compression ratio to generate Walsh-Haar function system is R=2, just like Haar function system. Bisecting input data in even-and-odd way, and outputting the transformed data in half-and-half way, we obtained the transformed data after m＋1＋logK times bisecting and several times ordering for a KR^m＋1 input data. The idea and method used to design the fast algorithm in this paper can be used to study the fast algorithms of other order discrete Walsh-Haar transformations with the same compression ratio.
出处
《华中科技大学学报（自然科学版）》
EI
CAS
CSCD
北大核心
2005年第10期80-82,共3页
Journal of Huazhong University of Science and Technology(Natural Science Edition)
基金
国家自然科学基金资助项目(60473015)
