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C编号Walsh函数及Manz算法

冯德修   

  1. 中国科学院生物物理所
  • 出版日期:1983-04-14 发布日期:1983-04-14

冯德修. C编号Walsh函数及Manz算法[J]. 计算数学, 1983, 5(4): 403-411.

C-ORDERED WALSH FUNCTIONS AND(FWHT)w WHICH WAS INTRODUCED BY MANZ

  1. Feng De-xiu Institute of Biophysics Academia Sinica
  • Online:1983-04-14 Published:1983-04-14
沃尔什编号Walsh函数是Walsh在1923年给出的;1931年,Paley定义了佩利编号Walsh函数;哈德玛编号Walsh函数是根据Hadamard 1893年的工作,由专用
The discrete Paley-ordared, Walsh-ordered, and Hadamard-ordered Walsh functionsare derived by iteration equations respectively. On the basis of the above-mentioned,in this paper a new iteration equation is deduced. We call the discrete Walsh functionsderived from this way C-ordered ones. C-ordered Walsh functions do not possess thesymmetry. Their transposed functions form C'-ordered ones. Relations between C-ordered and the ordinary three ordered correspond to those of the ordinary three or-dered transformations. Then, some new-ordered transformations rules are shown amongC'-ordered nd the three ordered functions. The four kinds of Walsh functions (Walsh-ordered, Paley-ordered, C-ordered, andHadamard) should coexist by iteration equations and relations among them. If regard-ing Walth-ordered and Paley-ordered as a pair, then C-ordered and Hadamard-orderedis a pair too. The algorithms are derived to yied the fast Walsh transforms in C and C' orders(FWCT And FWC'T): The features of the FWCT are: 1) it is analogous to theCooley-Tukey algorithm for the complex-exponential Fourier transform, 2) the transformremains its own inverse, and 3) it is the analytic version of the (FWHT)_w and the com-putation formula which was introduced by Manz when the bitreverse the input andorder it in ascending index order.
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