The Fast m-Transform: A Fast Computation of Cross-Correlations with Binary m-Sequences
The Fast m-Transform: A Fast Computation of Cross-Correlations with Binary m-Sequences
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快速 m 变换：二进制 m 序列互相关的快速计算
DOI：
10.1137/0220043
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发表时间：
1991
期刊：
影响因子：
--
通讯作者：
E. Sutter
中科院分区：
文献类型：
--
作者：
E. Sutter
给出了一种快速计算m变换的算法，m变换是一种与二进制m序列的模拟信号互相关密切相关的阿达玛变换。证明了m变换与Walsh - Hadamard变换属于相同的Hadamard等价类，因此可以通过快速Walsh变换（FWT）算法进行计算，前后都有一个置换。FWT在原始数据数组中就地执行，而排列在加载和读取该数组期间执行。用于加载和读取的数组地址的实时生成几乎不会增加FWT的执行时间。这里描述的实现特别适合于线性和非线性系统分析的应用。
An algorithm is presented for the fast computation of the m-transform, a Hadamard transform intimately related to cross-correlation of analog signals with binary m-sequences. It is shown that m-transforms are in the same Hadamard equivalence class as Walsh–Hadamard transforms and can, thus, becomputed by means of the Fast Walsh Transform (FWT) algorithm, preceded and followed by a permutation. The FWT is performed in place in the original data array, while the permutations are executed during loading and reading of this array. Real-time generation of the array addresses for loading and reading adds little to execution time of the FWT. The implementation described here lends itself particularly well to applications in linear and nonlinear systems analysis.