Fast algorithms for computing the forward and inverse sequency-ordered complex Hadamard transforms (SCHT) in a sliding window are presented. The first algorithm consists of decomposing a length- N inverse SCHT (ISCHT) into two length-N/2 ISCHTs. The second algorithm, calculating the values of window i + N/4 from those of window i and one length-N/4 ISCHT and one length-N/4 Modified ISCHT (MISCHT), is implemented by two schemes to achieve a good compromise between the computation complexity and the implementation complexity. The forward SCHT algorithm can be obtained by transposing the signal flow graph of the ISCHT. The proposed algorithms require O(N) arithmetic operations and thus are more efficient than the block-based algorithms as well as those based on the sliding FFT or the sliding DFT. The application of the sliding ISCHT in transform domain adaptive filtering (TDAF) is also discussed with supporting simulation results.

中文翻译：

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滑动序列有序复Hadamard变换计算的快速算法

介绍了用于在滑动窗口中计算前向和逆序复杂 Hadamard 变换 (SCHT) 的快速算法。第一种算法包括将长度为 N 的逆 SCHT (ISCHT) 分解为两个长度为 N/2 的 ISCHT。第二种算法，从窗口i的值和一个长度为N/4的ISCHT和一个长度为N/4的修正ISCHT（MISCHT）计算窗口i+N/4的值，通过两种方案实现，达到了很好的折衷在计算复杂度和实现复杂度之间。前向SCHT算法可以通过对ISCHT的信号流图进行转置得到。所提出的算法需要 O(N) 次算术运算，因此比基于块的算法以及基于滑动 FFT 或滑动 DFT 的算法更有效。