Peng Xian, Chen Yun'er, Wang Tao, Ding Lei, Tan Xiaodan
School of Biomedical Engineering, Southern Medical University, Guangzhou, Guangdong, China.
Stephenson School of Biomedical Engineering, University of Oklahoma, Norman, OK, USA.
Comput Math Methods Med. 2017;2017:3927486. doi: 10.1155/2017/3927486. Epub 2017 Feb 19.
The use of maximum length sequence (m-sequence) has been found beneficial for recovering both linear and nonlinear components at rapid stimulation. Since m-sequence is fully characterized by a primitive polynomial of different orders, the selection of polynomial order can be problematic in practice. Usually, the m-sequence is repetitively delivered in a looped fashion. Ensemble averaging is carried out as the first step and followed by the cross-correlation analysis to deconvolve linear/nonlinear responses. According to the classical noise reduction property based on additive noise model, theoretical equations have been derived in measuring noise attenuation ratios (NARs) after the averaging and correlation processes in the present study. A computer simulation experiment was conducted to test the derived equations, and a nonlinear deconvolution experiment was also conducted using order 7 and 9 m-sequences to address this issue with real data. Both theoretical and experimental results show that the NAR is essentially independent of the m-sequence order and is decided by the total length of valid data, as well as stimulation rate. The present study offers a guideline for m-sequence selections, which can be used to estimate required recording time and signal-to-noise ratio in designing m-sequence experiments.
已发现使用最大长度序列（m序列）有助于在快速刺激时恢复线性和非线性成分。由于m序列完全由不同阶的本原多项式表征，多项式阶数的选择在实际应用中可能存在问题。通常，m序列以循环方式重复发送。第一步进行总体平均，然后进行互相关分析以解卷积线性/非线性响应。根据基于加性噪声模型的经典降噪特性，在本研究中推导了测量平均和相关过程后的噪声衰减率（NAR）的理论方程。进行了计算机模拟实验以测试推导的方程，还使用7阶和9阶m序列进行了非线性去卷积实验以用实际数据解决此问题。理论和实验结果均表明，NAR基本上与m序列阶数无关，而是由有效数据的总长度以及刺激速率决定。本研究为m序列选择提供了指导，可用于在设计m序列实验时估计所需的记录时间和信噪比。
