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Computational and Mathematical Methods in Medicine
Volume 2017 (2017), Article ID 3927486, 9 pages
Research Article

Noise Attenuation Estimation for Maximum Length Sequences in Deconvolution Process of Auditory Evoked Potentials

1School of Biomedical Engineering, Southern Medical University, Guangzhou, Guangdong, China
2Stephenson School of Biomedical Engineering, University of Oklahoma, Norman, OK, USA

Correspondence should be addressed to Xiaodan Tan

Received 15 December 2016; Revised 19 January 2017; Accepted 26 January 2017; Published 19 February 2017

Academic Editor: Anne Humeau-Heurtier

Copyright © 2017 Xian Peng et al. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.


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.