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

Abstract

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.

Improved Transient Response Estimations in Predicting 40 Hz Auditory Steady-State Response Using Deconvolution Methods

“…Various measures (e.g., Wang et al, 2006 , 2013a ) have been proposed to deal with this issue since the first introduction of the CLAD method (Delgado and Ozdamar, 2004 ). The most important aspect of the CLAD sequence design is the sequence of ISI-jitters and its optimization to avoid unusual amplification of contamination noise in EEG (Ozdamar et al, 2007 ; Peng et al, 2017 ). The sequence used in the present study was a well-tuned impulse train containing eight clicks as presented in section Stimulation and Figure 1 .…”

“…The sequence used in the present study was a well-tuned impulse train containing eight clicks as presented in section Stimulation and Figure 1 . The appropriateness of this sequence could be measured by the noise gain factor, C dec , defined by Ozdamar and Bohorquez ( 2006 ), which was 0.55, or by an improved metric G dec (Peng et al, 2017 ), which was 0.79. Both values were close to the value from the optimal solution, indicating the applicability of the sequence.…”