  We propose a maximum entropy (ME) based approach to smooth noise not only in
data but also to noise amplified by second order derivative calculation of the
data especially for electroencephalography (EEG) studies. The approach includes
two steps, applying method of ME to generate a family of filters and minimizing
noise variance after applying these filters on data selects the preferred one
within the family. We examine performance of the ME filter through frequency
and noise variance analysis and compare it with other well known filters
developed in the EEG studies. The results show the ME filters to outperform
others. Although we only demonstrate a filter design especially for second
order derivative of EEG data, these studies still shed an informatic approach
of systematically designing a filter for specific purposes.
