A high precision digital filter for the analysis of EEG-type continuous spectrum data

A novel method is proposed to decrease the error of one-dimensional DFTDF (discrete Fourier transform digital filtering) caused by the leakage distortion of the DFT. This distortion depends mainly and sensitively on the DFT span-width, i.e. the length of the time-domain raw data for DFT. The proposed method utilizes this data length dependence of the DFTDF error and is based on parallel multimodal sampling to get a set of different span-width DFTDF results of the same raw data. The point is that these filtering errors of individual DFTDF signals are almost statistically independent of one another, and these different span-width DFTDF signals of the same raw data will be averaged to obtain a more precise result, which will be referred to as the parallel multimodal sampling digitally filtered (PMSDF) result. This averaging is performed by a resampling technique. For each set of DFTDF signals, computational simulation showed that the error of PMSDF result was always much less than the worst-case error of the set of DFTDF signals and was almost always less than the average error rate of the set of DFTDF signals