Enhanced period-peak analysis of the electroencephalogram using a fast Sinc function

EEG computer analysis is still not widely used in the clinic, and the need for advanced signal processing techniques is still warranted. The fast Fourier transform (FFT) is the method most frequently used for power spectrum estimation of the EEG. In an effort to reduce memory space and processing time required by the fast Fourier transform (FFT), a new method, the enhanced period-peak detection (EPPD), is investigated. The method is based on a combination of the Fourier transform (FT) and period-peak detection. The signal is considered as a train of truncated sinusoidal functions. Each truncated sinusoidal function is limited by two successive local extrema (a peak and a valley). The Fourier transform of the truncated sinusoidal function is the well known Sinc function. The summation of these Sinc functions yields an approximate frequency spectrum of the signal. The speed and performance of the FFT rely upon the number of data collected and the sampling frequency. On the other hand, the enhanced period-peak detection (EPPD) method does not require that the entire EEG data be stored. Only the extrema of the signal and time between the peaks are needed. Furthermore, the frequency resolution of the EPPD is independent of the number of data available and of the sampling frequency.