Fast method of interpolation for frequency estimation of sinusoidal and spindle data

Estimating the frequency of one or more sinusoidal waves is a problem belonging to the field of signal analysis. The frequency characteristics of sinusoidal waves can be measured by peaks or troughs of the waves. Because of (he limit of the sampling frequency, the peaks or troughs of sinusoidal and EEG waves in the sampling usually deviate from their original ones in the time domain. Starting from a sinusoidal wave analysis, we present a correction formula with which the deviation time t_d can be calculated so as to detect the position of the real peak or trough of the data as fast and as accurately as possible on the time axis. The wave of the sleep spindle in the EEG can be considered as an asymmetrical sinusoid. Then after the waves have been filtered, the formula can also be applied to analyse the spindle of EEG waves and it is shown to be useful in the measurement of the frequency of the spindle wave. Error analysis and practical examples are presented.