Combined frequency and time domain sleep feature calculation

In automated sleep analysis usually both frequency and time domain features are calculated from measured physiological (EEG, EOG, EMG) signals. Usually Discrete Fourier Transform (DFT) is used for different frequency domain measures and Digital Filtering (FIR or IIR) for time domain measurement. Here we demonstrate potential usefulness of using modified inverse DFT as a step for time domain feature calculation. Analytical formulas are shown for calculating interpolation, velocity and acceleration of filtered signals. Preliminary examples of electro-oculography (EOG) signal analysis during sleep are presented. Although same results could be obtained with conventional filtering followed by numerical differentiation the presented could be useful in some cases.