Instantaneous frequencies of simple waves and their application to sleep spindle detection

The paper introduces two different types of frequencies of which one is the Arccosine Instantaneous Frequency (ArccosineIF) for the so called axial simple waves (ASWs); and the other is the α-Counting Instantaneous Frequency (α-CIF) for a more general class of signals called simple waves (SWs). The classes ASW and SW contain a wide range of signals for which the concept instantaneous frequency has a perfect physical sense. Then under wavelet decomposition the two types of frequencies are used to analyze the time-frequency distributions of the biomedical EEG signals with comparison. A set of experiments on publicly available database clearly indicate that the proposed approaches are very promising.