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. © 2011 IEEE.