There have been different approaches to compute the analytic instantaneous frequency with a variety of background reasoning and applicability in practice, as well as restrictions. This paper presents a new non-analytic instantaneous frequency definition for a large class of so-called simple waves. Simple wave contains a wide range of signals for which the concept instantaneous frequency has a perfect physical sense. There are a number of automatic sleep spindle detection methods in the literature, however, due to the complexity of the sleep spindle characteristics from different people and absence of generally accepted sleep spindle definition in the literature, researchers are still exploring more practically acceptable and workable methods. A novel instantaneous frequency definition based semi-automatic sleep spindle detection approach is also proposed in this paper. A set of experiments on publicly available database clearly indicate that the proposed approaches are very promising. Copyright © 2012 John Wiley & Sons, Ltd.