  In this article, we investigate the debated Instantaneous Frequency (IF)
topic. Here, we show that IF is non-unique inherently. We explain how this
non-uniqueness can be quantified and explained from a mathematical perspective.
The non-uniqueness of the IF can also be observed if different methods of
adaptive signal processing are used. We will also show that even if we know the
physical origin of an oscillatory signal, e.g. linear second order ordinary
differential equation, the non-uniqueness is still present. All in all, we will
end up with the conclusion that, without any a priori assumption about the
relationship of the envelope and phase function of an oscillatory signal, there
is not any preferred neither best representation of the IF of such oscillatory
signal.
