Abstract
Frequency is a central concept in Mathematics, Physics, and Signal
Processing. It is the main tool for describing the oscillatory behavior
of signals, which is usually argued to be the manifestation of some of
their key features, depending on their nature. For instance, this is the
case of Electroencephalographic signals. Hence, frequency is
substantially present in the most common methodologies for analyzing
signals, as the Fourier Analysis or the Time-Frequency Analysis.
However, in spite of its importance as a keystone in Signal Processing,
and its seemingly simple meaning, its mathematical foundation is not as
straightforward as it may seem at first glance. A naive interpretation
of the different mathematical concepts modelling frequency can be
misleading, as their actual meanings essentially differ from the
intuitive notion which are supposed to represent.
In our opinion, this circumstance should be taken into account to
develop and apply appropriate signal analysis and processing tools in
some applications. In the current text we discuss this topic, with the
main goal to draw the attention of the mathematical and engineering
community to this point, often overlooked.