On the Concept of Frequency in Signal Processing

TL;DR

This paper critically examines the mathematical foundations of the concept of frequency in signal processing, highlighting potential misconceptions and urging for more precise interpretations to improve analysis tools.

Contribution

It clarifies the mathematical distinctions of frequency, emphasizing the need for careful interpretation beyond intuitive notions in signal analysis.

Findings

Mathematical concepts of frequency differ from intuitive notions.

Misinterpretations can lead to flawed signal analysis.

The paper calls for refined understanding in signal processing methods.

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 in order to develop appropriate signal analyzing 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.