Automatic Detection of the Common and Non-common Frequencies in Congruent Discrete Spectra. A Theoretical Approach

TL;DR

This paper introduces a theoretical method for automatically detecting shared and unique frequencies across multiple congruent spectra, aiding in spectral analysis automation.

Contribution

It provides a novel theoretical framework for automatic frequency detection in multiple spectra, enhancing spectral analysis automation.

Findings

Develops a theoretical basis for frequency detection

Enables automatic identification of common frequencies

Supports automation in spectral analysis

Abstract

Both sampling a time-varying signal, and its spectral analysis are activities subjected to theoretically compelling, such as Shannon's theorem and the objectively limiting of the frequency's resolution. Usually, the signals' spectra are processed and interpreted by a scientist who, presumably, has sufficient prior information about the monitored signals to conclude on the significant frequencies, for example. On the other hand, processing and interpretation of signals' spectra can be routine tasks that must be automated using suitable software, i.e. PC application. In the above context, the paper presents the theoretic bases of an intuitive and practical approach of the (automatic) detection of the common and non-common frequencies in two or more congruent spectra.