**1. Introduction**

The spectral analysis of signals is successfully adopted in several fields—from electrical [1,2] to typical industrial fields—for speed and fault detection on motors and bearings [3–5] in military applications [6], submarine applications [7], and medical applications [8]. Despite the adaptability of frequency analysis for varied applications [9], similar cases might require different approaches, requirements, and constraints; for this reason, they differ in the tuning of the analysis parameters, and the choice of the most suitable technique can be a difficult task to accomplish. For this reason, the designer of a measurement system for spectral analysis must have knowledge about the behaviour of the different techniques concerning the operating conditions. The case that will be considered is the realisation of a numerical instrument for the real-time measurement of the spectral components of a signal: amplitude, frequency, and phase.

**Citation:** Dello Iacono, S.; Di Leo, G.; Liguori, C.; Paciello, V. The Obtainable Uncertainty for the Frequency Evaluation of Tones with Different Spectral Analysis Techniques. *Metrology* **2022**, *2*, 216–229. https://doi.org/10.3390/ metrology2020013

Academic Editor: Simona Salicone

Received: 31 August 2021 Accepted: 17 February 2022 Published: 14 April 2022

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For this purpose, different signal processing techniques can be used that can be generally classified in parametric and non-parametric methods. The first class includes those methods that exploit the a priori knowledge about the signal parameters, such as the number of signal spectral components. Thus, a self-configuring procedure based on a parametric algorithm should include a preliminary evaluation of the number of components. The choice of the proper method among the several available approaches is fundamental for designing a procedure based on signal spectral analysis. Different aspects should be considered: the desired level of accuracy, the available elaboration resources (memory depth and processing speed), and the signal nature.

This paper will compare the most effective methods available in the literature for the spectral analysis of signals [10–25]. The considered methods for the comparison will be briefly described, and references from the literature will be given for each one of them. Their behaviour will be analysed in terms of obtainable uncertainty on the frequency evaluation. Residual errors and repeatability of the measured frequency directly influence the uncertainty of other tone properties, such as phase and amplitude.

The procedure and the criteria adopted for the comparison are described and, eventually, the results are reported and commented upon. Numerical simulations have been run in conditions similar to the real-world operation of a measurement system by studying the effects of added Gaussian noise or quantisation noise to the signal, and their results are shown in this article.
