**6. Concluding Remarks**

By comparing the obtained results, some useful conclusions can be drawn in order to guide a designer in choosing a method for the spectral analysis. Methods belonging to the class of parametric algorithms require a priori knowledge and allow the accurate estimation of the frequency only, but on the other hand, their performance is remarkable, with respect to the non-parametric algorithms. Specifically, ESPRIT shows very high performance even with a relatively small number of samples, so if there is any constraint on the number of samples, then the ESPRIT algorithm can be suggested as an optimal choice. If the number of tones (*Ns*) is precisely known, ESPRIT is not affected by systematic errors and is slightly affected by harmonic interference. It has excellent performance in the cases of high SNR values. On the other hand, the execution times are acceptable only when the autocorrelation matrix has a reduced size.

With the use of the proposal in Table 1, it is possible to estimate uncertainty a priori for numerous real-world conditions, without the need of extensive simulation, field acquisition, or data elaboration that needs expensive equipment or requires long time to be executed. Compared with the use of parametric approaches—where the need of a priori knowledge is indispensable in obtaining the optimal performance—this approach gives an indication of how good the result will be under certain circumstances.

As far as the other parametric approaches are considered, the performance of the MU-SIC algorithm can be compared with that of the ESPRIT method, but its systematic effects are worse than those of ESPRIT when the noise level is low. Due to its zero searching strategy, the IWPA method achieves the worst performance in the estimation of frequencies in the presence of phases difference between the tones. Among the considered non-parametric algorithms, IFFTc shows the best behaviour because it achieves a decent trade-off between metrological performance and elaboration times; the IFFT algorithm is the fastest one, but in the presence of harmonic interference, the residual error is significant.

In conclusion, IFFTc is the best choice for real-time applications whenever the elaboration time is a strong requirement, but if there are constraints on the number of samples, then ESPRIT should be chosen. Furthermore, hybrid solutions—based on a pre-processing algorithm for a preliminary estimation of the signal tones and the superimposed noise, followed by a decision algorithm to select the signal processing algorithm—could be taken into account to allow the minimum uncertainty on the frequency evaluation, and to obtain the best trade-off for different configurations of tone number, SNR ratio, required spectral resolution, and real-time needs; the latter are strictly associated with the analysed bandwidth.

**Author Contributions:** All authors have equally contributed to the article drafting, in particular: conceptualization, C.L.; methodology V.P.; software, S.D.I.; validation, G.D.L. All authors have read and agreed to the published version of the manuscript.

**Funding:** This research received no external funding.

**Institutional Review Board Statement:** Not applicable.

**Informed Consent Statement:** Not applicable.

**Data Availability Statement:** Not applicable.

**Conflicts of Interest:** The authors declare no conflict of interest.
