## 4 Discussion
RAE and ACC-1 also generally present statistical significance in the comparisons, especially when OBP is involved. On the other hand, results regarding ACC-10 are not statistically significant (all of the algorithms perform similarly). In general, differences between YIN and SWIPE within this picture appear to bear less statistical significance, being only significant for the TE--which is the most crucial metric for the scope of this study. These results in terms of time vs. accuracy are completely in line with the premises, since OBP was designed to be minimalistic, forgoing sheer, pinpointed accuracy (hence the lower ACC-1 values) but still staying within an acceptable range for most applications (hence the higher ACC-2 values), with an inherent observed robustness with respect to signal variations and to octave errors. It is worth noting that despite the average accuracy, the average RAE of OBP is comparable to the YIN algorithm. Moreover, all the presented algorithms have been used in one fixed setup with a fixed threshold. However, in real-world applications, hyperparameters can be tuned to better adapt to the nature and variation of the input: in fact, manually changing the threshold of the OBP algorithm provides better performances on certain datasets, especially the noisiest. The noisiest, most unclean dataset categories are full1, full2, 4 harm_4 part_wgn15 and 4 harm_high: on these sets, most algorithms provide poor performances. However, the average RAEs that would be obtained on all of the other sets are as follows:  
* YIN: 0.077680, i.e., 7.7% average error;
* SWIPE: 0.007548, i.e., 0.7% average error;
* NLS: 0, i.e., no errors. Due to its heuristic-powered nature, NLS is able to pinpoint discrete frequencies on synthetic datasets;
* OBP: 0.018396, i.e., 1.8% average error. On cleaner signals, such as those produced by many musical instruments that do not have added noise, OBP actually performs better in terms of error than YIN, while providing more than acceptable results overall. The minimalistic, stripped-down nature of OBP does not allow it to reach almost-perfect accuracy levels; however, it is critical to assess its \"acceptability\" ranges, given that it is by far the fastest [44]. YIN, on the other hand, is a fast and simple algorithm. It suffered from octave errors 12% of the time, but when the estimation was right, the precision was satisfying, with an 87% chance of obtaining a result with less than 1% error. The OBP algorithm presents a peculiar behavior because it has only a 4% chance of suffering from octave errors. An advantage of the mathematical model behind OBP over other similar autocorrelation-based methods is that, being based on the product of signals, the output heavily depends on the magnitude of the input and its variations. Because of that, an additional normalization process is usually needed, increasing the computational complexity, requiring knowledge of the energy of the signals and adding more multipliers. On the other hand, OBP only processes sign signals, inherently independent from the original magnitude, removing the need for explicit normalization procedures. Despite the performances reported in these tests, different environments and data see the algorithms behave differently, at least in terms of accuracy. In fact, SWIPE is one of the gold standards for feature extraction for medical or Machine Learning purposes, due to it being well suited for noisy environments and due to the applications not needing real-time elaboration. On the other hand, NLS is not robust with respect to the nature of the input and is more prone to suffer from octave errors, making it sometimes an inconsistent choice despite the high performances on the proposed synthetic dataset.