# Enhancement of Conventional Beat Tracking System Using Teager-Kaiser Energy Operator
## 5 Conclusions  
This study introduces an enhancement of the conventional beat tracking system by adding the TKEO into the pre-processing stage. It briefly describes the onset detection function and the beat tracking method with its possible application. The onset detection accuracy decreased in most analyzed tracks, but the accuracy of the GT detection and the ABD detection increased.  
The influence of the TKEO was tested on different recordings and it was found, that in the case of woodwind instruments, the TKEO increased the onset detection accuracy. This phenomenon willbe studied in our future work. We would like to focus on the possible applications of the TKEO on music recordings in general. The TKEO is changing the magnitude of frequency components in a signal and acts as a filter. This could be the cause of increased onset detection accuracy, e.g., for the clarinet example.  
The estimation of the GT was improved in the reference database. The average deviation from the reference GT in the reference database is 9.99 BPM (11.28%), which improves the conventional methodology, where the average deviation is 18.19 BPM (17.74%). P-values indicate that there is a clear difference between proposed systems. Both systems were also tested on the string quartet database. In this case, however, the results are not convincing. The proposed TS will be further used in the subsequent music analysis of the string quartet database. The aim is to create an automated system for capturing beat positions that are as close as possible to the actual beat positions in the recordings even for the complex music such as string quartet. In this way, it is possible to minimize the time required for manual processing and labelling. This study has a pilot character and provides some suggestions for improving the beat tracking system for music analysis.  
Conceptualization, M.I., Z.S. and L.S.; methodology, M.I.; software, M.I.; validation, M.I.; formal analysis, M.I., Z.S., L.S. and J.M.; investigation, M.I.; resources, M.I.; data curation, M.I.; writing--original draft preparation, M.I.; visualization, M.I.; supervision, Z.S., L.S. and J.M.; project administration, Z.S.; funding acquisition, Z.S. All authors have read and agreed to the published version of the manuscript.  
This research was funded by the grant LO1401. For the research, infrastructure of the SIX Center was used.  
The authors declare no conflict of interest.  
The following abbreviations are used in this manuscript:  
\begin{tabular}{l l} ABD & Average Beat Deviation \\ BPM & Beats Per Minute \\ DS & Default System without the TKEO \\ EAT & Estimated Average Tempo \\ EMG & Electromyography \\ GT & Global Tempo \\ MIR & Music Information Retrieval \\ STFT & Short-Time Fourier Transform \\ TKEO & Teager-Kaiser Energy Operator \\ TS & System with the TKEO included \\ \end{tabular}  
\begin{table}
\begin{tabular}{c c c c c c} \hline \hline \multirow{2}{*}{**Track No.**} & **Reference** & **TS** & **DS** & **TS** & **DS** \\  & **(BPM)** & **(BPM)** & **(BPM)** & **Dev. (BPM)** & **Dev. (BPM)** \\ \hline  
\hline Average & 76.78 & 83.75 & 88.97 & 9.99 & 18.19 \\ \hline \multicolumn{2}{c}{P-value} & 0.038 & 0.024 & & \\ \hline \hline \end{tabular}  
* TS—System with the TKEO; DS—Default system without the TKEO; Dev.—deviation from the reference global tempo; BPM—Beats Per Minute; P—\(p\)-value for the \(t\)-Test (Paired Two Sample for Means), \(\alpha=0.05\).  
\end{table}
Table 15: Reference GT and computed GT of the reference database.