# Enhancement of Conventional Beat Tracking System Using Teager-Kaiser Energy Operator
## 1 Introduction  
Onset time in audio signal analysis represents the time position of a relevant sound event: usually when a music tone is created. Onset detection functions are algorithms that capture onsets (onset time positions), and thus ideally all tones in audio recordings. They can create a representation or an evolution of onset structure in given time of particular audio recording. There are also offsets of tones (indicating the end time position of a tone in a signal), e.g., see [1, 2], but beat tracking systems do not need such information to work properly. The conventional beat tracking system is usually based on the calculation of repetitiveness of the dominant components in an onset function (onset curve) and its output represents a temporal framework, i.e., time instances, where a person would tap when listening to the corresponding piece of music. That is why it is important to have a robustand computationally effective onset detector. Calculation of the beat positions and global tempo (GT) is important for musicologists and the complex music analysis. With such automated systems, tempo and agogic changes can be measured much faster than only with manual approach alone. Thus, musicologists would have to spend less time correcting calculated beat positions. Therefore, we set a new parameter--the average deviation of reference beat positions to the calculated beat positions as the average beat deviation (ABD). Most of the onset detectors are based on energy changes in spectra: the calculation of spectral flux. For bowed string instruments there is a method called SuperFlux that can suppress vibrato in an expressive performance and reduce the amount of false-positive detections [3]. Some methods enhance the spectral flux onset detection using logarithmic spectral compression and then compute the cyclic tempogram for a tempo analysis [4]. There is also a method that calculates tempograms using Predominant Local Pulse [5]. Besides, the onset detection and beat detection could be performed in several toolboxes and libraries such as Tempogram Toolbox [6], LibROSA [7], MIR Toolbox [8], etc. [9]. The state-of-art onset detectors are usually based on deep neural networks [10, 11] using spectral components and parameters as their inputs. Beat detection systems contribute from the solid onset detectors, where periodicity is identified [6, 8, 12, 13, 14]. As in other MIR fields, neural networks are also used. While onset detection in percussive music is considered to be highly accurate (already at MIREX 2012 conference [15], algorithms achieved F-measure values greater than 0.95 for percussive sounds), detection of soft onsets produced by bowed string or woodwind instruments is still challenging. Although a lot of improvements in onset detection have been made, no system is truly universal for all musical instruments and all types of music. This work aims to enhance the conventional beat tracking system and to improve the tempo analysis methodology published in [16, 17] using the more sophisticated approach of tempo structure creation based on the automated beat tracking system with the Teager-Kaiser energy operator (TKEO) included. This nonlinear energy operator is used, e.g., for the improvement of onset detection in EMG signals (electromyography) [18], to decompose audio into amplitude and frequency modulation components [19], for the detection of Voice Onset Time [20], or the highly efficient technique for LOS estimation in WCDMA mobile positioning [21]. So far there is no extensive study on the use of TKEO for the analysis of musical instruments. Since we will focus on the detection of onsets of melody instruments with low-energy attacks, we will concentrate on the onset and beat detection method based on spectral changes. We have not chosen probabilistic models, because they are usually susceptible to noisy recordings, which can be a problem in the case of old recordings.