Accurate localization for signal peaks based on central Grünwald-Letnikov formula with −1<α<0

The signal peaks are its extremum points, which are important signal features. The locating signal peaks is crucial for accurately identifying signal characteristics, analyzing signal patterns, signal smoothing, signal classification and other post-processing processes. It is a key foundation for achieving precise signal analysis and optimization in fields such as biomedical signal analysis and biometric feature verification etc. We propose a high-precision signal peak detection method that is adaptable to various signal forms using the fractional-order G-L operator. Firstly, an in-depth study of the performance of fractional-order calculus in signal peak detection points out that the peak drift is the root cause of the poor performance of existing Left-handed Grünwald-Letnikov (LG-L) in peak detection. Peak drift means that the peak positions detected by the operators are different from the real peak positions. To quantitatively characterize peak drift, we define a series of peak drift metrics. Then, we find that Total Peak Drift Metrics (TPDMs) of LG-L and Right-handed Grünwald-Letnikov (RG-L) are with opposite directions. Therefore, we propose a new Grünwald-Letnikov (G-L) operator, central G-L (CG-L), to counteract the peak drifts caused by LG-L and RG-L. CG-L is a centrosymmetric operator that combines LG-L and RG-L together. CG-L is with linearity, positive weights, ∞ sum of weights, and the corresponding proofs are given in this paper. The numerical results of CG-L on simulation data and open dataset are presented. Experiments on the simulation data show that the peak drifts are related to support length of CG-L and fractional order α, and CG-L can achieve accurate locations of signal peaks. Finally, the CG-L are compared with some SOTA methods on two open dataset: PhysioNet and SVC2004 to verify the performance of CG-L in biomedical signal analysis and biometric feature verification. CG-L achieved satisfactory results in various fixed-point signals of the two datasets. Especially when the signal smoothness was high, the peak detection results of CG-L obtained the best evaluation indicators in both the Undetected Peaks (UPs) and Total Peak Drifts (TPDs). On the PhysioNet dataset, CG-L reduced the UPs and TPDs by 60 % compared to the existing best method while on the SVC2004 dataset, in the peak detection of the pen pressure signal (column 7), CG-L improved the UPs and TPDs by 0.63 and 3.86 respectively compared to the existing best method RG-L. In datasets with lower smoothness, although CG-L did not achieve the best processing results, the gap between its indexes and the best method was small, remaining within the acceptable range. Additionally, the indicator values of CG-L were always in the middle of those of RG-L and LG-L, verifying that CG-L can indeed suppress the peak drift of LG-L and RG-L and achieve satisfactory positioning results in various signal forms.