The tracking and reconstructing for sharp spikes of biomedical signals: An exploration for applications of tracking-differentiators

Biomedical signal processing is important for biologists and physicians. Because of the speciality and complexity of biomedical signals, they bring about many substantial troubles for the mathematical methods to deal with. In this paper, we discuss the tracking and reconstructing of sharp spikes of biomedical signals by exploring the new possibility for the applications of tracking-differentiators (TDs), which have been used successfully in many of industrial fields. Firstly, for tracking the observations with the spiking components, we try to find the proper parameters of tracking-differentiators, and to obtain the estimation of the generalized derivatives. Secondly, for the effective reconstruction of the signals with sharp spikes, we employ the Taylor's formula with generalized derivatives. Finally, simulation results on the tracking and reconstruction for the electrocardiogram (ECG) of a pregnant woman have been provided which indicate not only the possibility of applying TDs in the new area but also the effectiveness of the method.