Application of myriad filtering in real-time trend detection algorithms

Detecting nonlinear (with sharp changes) signal trends in pseudo-real-time is necessary in many digital signal-processing applications. In biomedical signal processing, it is essential to eliminate abrupt signal distortions caused by the patientʼs movements. Linear filtering can smooth the edges and other discontinuity transitions in a signal, which is a drawback. Nonlinear robust filters, as median-type algorithms, successfully process such signals. In particular, median hybrid filters with finite impulse response (FIR) are efficient for processing edges. The paper discusses the «in-place growing» FIR-median hybrid filter, successfully applied for nonlinear trend detection. The paper proposes modifying this filter by replacing determining a sample median with a sample myriad and adding weight (replications) to certain window elements. These modifications have successfully improved the filter's performance. The developed computer program implemented the considered nonlinear filtering algorithms and calculated statistical estimates of their efficiency using the mean square error (MSE) criterion for modelled test signals that imitate a nonlinear trend under the influence of additive Gaussian noise with variance at differing levels. The analysis of the filter output signals and plots illustrating the statistical estimates of the filtering efficiency according to the MSE criterion demonstrates the improvements achieved due to the proposed modification. Examples of processing biomedical signals show the high quality of suppression fluctuations and abrupt changes preservation in a signal.