Determination of the exact value of the regularization parameter in smoothness priors method with respect to the corresponding cut-off frequencies for designing filters

A filter is an electrical network or software that alters the amplitude and/or phase characteristics of a signal with respect to frequency. Recently, a new detrending method has been presented to remove the slow nonstationary trends from biomedical signals, which is equivalent to high-pass filtering that removes very low frequency components from the given signal. Although many recently published papers, related to the analysis of biomedical signals like the heart rate variability signal, have used the smoothness priors detrending method, there is no given exact relationship between the regularization parameter and the cut-off frequency of the corresponding high pass filter. In this study, we present this relationship by an empirical formula which would allow the researchers to calculate the parameter from the desired frequency response for not only a high pass filter but also other filter types.