CONTROL OF SMOOTHNESS IN NONLINEAR FILTERING OF GEOMAGNETIC DATA BY AONE-PASS METHOD WITH A PIECEWISE CUBIC POLYNOMIAL

A smoother realized by a one-pass method with a piecewise cubic polyno mial and a modified Powell criterion is termed a PCP filter. Since its action is data-adaptive, the PCP filter is non-linear. Furthermore, t his filter is also non-causal and in practice causes little phase shif t in the output and/or residual data as long as the input data has no dominant components with frequencies within its transition band. An av erage amplitude response of the PCP filter for sinusoidal inputs is de termined numerically for each value of the parameter mu, which appears in the modified Powell criterion and controls the smoothness in outpu t of the filter. An objective criterion for the selection of CL in the practical application of the PCP filter is then obtained from this re sponse. Furthermore, the cut-off frequency of the PCP filter is define d as the first frequency at which the attenuation of the average ampli tude response becomes 3 dB. It is found that the cut-off frequency is a good measure of the smoothness in output of the PCP filter. This fre quency decreases with increasing mu, meaning that the output of the PC P filter becomes smoother and the oscillations with longer periods can be separated as residuals as mu grows large. As CL increases, the ave rage number of sample points between two adjacent knots becomes larger and the computational cost increases for data processing by the PCP f ilter.