A study of Savitzky-Golay filters for derivatives in primary shock calibration

Abstract

This manuscript reports the result of an investigation into two types of digital filters for numerical differentiation of the displacement signal in the case of primary shock calibration of accelerometers. The first is a difference method with a 4<sup>th</sup>-order Butterworth low-pass (4<sup>th</sup> BW) filter; the other is a Savitzky-Golay (S-G) filter, which applies a moving polynomial approximation. The computational comparison was applied to low and high amplitude shocks using known excitation functions. Each sum of residuals was compared for the optimized conditions of the 4<sup>th</sup> BW and S-G filters. The results of computer simulation indicated that the S-G filters exhibited better performance for the derivatives than the 4<sup>th</sup> BW filters. In addition, an analytical comparison using experimental vibration data also indicated that the S-G filters exhibited better derivative characteristics than the 4<sup>th</sup> BW filters.<br />

A two-DOF model-based input prediction for high-shock accelerometer calibration

“…The signals u LDV1,2 (t i ) of both LDVs are subsequently demodulated by the well-established arctangents method. The transformation from the original optical phase information to the sought acceleration a LVD1,2 is accomplished by using a double differentiating Savitzky-Golay filter (SG) and a decimation to a rate of 10 MS s −1 which is consistent with the rate of the acquired accelerometer measuring chain voltage [7]. The bandwidth of the acceleration signal is, at the same time, limited to below 130 kHz.…”