Optimal digital filtering requires a different cut-off frequency strategy for the determination of the higher derivatives
Optimal digital filtering requires a different cut-off frequency strategy for the determination of the higher derivatives
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DOI：
10.1016/s0021-9290(97)00043-2
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发表时间：
1997-08-01
影响因子：
2.4
通讯作者：
Baltzopoulos, V
中科院分区：
文献类型：
--
作者：
Giakas, G;Baltzopoulos, V
本研究研究了四种不同的滤波和微分序列，用于在使用二阶巴特沃斯滤波器和一阶有限差分时从噪声位移数据计算高阶导数。这些是：（1）常规序列（即过滤位移数据然后微分）； (2)根据最佳0阶、1阶和2阶导数以不同的截止频率对位移进行滤波； （3）双重滤波和微分（仅用于加速）； (4) 微分，然后在每个导数域中分别进行过滤，即将噪声较高的导数视为单独的信号。将计算机生成的 30 个时域级别和 30 个频域级别的纯噪声信号叠加到 24 个参考信号上，模拟步行时附着在下肢节段的 8 个标记的内侧-外侧、前后和垂直位移模式。位移、速度和加速度数据的最佳截止频率被计算为在每个导数域中的参考数据和噪声数据之间产生最小均方根误差的频率。结果表明，必须重新考虑和修改传统策略，因为第二种策略获得了最佳结果。加速度的最佳截止频率低于速度所需的频率，而速度所需的频率又低于位移的最佳截止频率。本研究的结果将有助于现有和未来基于数字滤波的自动滤波技术的发展。 (C) 1997 爱思唯尔科学有限公司。
The present study investigated four different filtering and differentiation sequences for the calculation of the higher derivatives from noisy displacement data when using a second-order Butterworth filter and first-order finite differences. These were: (1) the conventional sequence (i.e. filtering the displacement data and then differentiating); (2) filtering the displacement with a different cut-off frequency depending upon optimal 0th, 1st and 2nd derivatives; (3) double filtering and differentiation (only for acceleration); and (4) differentiation and then filtering separately in each derivative domain, i.e. treating the noisy higher derivatives as individual signals. Thirty levels of time domain and 30 levels of frequency domain computer-generated pure noise signals, were superimposed oil 24 reference signals which simulated the medial-lateral, anterior-posterior and vertical displacement patterns of eight markers attached to the lower extremity segments during walking. The optimum cut-off frequency for the displacement, velocity and acceleration data was calculated as the one that produced the minimum root mean square error between the reference and noisy data in each derivative domain. The results indicated that the conventional strategy has to be reconsidered and modified, as the best results were obtained by the second strategy. The optimum cut-off frequency for acceleration was lower than that required for the velocity which in turn was lower than the optimum cut-off frequency for displacement. The findings of the present study will contribute to the development of existing and future automatic filtering techniques based on digital filtering. (C) 1997 Elsevier Science Ltd.