On the backwards difference filter
On the backwards difference filter
复制标题
关于后向差分滤波器
DOI：
10.1051/0004-6361:20077425
复制
发表时间：
2007
影响因子：
6.5
通讯作者：
J. Ballot
中科院分区：
文献类型：
--
作者：
R. A. García;J. Ballot
上下文。在日震学中，通常通过对时间序列应用高通滤波器来去除不需要的仪器低频趋势。然而，滤波器的选择是非常重要的，因为它可以保持整个频谱的周期信号。同时，这些滤波器不应该在剩余信号中引入任何杂散效应，这将改变傅里叶域中的周期特征。目标。最常用的滤波器之一是所谓的反向差分滤波器，它可以应用于定时采样的时间序列。该滤波器的问题是周期信号的幅值和相位在傅里叶域中被修改，因此，当周期信号的频率降低时，它们的提取幅值会有偏差。本研究报告的目的是给出一个可以应用于功率谱的修正，以克服这个问题。方法。我们正确地推导了后向差分滤波器的传递函数，并展示了如何将其应用于功率谱以校正振幅。对于振幅谱和时间序列，我们还推导了相位的校正。结果。由此产生的功率谱密度中周期信号的幅值从截止频率向下修正为零。
Context. It is usual in helioseismology to remove unwanted instrumental low-frequency trends by applying high-pass filters to the time series. However, the choice of the filter is very important because it can keep the periodic signals throughout the spectrum. At the same time, these filters should not introduce any spurious effects on the remaining signal, which would modify the periodic signatures in the Fourier domain. Aims. One of the most used filters is the so-called backwards difference filter that can be applied when the time series are regularly sampled. The problem of this filter is that the amplitudes and the phases of the periodic signals in the Fourier domain are modified and, therefore, their extracted amplitudes are biased when the frequency of the periodic signals decreases. The objective of this research note is to give a correction that could be applied to the power spectrum to over come this problem. Methods. We properly derive the transfer function of the backwards difference filter and we show how this can be applied to the power spectrum to correct the amplitudes. For the amplitude spectrum and the time series, we also derive a correction for the phase. Results. The amplitudes of the periodic signals in the resultant power spectrum density are corrected from the cut-off frequency down to zero.