  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. 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. 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. The amplitudes of the periodic signals in the
resultant power spectrum density are corrected from the cut-off frequency down
to zero.
