5.4.1 Because any acceleration time-history is
composed of many sinusoids of different frequencies and amplitudes,
it often contains sinusoids with frequencies that are of little importance
or insignificant. These unwanted or unimportant frequencies can be
removed from the time-history. This process is called data filtering.
Filtering is performed for many reasons. Perhaps frequencies above
some value are not significant for some reason. This is the case with
occupant acceleration forces in free-fall lifeboats. Frequencies above
20 hz do not have a significant affect on the body and can be removed
from acceleration force time-histories when evaluating occupant response.
At other times electrical interference can cause frequencies of some
magnitude to be introduced into the data; these should be removed
before the data is evaluated.
5.4.2 In general, there are four types of filters:
lowpass, highpass, bandpass, and notch. When using a lowpass filter,
only those frequencies below a certain frequency are retained. The
opposite is true for a highpass filter; only those frequencies above
a certain frequency are retained. When using a notch filter, all frequencies
except those within a specified range are retained; those frequencies
within the specified range are discarded. A bandpass filter, on the
other hand, is used to remove frequencies with a specified range and
retain all others. After the appropriate frequencies have been discarded,
the filtered time-history can be computed using Equation 5.3 and only
those frequencies that were retained.
5.4.3 This concept of filtering can be represented
graphically by again considering the data presented in Figure 5.3.
Let us assume that we measured the data represented by the combined
curve shown in that figure. Let us further assume that we want to
filter this measured data with a 10 hz lowpass filter; any frequency
greater than 10 hz will be removed from the data. The amplitude of
the filtered time-history can be computed from:
Notice that Equation 5.5 is the same as Equation
5.2 after deleting the term involving the 20 hz frequency. The filtered
curve represented by Equation 5.5 is shown in Figure 5.8. It is superimposed
over the combined curve from Figure 5.3 so that the effects of filtering
can be observed. As can be seen, the filtered curve is much smoother
than the unfiltered curve.
This is characteristic of data
that has been filtered with a lowpass filter.
Figure 5.8 Filtered Time-History
5.4.4 Acceleration force time-histories can be
filtered using either analog or digital filters. Digital filters include
Fourier, Butterworth, and Chebyshev filter functions. In addition,
data can be filtered in either the time domain or in the frequency
domain. A complete discussion of filter functions and procedures to
use them is well beyond the scope of this Circular. Interested readers
are referred to Press, et. al. (1989) and Ziemer, et. al. (1983) for
a more extensive discussion about filtering measured data.