Spectra Filtering

It is possible to filter time histories using an ideal filter in the frequency domain.

The band pass filter is defined as follows

Figure 1. EQUATION_DISPLAY
Tω1,ω2bp(ω)={1, ω∈[ω1, ω2]0, ω∉[ω1, ω2]}
(536)

with the band stop filter defined as the inverse of Eqn. (536).

Figure 2. EQUATION_DISPLAY
ω1=2πf1
(537)

where f1 is the low cut-off frequency.

Figure 3. EQUATION_DISPLAY
ω2=2πf2
(538)

where f2 is the high cut-off frequency.

The filtering operation is then a product in the frequency domain. A frequency filtered time history h′(x;t) can then be defined as follows

Figure 4. EQUATION_DISPLAY
h′(x;t)=FTt−1[Tω1,ω2bp(ω)g(x;ω)]
(539)