Digital Filtering により得られる波形の精度に関する数値実験

抄録

Comparison between strictly rectangular filters and approximate ones are discussed in the time domain using theoretical seismograms calculated for a Gutenberg-Bullen A′ earth model. Filtering is accomplished by a process of convolution. Main results are as follows.
Digital filtering is, on the whole, carried out successfully even in dealing with complicated disturbances consisting of many spectral components of varying strength. The deviation of output from approximate filters from ideally filtered output depends largely on relative spectral amplitude of input data near the cut-off frequencies of a designed filter and little on the band width. It is possible to estimate the deviation without knowledge of ideally filtered output when some conditions are satisfied, that is, (f_n)_min·(t₂-t₁)>>1, (f_i-f_j)_min·(t₂-t₁)>>1, where f_n is the eigen-frequency, t₂-t₁ the time interval employed in filtering and f_i>f_j.
Concerning a problem of aliasing, Fourier amplitude spectrum and filtered results of inadequately digitized data are given.