Bilinear Transform derivative
A reference for the theory of the bi-linear method of filter design can be found
in Gold and Rader (5). Mathematically, the Z-transform for the
derivative is given as
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(49) |
where
is the sample interval,
, is the input signal
Z-transform, and
is the output (ie. derivative of X), Z-transform.
Feedback is used in an auto-regressive-moving-average (ARMA) operator to realize
this equation in the time domain:
 |
(50) |
Figure 63:
Plot of file bdifwavV.seg, differentiated wavV.seg
simulates what a velocity geophone might see. Only near offset signals are shown
for easier comparison.
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