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For the helix derivative filter, the response is nearly a linear function
of and does not have the ``cut-off
frequency''. The main feature here is the zero-frequency response.
Figure 8 shows the zero-frequency response *R*_{0}
as the function of filter length when . *n*_{a} is the half
size of the filter. I find that *R*_{0} decreases as *n*_{a} increases
and . The empirical relationship between *R*_{0}
and *n*_{a} is
| |
(7) |

*R*_{0} is the sum of the helix filter's coefficients, so when ,according to Equation (3), the
zero-frequency response is
| |
(8) |

**drv-r0f-ar0
**

Figure 8 The zero-frequency response of helix
derivative filter when . The approximate zero-frequency response
is .

The zero-frequency response of the enhanced helix derivative filter is
controlled
by both *n*_{a} and , I can compute the approximate value of *R*_{0}
using Equation (8).

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Stanford Exploration Project

4/20/1999