Figure 9 is the zero-frequency response and
cut-off
frequency of a 100-point low-cut filter for different k0 when .I find that cut-off frequency f0 is almost the same as k0.
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(9) |
The difference of the cut-off frequencies at various azimuths is very small when k0 > 0.1 and can be ignored. For k0 < 0.1, the difference is obvious.
In Figure 9, the zero-frequency
response decreases as k0 increases.
For and k0>0.03,
, the empirical
relationship between the
zero-frequency response of 100-point and k0 is
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(10) |
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Figure 10 shows the effect of na on helix low-cut
filter when k0 = 0.3 and .For small na, the numerical anisotropy is very strong. Although the
mean value of the cut-off frequency remains the same, the azimuthal
difference becomes larger when na becomes smaller.
The zero-frequency response increases
as na decreases, and when k0 =0.3 and
, the empirical
expression is
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(11) |
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directly controls the zero-frequency response and affects the
cut-off frequency as well.
Figure 11 shows the cut-off frequency of the
100-point helix low-cut filter as the function of k0 when
and
.For larger
, the numerical anisotropy is stronger, especially
when k0 is small. Compared with Figure 9, the cut-off
frequency at small k0 increases slightly with
.
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Based on the proceeding analysis, I can derive the composed effects of the adjustable parameters on the helix low-cut filter.
The cut-off frequency is mainly governed by k0.
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(12) |
The zero-frequency response R0 is under the direct control of and
influenced by na and k0.
If I assume that the influences of na
and k0 are independent, the empirical expression of R0 would be
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(13) |
Equations (8), (12) and (13) describe the quantitative effects of the helix derivative / low-cut filter's adjustable parameters. These empirical formulas make it quantitative for us to choose the adjustable parameters of the helix filter in practice.