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360 Other Direct Filter Design Methods
The integers in the element data refer to the trap pOSItions. Note that they
alternate from end to end in the filter so that only positive element values are
obtained, as mentioned in connection with the permutation algorithm (Section
9.3.3). The precision test number is the relative discrepancy between the values
of the central element calculated from either port.
9.3.5. Antimetric Type-a, Type-b, and Type-c Filter Program Antimetric
filters have even-degree N, and the number of traps is M~N/2. Figure 9.22
shows the lowpass and highpass midshunt and midseries topologies, respectively,
that Program B9-3 (Appendix B) designs.
Typical outputs for antimetric type-a, type-b, and type-c filters are shown
in Figures 9.23, 9.24, and 9.25, respectively. Observe that the input data
include the "half degree"; this is also the number of traps. Frequencies are in
radians. The initial output from U through the last RF variable consists of
data concerning the natural frequencies; interested readers are referred to
Amstutz (1978). The trap sequence alternates from one end of the network to
the other, as seen by comparing the integers in the output data to Figure 9.22.
The first precision test number is the relative discrepancy between the
L, L, L, L, L,
'1 '1 1
l
tc, fc, t c, .lc
R
c
T'
0
F, F, F, F,
(L 2
) (L 4
) (LJl (L 1
)
--1_IC
_,_I
1 IC,)
F, F. F, F,
IR)
T~
Figure 9.22. Lowpass, midshunt and highpass. midseries topologies computed by Program 89-3
for antimetric type-a, type-b, and type-c filters. [From Amstutz. P.. IEEE Trans. Circuits Syst.,
Vol. CAS-25, No. 12, p. 1009, December 1978. © 1978 IEEE.]