Passive, active, and digital filters (3ed., CRC, 2009) - tiera.ru

23-14 Passive, Active, and Digital Filtersω 2ω 22ω 21ω 11ω 1ω 1(a)ω 12ω 12 0ω 2ω 21ω 11(c)ω 2ω 2210.80.60.4ω 1 0.210.50–0.5 –0.5–1 –100.51(b)(d)FIGURE 23.10 Amplitude response for the filter of Example 23.1: (a) specified response; (b) response of the 2Dlow-pass filter; (c) response of the 2D high-pass filter; (d) 3D plot of the amplitude response of a real 2D IIR filter.23.3.2 Design of Half-Plane Symmetric FiltersA 2-D filter is said to be half-plane symmetric if its amplitude response satisfies H(z1 , z 2 ) ¼ Hz1 *, z 2* ð Þ (23:33)butjH(z 1 , z 2 ) j 6¼ jHz ð *, 1 z 2 Þj 6¼ jHz ð 1 , z*2 Þj (23:34)that is, half-plane symmetry does not imply quadrantal symmetry.The design of those filters can be accomplished by cascading two quadrant pass filters derivedpreviously in Section 23.2.2.2 with quadrantally symmetric filters, as is demonstrated in Example 23.2.Example 23.2Design a 2-D half-plane symmetric filter whose passband is defined in Figure 23.11a.Solution1. Follow the steps 1 to 3 in Example 23.1 to construct a 2-D bandpass filter with the passband beingthe area between two overlapping rectangles, as shown in Figure 23.10a.