FREQUENCY RESPONSE, FILTERS, AND RESONANCE
and stop others (the stop-band). Ideally, in the pass-band, Hð j!Þ ¼ 1 and in the stop-band, Hð j!Þ ¼ 0. We therefore recognize the following classes of ﬁlters: low-pass [Fig. 12-15(a)], high-pass [Fig. 12-15(b)], bandpass [Fig. 12-15(c)], and bandstop [Fig. 12-15(d)]. Ideal ﬁlters are not physically realizable, but we can design and build practical ﬁlters as close to the ideal one as desired. The closer to the ideal characteristic, the more complex the circuit of a practical ﬁlter will be. The RC or RL circuits of Section 12.2 are ﬁrst-order ﬁlters. They are far from ideal ﬁlters. As illustrated in the following example, the frequency response can approach that of the ideal ﬁlters if we increase the order of the ﬁlter.