Figure 10.12 shows the frequency response of the dc blocker for several values of . The same plots are given over a log-frequency scale in Fig.10.13. The corresponding pole-zero diagrams are shown in Fig.10.14. As approaches , the notch at dc gets narrower and narrower. While this may seem ideal, there is a drawback, as shown in Fig.10.15 for the case of : The impulse response duration increases as . While the ``tail'' of the impulse response lengthens as approaches 1, its initial magnitude decreases. At the limit, , the pole and zero cancel at all frequencies, the impulse response becomes an impulse, and the notch disappears.
Note that the amplitude response in Fig.10.12a and Fig.10.13a exceeds 1 at half the sampling rate. This maximum gain is given by . In applications for which the gain must be bounded by 1 at all frequencies, the dc blocker may be scaled by the inverse of this maximum gain to yield