Parallel, Real, Second-Order Sections

Figure 3.17 shows the impulse response of the real two-pole section

$$H^r_2(z) \isdef H_2(z) + H_3(z) = \frac{0.3788 -0.2413z^{-1}}{1 - 1.4562z^{-1}+ 0.8100z^{-2}},$$

and Fig.3.18 shows its frequency response. The frequency axis unnecessarily extends all the way to the sampling rate ($f_s=1$).

Figure 3.17: Impulse response of real two-pole section $H^r_2(z)$ of the real partial-fraction-expansion of the example filter.

Figure 3.18: Frequency response of real two-pole section $H^r_2(z)$.

Finally, Fig.3.19 gives the impulse response of the real two-pole section

$$H^r_3(z) \isdef H_4(z) + H_5(z) = \frac{0.4555 + 0.0922z^{-1}}{1 + 0.5562z^{-1}+ 0.8100z^{-2}},$$

and Fig.3.20 its frequency response.

Figure 3.19: Impulse response of real two-pole section $H^r_3(z)$ of the real partial-fraction-expansion of the example filter.

Figure 3.20: Frequency response of real two-pole section $H^r_3(z)$.