and Fig.3.10 shows its frequency response, computed using the
matlab utility myfreqz listed in §7.5.1. (Both
Matlab and Octave have compatible utilities freqz, which
serve the same purpose.) Note that the sampling rate is set to 1, and
the frequency axis goes from 0 Hz all the way to the sampling rate,
which is appropriate for complex filters (as we will soon see). Since
real filters have Hermitian frequency responses (i.e., an
evenamplitude response and oddphase response), they
may be plotted from 0 Hz to half the sampling rate without loss of
information.

Figure 3.9:Impulse response of section 1 of
the example filter.

Figure 3.10:
Frequency response of section 1 of the example filter.

Figure 3.11 shows the impulse response of the complex
one-pole section

and Fig.3.12 shows the corresponding frequency response.

Figure 3.11:
Impulse response of complex
one-pole section 2 of the full partial-fraction-expansion of the
example filter.

Figure 3.12:
Frequency response of complex
one-pole section 2.

The complex-conjugate section,

is of course quite similar, and is shown in Figures 3.13 and 3.14.

Figure 3.13:
Impulse response of complex
one-pole section 3 of the full partial-fraction-expansion of the
example filter.

Figure 3.14:
Frequency response of complex
one-pole section 3.

Figure 3.15 shows the impulse response of the complex one-pole
section

and Fig.3.16 shows its frequency response. Its complex-conjugate
counterpart, , is not shown since it is analogous to
in relation to .

Figure 3.15:
Impulse response of complex
one-pole section 4 of the full partial-fraction-expansion of the
example filter.

Figure 3.16:
Frequency response of complex
one-pole section 4.