FirstOrder
Parallel Sections
Figure
3.13 shows the
impulse response of the real one
pole section
and Fig.
3.14 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
even amplitude response and
odd phase response), they
may be plotted from 0 Hz to half the sampling rate without loss of
information.
Figure 3.13:
Impulse response of section 1 of
the example filter.

Figure 3.14:
Frequency response of section 1 of the example filter.

Figure
3.15 shows the impulse response of the
complex
onepole section
and Fig.
3.16 shows the corresponding frequency response.
Figure 3.16:
Frequency response of complex
onepole section 2.

The complexconjugate section,
is of course quite similar, and is shown in Figures
3.17 and
3.18.
Figure 3.17:
Impulse response of complex
onepole section 3 of the full partialfractionexpansion of the
example filter.

Figure 3.18:
Frequency response of complex
onepole section 3.

Figure
3.19 shows the impulse response of the complex onepole
section
and Fig.
3.20 shows its frequency response. Its complexconjugate
counterpart,
, is not shown since it is analogous to
in relation to
.
Figure 3.19:
Impulse response of complex
onepole section 4 of the full partialfractionexpansion of the
example filter.

Figure 3.20:
Frequency response of complex
onepole section 4.

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