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SUMMARY OF FILTER CHARACTERISTICS
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Figure 5-3. Amplitude, Phase, And Time-Delay
Characteristics Of Lowpass
Prototype Filters
5.4.2 Transient Response and Selectivity
Because the use of all pass networks allows the synthesis
of a phase characteristic independent of the amplitude
response, it is of interest to know how phase lineariza-
tion of standard minimum phase filters affects their
transient response. A study of the step response of such
synchronously tuned filter stages as the passive RC net-
works indicates that the rise time of the filter decreases
(Le., responds faster), when its phase characteristic is
linearized. The step response of a single-pole network is
illustrated in Figure 5-5. Because the rise time of cas-
caded filter sections is approximately equal to the
5-5
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Figure 5-4. Impulse And Step Response Of
Lowpass Prototype Filters
18
square root of the sum of the squares of the individual
stage rise times, the results for a single stage can be
extended to mUltiple stages.
An interesting result of the analysis of such filter
characteristics as selectivity and overshoot appears
when percent overshoot (in response to a step input) is
plotted as a function of filter selectivity. Two separate
curves arise which are related to the phase char-
acteristics of the filters. Linear or nearly linear phase
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