DESIGN AND ANALYSIS OF ANALOG FILTERS A Signal ...

314 DESIGN AND ANALYSIS OF ANALOG FILTERS:
Example 9.22
Suppose is a 3rd-order Butterworth lowpass prototype transfer
function, as in Example 9.14. As was determined in Example 9.14,
and . From (9.48):
If and then, from (9.39), and
1104.988, and it follows that and
Time-Domain Response
As noted in Example 9.16, the bandstop transfer function may be represented
as the sum of a lowpass transfer function and a highpass transfer function:
It follows that
and
Since includes an impulse, so will . Since converges to unity
as and converges to zero, converges to unity.
Example 9.23
Suppose the lowpass prototype filter is a 5th-order elliptic filter with
at and This results in
and Suppose a bandstop filter is obtained from this prototype
with and Whereas the poles of the lowpass filter
are as follows:
Chapter 9 Frequency Transformations