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Haar Example
Before we leave the case of amplitude-complementary, two-channel,
critically sampled, perfect reconstruction filter banks, let's see
what happens when
is the simplest possible lowpass filter
having unity dc gain, i.e.,
 |
(12.29) |
This case is obtained above by setting
,
, and
. The polyphase components of
are clearly
 |
(12.30) |
Choosing
, and choosing
and
for
aliasing cancellation, the four filters become
Thus, both the analysis and reconstruction filter banks are scalings
of the familiar Haar filters (``sum and difference'' filters
). The frequency responses are
which are plotted in Fig.11.16.
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