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Using a length
running-sum filter, let's make
bandpass filters
tuned to center frequencies
|
(10.11) |
Since the bandwidths, as defined, are
, the filter pass-bands
overlap by 50%. A superposition of the bandpass frequency responses
for
is shown in Fig.9.14. Also shown is the
frequency-response sum, which we will show to be exactly
constant and equal to
. This gives our filter bank
the perfect reconstruction property. We can simply add the
outputs of the filters in the filter bank to recreate our input signal
exactly. This is the source of the name Filter-Bank Summation
(FBS).
Figure:
Example filter-bank channel frequency
responses for
|
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