Each channel of an STFT filter bank implements the processing shown in
Fig.9.4. The same processing is shown in the frequency domain
in Fig.9.5. Note that the window transform
is
complex-conjugated because the window
is flipped in the time
domain, i.e.,
when
is real
[264].
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These channels are then arranged in parallel to form a filter
bank, as shown in Fig.9.3. In practice, we need to know under
what conditions the channel filters
will yield perfect
reconstruction when the channel signals are remodulated and summed.
(A sufficient condition for the sliding STFT is that the channel
frequency responses overlap-add to a constant over the unit circle in
the frequency domain.) Furthermore, since the channel signals are
heavily oversampled, particularly when the chosen window
has low
side-lobe levels, we would like to be able to downsample the channel
signals without loss of information. It is indeed possible to
downsample the channel signals while retaining the perfect
reconstruction property, as we will see in §9.8.1.