As a familiar special case, set
![]() |
(12.66) |
![]() |
(12.67) |
![]() |
(12.68) |
The channel analysis and synthesis filters are, respectively,
where
, and
![]() |
(12.69) |
Looking again at the polyphase representation of the
-channel
filter bank with hop size
,
,
,
dividing
, we have the system shown in Fig.11.25.
Following the same analysis as in §11.4.1 leads to the following
conclusion:
Our analysis showed that the STFT using a rectangular window is
a perfect reconstruction filter bank for all
integer hop sizes in the set
.
The same type of analysis can be applied to the STFT using the other
windows we've studied, including Portnoff windows.