This is the sliding-window STFT implementation, where
is
the sliding window ``centered'' at time
, and
is
the kth DTFT bin at time
.
After remodulating the DTFT channel outputs and summing, we obtain
perfect reconstruction of
provided
is Nyquist(N).
For
to be a good anti-aliasinglowpass filter, its
length must exceed the number of bins in the DTFT. (Otherwise, the
best we have is the rectangular window, which gives only -13 dB
stopband rejection.) This means we must use a Portnoff window of some
length larger than the DFT length.
Let the window length be
.
In Lecture 7, it is mentioned that we can still use a length FFT
provided
is replaced by
. I.e., it is
time-aliased down to length
.
With polyphase analysis we obtain this result, along with an
efficient FFT implementation: