Specific Windows
- Recall that the rectangular window transform is
, implying the rectangular window itself is
,
which is obvious.
- The window transform for the Hamming family is
,
implying that Hamming windows are
, which we also knew.
- The rectangular window transform is also
for any integer
, implying that all hop sizes given
by
for
are COLA.
- Because its side lobes are the same width as the sinc side lobes,
the Hamming window transform is also
,for any integer
, implying hop sizes
are good, for
. Thus, the available hop sizes for the Hamming
window family include all of those for the rectangular window
except one (
).
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The Nyquist Property on the Unit Circle
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Inverse DFT and the DFT Filter Bank Sum