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or
From the DFT case, we know this is true when
and
are each
complex sequences of length
, in which case
and
are length
. Thus,
where we have chosen to keep frequency samples
in terms of
the original frequency axis prior to downsampling, i.e.,
for both
and
. This choice allows us to easily take
the limit as
by simply replacing
by
:
Replacing
by
and converting to
-transform
notation
instead of Fourier transform notation
,
with
, yields the final result.
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Download JFB.pdf
Download JFB_2up.pdf
Download JFB_4up.pdf
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