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Ideal Spectral Interpolation
Ideally, the spectrum of any signal
at any frequency
is obtained by projecting the signal
onto the
zerophase, unitamplitude, complex sinusoid at frequency
[264]:

(3.43) 
where
Thus, for signals in the DTFT domain which are time limited to
,
we obtain

(3.44) 
This can be thought of as a zerocentered DFT evaluated at
instead of
for some
. It arises naturally from taking the DTFT of a
finitelength signal. Such timelimited signals may be said to have
``finite support'' [175].
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