### Ideal Spectral Interpolation

Ideally, the spectrum of any signal
at any frequency
is obtained by *projecting* the signal
onto the
zero-phase, unit-amplitude, 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 zero-centered DFT evaluated at instead of for some . It arises naturally from taking the DTFT of a finite-length signal. Such time-limited signals may be said to have ``finite support'' [175].

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Interpolating a DFT

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Spectral Roll-Off