### Interpolating a DFT

Starting with a sampled spectrum , , typically obtained from a DFT, we can interpolate by taking the DTFT of the IDFT which is*not*periodically extended, but instead

*zero-padded*[264]:

^{3.8}

*ideal*,

*time-limited interpolation*in the frequency domain using the aliased sinc function as an

*interpolation kernel*. We can almost rewrite the last line above as , but such an expression would normally be defined only for , where is some integer, since is discrete while is continuous. Figure F.1 lists a matlab function for performing ideal spectral interpolation directly in the frequency domain. Such an approach is normally only used when

*non-uniform*sampling of the frequency axis is needed. For uniform spectral upsampling, it is more typical to take an inverse FFT, zero pad, then a longer FFT, as discussed further in the next section.

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Zero Padding in the Time Domain

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Ideal Spectral Interpolation