Spectral Interpolation

The need for spectral interpolation comes up in many situations. For
example, we always use the DFT in practice, while conceptually we
often prefer the DTFT. For *time-limited signals*, that is,
signals which are zero outside some finite range, the DTFT can be
computed from the DFT via *spectral interpolation*. Conversely,
the DTFT of a time-limited signal can be *sampled* to obtain its
DFT.^{3.7}Another application of DFT interpolation is *spectral peak
estimation*, which we take up in Chapter 5; in this
situation, we start with a *sampled* spectral peak from a DFT,
and we use interpolation to estimate the frequency of the peak more
accurately than what we get by rounding to the nearest DFT bin
frequency.

The following sections describe the theoretical and practical details of ideal spectral interpolation.

- Ideal Spectral Interpolation
- Interpolating a DFT
- Zero Padding in the Time Domain
- Practical Zero Padding
- Zero-Padding to the Next Higher Power of 2
- Zero-Padding for Interpolating Spectral Displays
- Zero-Padding for Interpolating Spectral Peaks

- Zero-Phase Zero Padding

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