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.^3.7Another application of DFT interpolation is spectral peak estimation, which we take up in Chapter 4; 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.

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Subsections

• Ideal Spectral Interpolation
• Interpolating a DFT
• Zero Padding in the Time Domain
  • Practical Zero Padding
  
  
• Zero-Phase Zero Padding
  • Matlab/Octave fftshift utility

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About the Author: Julius Orion Smith III
Julius Smith's background is in electrical engineering (BS Rice 1975, PhD Stanford 1983). He is presently Professor of Music and Associate Professor (by courtesy) of Electrical Engineering at Stanford's Center for Computer Research in Music and Acoustics (CCRMA), teaching courses and pursuing research related to signal processing applied to music and audio systems. See http://ccrma.stanford.edu/~jos/ for details.