Sinusoidal Peak Interpolation

In §2.5, we discussed ideal spectral interpolation (zero-padding in the time domain followed by an FFT). Since the FFT is an efficient algorithm, this is an efficient interpolation method. However, in audio spectral modeling, there is usually a limit on the needed accuracy due to the limitations of audio perception. As a result, a ``perceptually ideal'' spectral interpolation method that is even more efficient is to zero-pad by some small factor (usually less than 5), followed by quadratic interpolation of the spectral magnitude. We call this the quadratically interpolated FFT (QIFFT) method [255,1]. The QIFFT method is usually more efficient than the equivalent degree of ideal interpolation, for a given level of perceptual error tolerance (specific guidelines are given in §4.7.2 below). The QIFFT method can be considered an approximate maximum likelihood method for spectral peak estimation, as we will see.

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Subsections

• Quadratic Interpolation of Spectral Peaks
  • Phase Interpolation at a Peak
  • Matlab for Parabolic Peak Interpolation
  
  
• Bias of Parabolic Peak Interpolation

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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.