Sinusoidal Peak Interpolation

In §2.5, we discussed *ideal* spectral
interpolation (zero-padding in the time domain followed by an FFT).
Since FFTs are efficient, 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*
[271,1]. 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 §5.6.2 below). The QIFFT method can be considered an
*approximate maximum likelihood method* for spectral peak
estimation, as we will see.

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Center for Computer Research in Music and Acoustics (CCRMA), Stanford University