Phase Interpolation at a Peak

Note that only the spectral magnitude is used to find in the parabolic interpolation scheme of the previous section. In some applications, a phase interpolation is also desired.

In principle, phase interpolation is independent of magnitude interpolation, and any interpolation method can be used. There is usually no reason to expect a ``phase peak'' at a magnitude peak, so simple linear interpolation may be used to interpolate the unwrapped phase samples (given a sufficiently large zero-padding factor). Matlab has an unwrap function for unwrapping phase, and §G.4 provides an Octave-compatible version.

If we do expect a phase peak (such as when identifying chirps, as discussed in §9.10), then we may use quadratic interpolation separately on the (unwrapped) phase.

Alternatively, the real and imaginary parts can be interpolated separately to yield a complex peak value estimate.

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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.