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Phase Interpolation at a Peak

Note that only the spectral magnitude is used to find $ p$ 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 §F.4 provides an Octave-compatible version.

If we do expect a phase peak (such as when identifying chirps, as discussed in §10.6), 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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``Spectral Audio Signal Processing'', by Julius O. Smith III, W3K Publishing, 2011, ISBN 978-0-9745607-3-1.
Copyright © 2022-02-28 by Julius O. Smith III
Center for Computer Research in Music and Acoustics (CCRMA),   Stanford University