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 §F.4 provides an Octave-compatible version.
Alternatively, the real and imaginary parts can be interpolated separately to yield a complex peak value estimate.
Matlab for Parabolic Peak Interpolation
One Sine and One Cosine ``Phase Quadrature'' Case