Quick Intro

Quick summary: When we have phase and frequency data to synthesize in SMS, using ``conventional'' cubic phase interpolation can create wild and inaccurate frequency deviations. Normalized parabolic spline phase interpolation can reduce the problem significantly. Recall general sinusoidal model:

$$s(t) = \sum_{m=1}^M A_m(t)sin[\theta_m(t)]$$ (1)

$$\theta_m(t) = \int_0^t \omega_m(\sigma) d\sigma + \eta_m$$ (2)

where $\omega_m$ is the instantaneous frequency, and $\eta_m$ is the phase offset (or detected phase).