Parabolic Interpolation

Assume a parabola centered at $p$ :

$$y(x) \mathrel{\stackrel{\Delta}{=}}a(x-p)^2+b$$

Evaluating at three adjacent bins about the peak, we have

$$\begin{eqnarray*} y(-1) &=& \alpha \\ y(0) &=& \beta \quad \mbox{(peak)}\\ y(1) &=& \gamma \\ \end{eqnarray*}$$