# Additive & Spectral: Parabolic Interpolation

## Quadratic Interpolation¶

The detection of local maxima in a spectrum is limited to the DFT support points without further processing. The following example shows this for a 25 Hz sinusoid at a sampling rate of 100 Hz.

Quadratic or parabolic interpolation can be used to estimate the true peak of the sinusoid. using the detected maximum $a$ and its upper and lower frequency bin.

$p = 0.5 (\alpha-\gamma)/(\alpha-2\beta+\gamma)$

$a^* = \beta-1/4(\alpha-\gamma)$