Parabolic Peak Interpolation

Python. I applied interpolation technique to the spectral peak based on fundamental frequency after FFT was taken. It is basically to find a better estimation of the peak by using the max spectral bin (of fundamental), its left and right bins with parabola equation. In other words, it is to fit a parabola onto those frequency bins.

I used a strings fragment to test.  Sometimes, the second and/or third harmonic might be louder than the fundamental. For example, some of trumpet or guitar string effects. That’s why, I implemented the fundamental frequency finding stage at first. In this audio file, the fundamental is around 1180.3144 Hz. After the interpolation implementation, it shows 1180.3156 Hz. However, this implementation is only for a pedal note (if we use an instrument sound, like I did).  As a conclusion, this implementation for the idea is very weak. It will be good to apply this interpolation technique for different manipulations.


[1] Mathematics of the Discrete Fourier Transform, Julius O. Smith III

[2] Improving FFT Frequency Measurement Resolution by Parabolic and Gaussian Interpolation, M. Gasior, J.L. Gonzalez

[3] Is It Possible for a Harmonic Louder than the Fundamental Frequency