Is it possible to use successive parabolic interpolator for doing sub pixel interpolation. In the case of non sub pixel interpolation it is very easy to apply successive parabolic interpolation as you have a continuous function but in the case of subpixel interpolation the data is discrete and it doesnot have function values at floating point $x$. In the successive parabolic interpolator matlab code, shown below as an image
You can see the line highlighed $y =f(x)$. My question is how will you implement successive parabolic interpolation in the case of a function $f$ which has values only on integer indexes.
Thanks