Below are discrete samples { t1, f(t1) }, { t2, f(t2) }, ... ,{ tn, f(tn) } using Mathematica syntax.
{{7.0,0.354887404925574},{7.3,0.4003399403324751}, {7.6,0.5849632195845474},{7.9,0.8785638270289906}, {8.2,1.235637591701261},{8.5,1.6025351028031707}, {8.8,1.925797159944803},{9.1,2.160385431197419}, {9.4,2.276553177467603},{9.7,2.2643104784151262}, {10.0,2.1348061618705962},{10.3,1.9184189440030162}, {10.6,1.6598520161702173},{10.9,1.4109826017641867}, {11.2,1.2225616685298717},{11.5,1.1360369427321668}}
Now I plot the samples.
The samples are from a bandlimited function f(t) that I defined. However, suppose they are discrete samples of an unkown function, but we know the Fourier spectrum of f(t) is band-limited to frequencies 0.25 Hz and below. What would be a good method to use for interpolating between the samples and extrapolate beyond the samples? Here I mentioned that polynomial interpolation has less error than cubic spline interpolation in a case like this? What method would have even less approximation error in a case like this?