# Fourier transform by FFT : by using cubic splines to interpolate between data points, do we change the frequency content of the Fourier transform?

I have a data file with some points equally spaced. These represent some function. I have to calculate the Fourier transform of this set of points. The thing is, I'm tempted to take a cubic spline of these data points to calculate the Fourier transform by FFT (actually I'm more than tempted, since I have done it already). But I'm wondering, isn't this cubic spline adding noise to the Fourier transform ?

I have tested this idea on some particular analytical function. I calculated the FFT in different ways (with and without spline) and compared it to the analytical Fourier transform and it actually added some contribution at large frequency. But is this always the case ?

Is there some work that has already been done on this ?

• After you calculate the cubic spline I assume that you also sampled those to get more data between the original data and calculated the FFT? – fibonatic Sep 13 '16 at 14:07
• @fibonatic Yes, indeed :) – mwoua Sep 13 '16 at 15:40