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 ?