Are there any algorithms that numerically compute the continuos Fourier transform of a given function f? I find plenty of implementations of the discrete Fourier transform, using FFT, but, if I´m not mistaken, DFT is not a discrete approximation of the continuous Fourier transform, but a different, although related, concept.
The fast Fourier transform (FFT) is used to compute numerical approximations to continuous Fourier transforms (CFT). This is not apart from its application or correspondence to Discrete Fourier of course. A numerical approximation of the CFT requires evaluating a large number of integrals, each with a different integrand, since the values of this integral for a large range of the variable are needed. The FFT can be effectively applied to this problem. There are however cases where FFT in brotherhood with DFT are not accurate; e.g. DFT is periodical and spectrum aliasing may occur, other approximations are elaboreted on the spot such as here>>>
Also cross reference Here>>>