Fourier transforms

By Fourier transform of a function $f$ we mean the function $Tf(t)$ defined in 2.2. This is not the same as a single FFT, and the computation requires several FFTs, as explained in 2.2. To define the Fourier transform of a function (real or complex), the command def_four is used (cf 3.4). For example, if f1 is a real function, the instruction

def_four tr f1 1024

computes the parameters associated to the Fourier transform of the function f1, which are stored in the object tr. The FFT's are made on 1024 points. Given a complex function C the instruction

trans_four tr C

will then compute the Fourier transform of f1 at the points of the x-range of C and put the result in C. It is of course possible to use several times the object tr (for other C).

See 3.4 for more details on these commands.