We will first define what we mean by the FFT of a function on
points. Suppose that the function is defined on the interval . Then
we take the values
, , and make the usual
FFT transform of them, which give
Now what we call FFT transform of here is the continuous function which is the same as at the points , and which is linear between and .
The command to compute FFTs is the following :
- funct -> fft f1 f2 N
Here f1 is a real or complex function, f2 a complex function with the same precision as f1. This command computes the FFT of f1 on N points and puts the result in f2 (N must be a power of 2).As for the other commands of funct involving functions, f1 and f2 can have any x-ranges.