I have a signal that I would like to perform a Fourier transform on in Python. Specifically, I have four lists describing the signal: a series of time values t, the amplitude of the signal at each time A(t), the instant frequency at each time f(t), and the phase at each time, omega(t). My question is, how can I perform a Fourier transform on this data in Python to get A(f)? I know numpy and scipy have fft functions, but these take as input the raw data of the signal, which I do not have as such.
Note, A(t) and f(t) are not constant with t; A(f) would be its frequency spectrum/amplitude spectral density.