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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.

77topaz
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  • What is this *f(t)* data you have? How is it determined? The instant frequency alone does not characterize the signal, you need the phase as well. Is *f(t)* complex-valued? And does *A(t)* not describe the full signal? Or is it the envelope of the signal? – Cris Luengo Sep 10 '20 at 05:31
  • I have the instant frequency as well as the phase (should have clarified that in the OP); f(t) is real-valued. A(t) is the envelope. – 77topaz Sep 10 '20 at 06:07

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