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Given a time-and-space-dependent signal like the following:

$$F(z,t) = \dfrac{a_0}{2} + \sum_{n = 1}^{\infty} [a_n \cos(k_n z + w_n t + \phi_n)].$$

How do I extract both the temporal and spatial frequency components of this signal, i.e., $(a_n, k_n, w_n, \phi_n)$?

I am not sure what sort of Fourier transform could apply in this case. If someone can also suggest a python package that helps to do this task, that will be appreciated.

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  • $\begingroup$ As it is written, your question is hard to understand. If you have such an equation, can't you just read off the frequency components? $\endgroup$ Nov 22, 2019 at 21:38
  • $\begingroup$ @AnonSubmitter85 Hi, I have the data for it not the equation that produces the data. $\endgroup$
    – Alejandro
    Nov 25, 2019 at 8:54
  • $\begingroup$ What is the format of your data? Is it a 2-D array with space in one dimension and time in the other? The more information you can provide and the more specific you can be, the more likely you are to get help. $\endgroup$ Nov 25, 2019 at 16:28
  • $\begingroup$ @AnonSubmitter85 Exactly, it is a 2-D array where one dimension represents the time(t) and one the position(z). I corrected the formula in the question to be f(z,t) $\endgroup$
    – Alejandro
    Nov 25, 2019 at 19:00
  • $\begingroup$ Taking the DFT in the time dimension will yield the temporal frequency and taking the DFT in the spatial dimension will yield the spatial frequency. $\endgroup$ Dec 6, 2019 at 21:21

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