# How can I find the Fourier series from discrete data?

I would like to define the function with Fourier series when I just have discrette data. (I don't have a specific function).

I can draw the graph using the data, but I don't have a idea how can I get this function. The plot is a periodic.

I want to obtain a function that will work like a Fourier series expansion. How can I define such a function?

Graph

Horizontal-axis is Time. Vertical-axis is Space.

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Use Fourier[]. It calculates the FFT of the data. Then you can change the magnitude and phase information into a sum of sinusoids. See the answer to this question: How to approximate a given WAV file with trigonometric series? for details on how to do it.

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