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I have data from the changes in apparent brightness of a star, and these data points form a periodic trigonometric relationship. However, these data points are unevenly spaced, so I cannot use the regular DFT algorithm on them. Is there a method to convert this signal into regularly spaced data? I have been trying to find a method but I cannot find anything suitable.

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    See [density estimation](https://en.wikipedia.org/wiki/Density_estimation) and [kernel density estimation](https://en.wikipedia.org/wiki/Kernel_density_estimation) which is no more than a modified convolution : $g(n) = \sum_m f(m) h(n-m)$ becomes $g(n) = \frac{\sum_i y_i h(n-x_i)}{\sum_i h(n-x_i)}$ – 2017-02-16
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    Thank you for your response! As far as I can see from these pages, the density estimation finds the curve as a probability estimation; this is something beyond what is currently required of me. I just need a formula which extracts evenly spaced data points from my massive data set. Is there a way of doing this, preferably in Excel? Once again, thank you for your previous response! – 2017-02-18
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    Did you try programming my last formula ? It needs 3 formulas and 3 columns in excel – 2017-02-18
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    I attempted to do so, but I couldn't figure out the variables. I understand that y_i and x_i are data points, but how could I find h? The Gaussian function for the bandwidth requires me to calculate the standard deviation, something that I cannot do since my data is periodic. Do you have any ideas as to how I could approach this? I am also a little lost as to how I could then connect this the DFT. I would be extremely grateful if you could help me out with this issue! – 2017-02-20
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    Yes take any [window function](https://en.wikipedia.org/wiki/Window_function#Generalized_Hamming_windows) – 2017-02-20
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    Thank you for your suggestion! So If I understand correctly, the function h is the window function, but what is the the value of n? Is it an arbitrary value dependent on how small I want the intervals to be? – 2017-02-22
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    Why don't you try with a toy dataset, say 5 or 6 points ? – 2017-02-22
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    This is what I am trying to do, but my question was more regarding what the actual values represent. From my understanding, in the kernel density estimation, is the h(n-x) the window function? Also what does this value of n represent? – 2017-02-22
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    You really need to try the simple formula I wrote $g(n) = \frac{\sum_i y_i h(n-x_i)}{\sum_i h(n-x_i)}$. Your data $(x_i,y_i)$ is a set of isolated peaks, around each peak : put the window function $h(x)$, sum everything, at the end apply a weight $w(n) = \frac{1}{\sum_i h(n-x_i)}$ depending on the "density of peaks" around the $n$th sample – 2017-02-22
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    [1]: https://i.stack.imgur.com/BLDHG.png – 2017-02-22
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    I obtained this graph after applying the Hanning window function. Would I now apply the DFT to this? – 2017-02-22
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    What was the input data ? – 2017-02-22
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    Time Absolute mag. 42112.42 10.311 42112.46 10.32 42112.48 10.4 42113.42 10.952 42113.45 10.918 42113.47 10.927 42114.45 11.549 42114.47 11.549 – 2017-02-22
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    I attached a small part of the data set above. I was working from 67 data points in total. Just to make things explicit, the time is in Julian calendar date, and the absolute magnitude is how big the star appears to be. These are a finite number of measurements as taken from a telescope. – 2017-02-22
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    Come on... I don't care of your data, I'm asking if it fits with what you got... And your input data is of the form $(x_i,y_i)$ ... – 2017-02-22
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    It works but I wanted to generate an equation that would predict the curve. In other words, I need to find a function that generates an output when given a single x input. This function needs to be fitted to a set of data points. This is why I was trying to use the DFT to obtain an equation that could predict the curve at multiple points. The function that you have shown me, while useful, requires both the x and y values as input. The function that I am trying to obtain requires only the x input and predicts a y value on the curve. – 2017-02-22

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