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I have a feeling this question has a very simple answer, yet I cannot find it anywhere online.

Let's say that I have a data set that represents and evenly-spaced sample of a function, taken uniformly over the interval [tex] (a,b) \qquad a,b \in \mathbb{Z} [/tex]

I perform a discrete fourier transform to map this function within the frequency domain. In the computer program I am using, I get a list of values, but not the frequencies at which they occur. What is the appropriate interval to scale these values over, such that the position along the horizontal axis will give me the correct frequency of the mode. I would like to be able to read off resonant modes from peaks on the graph.

For example, let's say I use Mathematica to do a DFT on 100 evenly spaced samples of Sin[x] over the range [tex][0, 3\pi][/tex]. My output will be just a list of values, but I will not know where those values out to occur (ie, I need to know how the bounds of the domain of the input function transform)

Thanks for any help.

Let's say that I have a data set that represents and evenly-spaced sample of a function, taken uniformly over the interval [tex] (a,b) \qquad a,b \in \mathbb{Z} [/tex]

I perform a discrete fourier transform to map this function within the frequency domain. In the computer program I am using, I get a list of values, but not the frequencies at which they occur. What is the appropriate interval to scale these values over, such that the position along the horizontal axis will give me the correct frequency of the mode. I would like to be able to read off resonant modes from peaks on the graph.

For example, let's say I use Mathematica to do a DFT on 100 evenly spaced samples of Sin[x] over the range [tex][0, 3\pi][/tex]. My output will be just a list of values, but I will not know where those values out to occur (ie, I need to know how the bounds of the domain of the input function transform)

Thanks for any help.

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