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I understand that there is a sampling frequency and there is a total number of data points. What confuses me is the unit of time. Most of what I see deals with Hz and samples/sec but my samples are done at 15 minute intervals. Suppose I have 4096 data points each at the rate of 15 minutes giving 4096*15=61440 minutes of duration. Then how can I calculate the units of the x axis on the Fourier transform.

Is it fs = Data points/duration = 4096/(15*4096) = 1/15 samples/minute and then each bin corresponds to 1/(4096*15) minutes?

Or fs = Data points/duration = 4096/(15*60*4096) = 1/(15*60) samples/sec with each bin corresponding to 1/(4096*15*60) seconds?

SherylHohman
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Aaron
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  • https://stackoverflow.com/questions/10272644/fast-fourier-transform-results-frequency-axis-scale?rq=1 – Aaron Jan 13 '18 at 21:59
  • I am tempted to mark this as a duplicate of [this post](https://stackoverflow.com/questions/3224823/how-exactly-do-you-compute-the-fast-fourier-transform), but it doesn't *directly* offer the information that you need. However, one of the answers contains [this link](http://blogs.zynaptiq.com/bernsee/dft-a-pied/), which I think gives a very good explanation. – meowgoesthedog Jan 13 '18 at 22:25
  • I feel like there is a general solution to this. If I have N samples at the rate of s sample/t unit time, what are the units of the FFT? Quoted on the linked post: "The FFT gives you linearly spaced frequency bins up to the sampling frequency. This means that the spacing between the bins is (sample frequency) / (number of bins)." so my thoughts say the ith bin has frequency (i/N)/(s/t) so that the last bin is (N/N)*(s/t)=s/t. In this particular case N=4096 and s/t=1/15min so each bin is i*15/4096 minutes. – Aaron Jan 14 '18 at 00:40
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    See [this answer](https://stackoverflow.com/a/4371627/253056) ? – Paul R Jan 14 '18 at 09:44

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