# For what range of frequencies is the Fourier function defined?

I am interested in evaluating the discrete Fourier transform for a list of data. The problem is the results given by the function Fourier depends on the length of the data.

For example, if the list of data is simply Table[Sin[20 π t], {t, 0, 10, x}] for different values of x I will obtain the same shape from Fourier when I plot the obtained numbers but the values on the $x$ axis will change.

For $x=0.001$ I will get:

But for $x=0.01$ I get:

• Possible duplicates: 105439, 33149 and 44237 – Lukas Lang Aug 26 '17 at 21:16
• The answer to your question is here. – andre314 Aug 26 '17 at 22:04

You can transform the axes however: The frequency spacing $\delta f$ and total bandwidth $\Delta f$ is defined the following way:
$\delta f=\frac{1}{\Delta t}$
$\Delta f=\frac{1}{\delta t},$
where $\delta t$ is the time domain spacing and $\Delta t$ is the total time span of the data.