= Fourier frequency resolution
{c}
{title2=$\Delta f=1/T_{\mathrm{obs}}$}
For $N$ equally spaced samples at <sampling rate> $f_s$, the <discrete Fourier transform> has <frequency> bins spaced by $f_s/N=1/T_{\mathrm{obs}}$. A rectangular observation window broadens a sinusoid into a <sinc function> profile whose nearest zeros are $1/T_{\mathrm{obs}}$ from its central <frequency>. This sets a conventional scale for distinguishing nearby spectral components. It is not a universal lower bound on the uncertainty of <frequency estimation> for an isolated tone: a specified signal model and noise level can allow precision finer than the bin spacing. Padding with zeros interpolates the spectral display without increasing the observation duration.
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