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Spectroscopic Resolution

The ability to distinguish between closely spaced signals in an NMR spectrum, dependent on pulse width, relaxation times, and spectral acquisition parameters.
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The statement of the theorem

Let Δνmin\Delta\nu_{min} be the minimum detectable frequency separation between two signals, ν1\nu_1 and ν2\nu_2. The spectroscopic resolution RR is defined by the ratio of the frequency separation to the linewidth (ΔνL\Delta\nu_{L}) at the signal peak: R=∣ν1−ν2∣ΔνLR = \frac{|\nu_1 - \nu_2|}{\Delta\nu_{L}} The practical resolution is limited by the acquisition time TacqT_{acq} and the Fourier Transform window function W(t)W(t), such that the minimum resolvable separation Δνres\Delta\nu_{res} satisfies Δνres∝1Tacq\Delta\nu_{res} \propto \frac{1}{T_{acq}}. For optimal resolution, the linewidth ΔνL\Delta\nu_{L} must be significantly smaller than the minimum required separation.