This expression is plotted in Fig. . From this, we anticipate that useful sensitivity increases may be obtained, for example, 44% in the case of 40 s -1 resolution enhancement and 100 ms acquisition time used in the example below (ΓT = 4). However, due to the increasing number of scans at long acquisition times, the noise level will also increase exponentially during the FID, which may lead to a degradation in the quality of the spectrum baseline or the ability to extend the FID through linear prediction. In addition to this sensitivity-optimised sampling scheme (α = 1), we have also identified a second NUWS scheme of interest. In this case, α = 2 (Fig. , red), additional scans are acquired, such that when re-scaled by the apodization function h(t) ≈ e -Γt the noise level remains constant (except for small deviations arising from integer sampling weights). Resolution enhanced FIDs obtained using this scheme are therefore truly free of artefacts. While the sensitivity per unit time of this approach is identical to uniform sampling (α = 0, Eq. 5), the disadvantage of this scheme is the increased acquisition required to accumulate the larger number of scans at later time points. However, the effectively perfect resolution enhancement and uniform noise obtained using this NUWS scheme may be used in conjunction with sparse non-uniform sampling (NUS) and reconstruction to reduce the overall acquisition time. It would also be possible to apply a second apodization function, e.g. cosine or cosine squared, to the resolution-enhanced FID using NUWS methods, in which case the time consuming acquisition of late points would be avoided. However, this approach would prevent extrapolation of the FID using linear prediction or other methods. As this seems counter-productive to the main goal of resolution enhancement, we have not explored this possibility further.