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Non-uniform weighted sampling (NUWS) is a simple method for multi-dimensional NMR spectroscopy in which window functions are applied during acquisition by sampling varying numbers of scans across indirect dimensions. While NUWS was previously shown to provide modest increases in sensitivity, here we describe a complementary application to enhance spectral resolution by increasing the sampling of later points of the time domain signal. Moreover, by combining NUWS with carefully constructed apodization functions signal envelopes can be modulated in an arbitrary manner while retaining a uniform noise level, permitting further signal manipulations such as linear prediction and non-uniform sampling (NUS). We leverage this to develop a combined NUWS-NUS scheme for broadband homonuclear decoupling, with substantially increased sensitivity in comparison to constant time experiments.