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Envelope detection is an integral step of the surface NMR data processing workflow to estimate these parameters. We present a new method for retrieving NMR signal envelopes using spectral analysis and the subsequent inversion scheme with the new data space. By exploiting the fact that the spectral magnitude at the Larmor frequency is proportional to the product of the initial amplitude and relaxation time, a high-SNR complex envelope can be extracted by Fourier transform for a number of sliding windows. However, SA estimated envelopes are weighted by the NMR relaxation time during processing and the envelopes have units of volt-seconds. We propose to modify the surface NMR forward model such that it predicts data directly in the voltage-time data space. Field data inversions are presented to demonstrate advantages of pairing the SA envelope detection scheme with a forward model that works in the voltage-time data space.