Envelope detection is an integral step of the surface NMR data processing workflow. A promising approach to produce high signal-to-noise ratio envelopes involves a scheme referred to as spectral analysis (SA) envelope detection – a scheme based upon a series of discrete Fourier transforms for sliding windows of observed NMR data. This method has the advantage that it naturally handles the narrow-band character of the NMR signal without corrupting the early portion of the time-series – both of which are challenges confronting traditional surface NMR processing schemes. However, SA estimated envelopes are weighted by the NMR relaxation time during processing and the envelopes have units of volt-seconds, whereas the unit of the data space employed by traditional surface NMR forward models is volts. To better integrate the SA envelope detection scheme within the surface NMR workflow, we propose to modify the surface NMR forward model such that it predicts data directly in the voltage-time data space. Synthetic and field data inversions, as well as a parameter resolution study, are presented to demonstrate advantages of pairing the SA envelope detection scheme with a forward model that works in the voltage-time data space. The method is shown to improve parameter resolution and does not require significant modifications to existing surface NMR inversion platforms.