Segmented-overlap Fourier filtering and averaging (SOFFA) approach to improve concentration sensitivity of magnetic...

The segmented-overlap Fourier filtering and averaging (SOFFA) data acquisition method is described in detail for magnetic resonance spectroscopy. In this work, the four processes that encompass the SOFFA data acquisition method are detailed: (i) oversampling spectral segments, (ii) Fourier block-filtering, (iii) segment-overlap averaging, and (iv) decimation. Three experimental examples are shown: first, conventional continuous-wave (CW) electron paramagnetic resonance (EPR) is compared to SOFFA-CW of a single reduced $[4\mathrm{Fe}\text{-}4S{]}^{+}$ ( $S=1/2$ ) at concentrations of 1 mM, 100 $\mu M$ , and 10 $\mu M$ , showing an average increase in concentration sensitivity by a factor of 5.6 in a 100 min measurement time. Second, an experimental comparison of CW and SOFFA non-adiabatic rapid-scan (SOFFA-NARS) data with similar filter parameters and field modulation amplitude demonstrates a factor of 10.3 in signal-to-noise (SNR) improvement (32 min measurement time) for a 150 $\mu M$ site-directed spin-labeled hemoglobin in 82 % glycerol at 18 $°C$ . Finally, an SNR-matched experiment of free TEMPO at 10 $\mu M$ concentration is presented, where CW was performed at 400 scans (273 min) compared to SOFFA-CW with an overlap factor of 100 (20 min). Also shown is the effect of $1/f$ noise on these CW and SOFFA-CW experiments. Ultimately, the SOFFA algorithm achieves sensitivity enhancement by combining massive digital oversampling and out-of-band noise filtration with coherent spatial accumulation of highly overlapped spectral segments. The gains reported here are phenomenological and are grounded in established digital signal processing principles but are validated through experiments rather than closed-form analytical prediction. This fundamental restructuring of the acquisition chain successfully decouples high-frequency filtering from low-frequency averaging while providing a data collection scheme that suppresses $1/f$ noise. The SOFFA method can be implemented to perform real-time segmented processing and, combined with more sophisticated averaging methods, will push the state-of-the-art sensitivity in magnetic resonance spectroscopy.